Can anyone give me a clear definition of a third order covariance matrix? The only thing I can find on the net is at mathworld but it is not clear to me what is meant by the superscript notation mn --Will
If I know that Wikipedia reached 500,000 articles on March 17 2005, 666,666 articles on August 4 2005, and 1,000,000 articles on March 2, 2006, and I know that Wikipedia "currently" has x articles, then how can I make this into a third-degree polynomial approximating Wikipedia's growth and solve it to get the time Wikipedia will reach a given milestone? JIP | Talk 08:17, 2 March 2006 (UTC)
Simplify, and solve using
Newton's method. --
Meni Rosenfeld (
talk)
08:31, 2 March 2006 (UTC)
Wait, you got me mixed up. With 3 points of data you only get a quadratic polynomial. So you can solve it directly. -- Meni Rosenfeld ( talk) 08:34, 2 March 2006 (UTC)
Or perhaps you meant there's an additional point, the current time x0 and the current articles y0? Stick it to the formula and you get
And see also Lagrange polynomial. -- Meni Rosenfeld ( talk) 08:40, 2 March 2006 (UTC)
This isn't my best day. You can also solve a third-degree polynomial directly, but I guess Newton's method is simpler. -- Meni Rosenfeld ( talk) 08:42, 2 March 2006 (UTC)
Under which additional conditions (on the function f(x)) is the Fourier transform of a real, positive semidefinite function f(x), defined for the whole real axis, again real and positive semidefinite? --CA
(Please sign your questions.) The Fourier transform is a change of basis. Contemplate the definition of positive semidefinite. -- KSmrq T 13:06, 2 March 2006 (UTC)
(I have signed and made slightly more specific the question.) I do not understand your answer. If you want to insinuate that the Fourier transform F(k) of every real, positive semidefinite function f(x) is again real and positive semidefinite, then this is not correct. First of all, f(x) has to obey f(x) = f(-x) in order to have F(k) real. Within this class of functions, a simple counterexample is the symmetric, rectangular pulse. Indeed, if f(x) is
f(x) = 1 for -a <= x <= a f(x) = 0 for |x| > a
(here a is a positive, real constant and <= means "less or equal") then its Fourier transform F(k) is (up to a factor)
F(k) = sin(ak)/k
which certainly is not positive semidefinite. --CA
I need to prove that the area bounded by a unit hyperbola and a line from the origin to the hyperbola is equal to twice the angle of that line.
I know that the point where the line and the hyperbola meet is (cosht, sinht). Using that, I was able to find the equation of the line: y = xtanht. Im running into trouble with the integral. I think I did it right. I wish I could show it better, but I can't get the syntax of the math language to work: I figured I have to integrate along the y axis, from sinht to 0, because sinht is the y value of the intercection. Assuming I did it right, I got an integral of sqrt(y^2+1) - y/tanht. Please let me know if I am on the right track, and if you can help me out with the math formatting, that would help too. Thanks a lot. -- Chris 17:07, 2 March 2006 (UTC)
I've been told that the Riemann hypothesis has many broad implications, if only it were proven, but what are those implications? And why should I, a person who has an interest in math but doesn't spend all day looking at numbers (though I read quite a bit about philosophy, science and computers) care about it?
(Also, couldn't we construct a statement along the lines of "X is true iff the Riemann hypothesis is true." And then see if X is true or not, and use that information to either prove or disprove the Riemann hypothesis?) - 86.138.233.25 20:09, 2 March 2006 (UTC)
Suppose you were to define an arbitrary operator, Û, in 3-space, using cartesian coordinates, as
Would it reduce all linear functions it was applied to, to 0?-- 64.12.116.11 01:43, 4 March 2006 (UTC)
What command should I use in TeX to get double contour integral?
So, I'm looking up information on logarithms, and it says that Briggs and Napier decided that the log of 10 shuld be one, and the log of 1 should be zero, and that at first they thought log 10 should be 10^10 to avoid fractions. Was there some mathematical basis for this that someone would be willing to explain to me, or were they just making it all up for fun? Ductape Daredevil 17:06, 6 March 2006 (UTC)
Hello, I have already seen in the article about plus and minus signs that the Jewish usually do not use the plus sign. However, they use an inverted T. I am interested if Arab countries use the usual symbol or another (as + may resemble a Christian cross). Thank you. -- 84.21.200.224 18:38, 6 March 2006 (UTC)
I am calculating average values in a database of a few million records. It takes a very long time to scan each record and decide if it should be included in the running average. So, I'd like to do standard deviation on the fly rather than go through all the records once to get the mean and then go through them all to get the standard deviation. Is that possible? -- Kainaw (talk) 16:00, 7 March 2006 (UTC)
If there are only a few million of them, why not make one pass in which you decide whether a record should be included and cache the value on which you want the statistics? Then make a second pass through those values and get your s.d. It should all fit in physical memory so it will be very fast, and you won't have to worry about the roundoff-error problem. -- Trovatore 18:23, 7 March 2006 (UTC)
SELECT ave(SALARY) FROM EMPLOYEE_TABLE WHERE STATUS != "TERMINATED" AND SALARY > 0.00 AND SALARY < 99999999999.99;
SELECT ave(SALARY),stdev(SALARY) FROM EMPLOYEE_TABLE WHERE STATUS != "TERMINATED" AND SALARY > 0.00 AND SALARY < 99999999999.99;
This question shouldn't be too hard, which is good, since I need this done tonight. I have managed to be pretty ignorant in probability to this point in my life, which is very sad. I should be able to get this from the article, but it's very technical and I'm having trouble reading it.
How do I get the cumulative distribution function for the log-normal distribution? Let's say I have a silly program which will give me the CDF of the normal distribution, but not the lognormal. I know the values , which isn't a mean but kinda looks like one, and .
So if z is a random variable with the lognormal distribution with that and , what exactly is the probability that where X is some number I also have? moink 10:12, 8 March 2006 (UTC)
hi, please i would like to know the difference between exponential distance and linear distance? i would also like to know if the impact of distance on the visibility of an object is either exponential or linear...thanks
Three cake boxes are stacked. Find the surface area of the entire stack if all the prism bases are squares. Top Box: L=12 W=12 H=6 Middle Box: L=26 W=26 H=6 Bottom Box: L=36 W=36 H=6
It seems that some assumptions must be made. These would be my assumptions:
1) The area each box has in contact with another box is not counted as surface area for either box.
2) The area the bottom box has in contact with the table is not counted.
3) The boxes are stacked such that the largest possible area is in contact with the table or box underneath it. That is, none are lying on their sides or hanging over the edge of the table or box underneath. StuRat 21:21, 13 March 2006 (UTC)
We do not need to know the table area.
How did 'Renee' prove that '1=0'? ( If she ever existed and what I read isn't just part of a novel).-- Cosmic girl 19:20, 8 March 2006 (UTC)
thanks :D.-- Cosmic girl 20:54, 8 March 2006 (UTC)
do my homework-- Gefploxer 21:56, 8 March 2006 (UTC)
What is infinity divided by infinity? —The preceding unsigned comment was added by Biofireball ( talk • contribs) .
Isn't infinity/infinity = 0 or 1?.-- Cosmic girl 23:55, 8 March 2006 (UTC)
Long time ago I remember reading a problem and solution which I can no longer recall. Problem is to cut and distribute a completely homogeneous cake into n pieces among n people such that each person perceives that he received fair share of cake. Note that it is not important whether it is fair share or not, but all must believe that it is. For n=2, solution is one person cuts the cake and another choses his piece. Thus person cutting the cake will know that both pieces are equal since he cut it (and took atmost care on his behalf) and person picking will get to pick whichever he thinks is bigger share. I remember that solution exists for n=3 or more, but I don't know what. Can someone help me here? Again, cake is plain, no fancy icing, and all participants have no preference over piece except its size/volume. Thanks. AshishG ( talk · contribs)
Actually this page has some information, including solution for n=3 which is different & much complex then one proposed above. And it says that n=4 or more is just too difficult. So I take back my question. By the way, this reference desk is great place for fun! AshishG ( talk · contribs)
Suppose X has a normal distribution with expected value 0 and variance 1. Let
Y = -X if -C<=X<=C or Y=X if |X|>c,
where c is a positive number to be specified below. If c is very small, then the correlation corr(X, Y) is near 1; if c is very large, then corr(X, Y) is near -1. Since the correlation is a continuous function of c, the intermediate value theorem implies there is some particular value of c that makes the correlation 0. That value is approximately 1.54. In that case, X and Y are uncorrelated, but they are clearly not independent, since X completely determines Y.
So, I've been told that the square root of -1 is i. I've looked at the square root article but it doesn't say anything about this. I understand sqrt(-1) has no integer number, so why i? Any help would be greatly appreciated :) -Benbread 20:08, 10 March 2006 (UTC)
arch z = -i cos^-1 z = -i arccos z. But |z| < 1. So let's say M * arch 0,11 = 1000 * -i * 1,46057328 = -1460i. Another question please. -- DLL 11:23, 11 March 2006 (UTC)
the question comes along a story one person in SriLanka rented out a room for 3 persons,each one must pay him ten rupees as key money and he will get totally 30rupees.When he collected 30rupees and returned home his wife said that the 10 rupees for each one is too much and return them 5 rupees,so owner called his servant and gave him a 5 rupee coin and ordered him to handover it to the new boardes,servant took it and walked .While the way he think to buy a toffee for him and bought one spending 2 rupees.Finally he return only three rps to boarders.Only now the question begins,when the servant returned the 3rps each boarder gets 1 rupee.So actually each one have spent only 9rps for the room.Finally if we see through the account, the boarders spent money=9+9+9=27rps.the servant spent for toffee=2rps.so the total money spent in this story is 29rps.But initially we got 30 rupees,so where is that one rupee? -- 222.165.169.196 12:09, 11 March 2006 (UTC)
Earlier this week while discussing a question regarding the angles between clock hands with some of my friends, I posed them a question of my own: assuming a clock with second, minute and hour hands, in which all hands move continuously (ie. the minute hand doesn't wait until the second hand reaches 12 to move), at what time(s) will the angle between each pair of hand be 120 degrees? I figured, while it might take some figuring out, it wouldn't be that difficult.
Not knowing the answer myself, I've spent the week trying to figure it out to no avail. I've tried doing some series of equations to express the angle of each in terms of hour, minutes and seconds, but that hasn't worked. I've tried doing it simply in seconds, but dealing with the number of complete rotations of the second hand has proved troublesome. My friends are equally stumped. Any suggestions on how to go about solving such a problem would be much appreciated.
-- Elzaban 16:22, 11 March 2006 (UTC)
I have these two equations:
The two unknowns are and Xmax. How can I solve this. I'm not even sure if I have sufficient information to solve, since one of the unknowns is a function. Help would be highly appreciated. deeptrivia ( talk) 02:15, 12 March 2006 (UTC)
Thanks! I found a missing equation. I still don't know how to solve it, but I haven't tried much. It's not a design problem, and there has to be a unique solution. Thanks for your help :) deeptrivia ( talk) 18:16, 13 March 2006 (UTC)
Yes, this is homework, but I have done most of the work. We have been given the function y=exp(-x2). We are asked: What are the dimensions and area of the largest rectangle that fits into the curve and the x axis, as shown on the below:
Let x equal the distance between one of the vertical sides of the rectangle and the y-axis. The area of the rectangle is therefore 2x(exp(-x2)-x) (length times breadth). I call this function A(x), and it has a maximum when I graph it on my calculator. To find the maximum, I use calculus, letting the derivative of A(x) equal zero:
How on earth would I solve the last equation for x? The closest I can get to is:
Taking natural logs will get rid of the exponential expression on the left, but leave a log on the right. I'm sure I haven't been taught the tools to deal with equations like this. (Year 12 Specialist Mathematics, Victoria, Australia).
Did I miss an easier way? Can the above be solved using high-school mathematics? -- Alexs letterbox 04:58, 12 March 2006 (UTC)
I changed the format of the first two equations and another, just for legibility, in case anyone else had trouble reading it. D. F. Schmidt 02:39, 18 March 2006 (UTC)
I ran into a problem recently while trying to solve a pair of equations that appeared to be fairly easy, but had me stumped when I actually tried to do them. It was part of my maths work at school, and the thing that had me most puzzled was that it was only the lead-in part to the harder part of the question which was on some basic integration.
The specific question asked for the points of intersection of and . I couldn't do it at all, so I'd appreciate it if anyone could demonstrate a reasonably simple method, because it should be doable with fairly basic maths. I'm fine with manipulating them around and so forth, it's just I can't work towards something with less than two unknowns, for instance.
I can solve most simultaneous equations but when it came to this I wasn't sure how to communicate a decent proof on paper. In connection with solving this I decided to see if I could solve which I can easily see answers to in my head. I couldn't, however, prove my answers elegantly on paper. So it would appear that my problem lies in not being able to get down to one unknown when I'm restricted by the sine function, and if anyone could offer any general help on that it'd be most welcome. 81.157.152.22 19:44, 12 March 2006 (UTC)
I got this question as a homework assignment and i just can't figure it out. Here's the question: What is the least value of N such that N! is greater than a googol?
I have to solve the equations:
and
for . Here, F is the incomplete elliptic integral of the first kind. e, k and L are known.
I am doing this in MATLAB as follows:
opt = optimset('Display','notify','TolFun',1e-8,'TolX',1e-8,'MaxFunEvals',10000); pfunc=inline('L - (mfun(''EllipticF'',sqrt(1/p^2-e^2*k^2/4),p)-mfun(''EllipticF'',sin(pi/4),p))*p/k','p','e','k','L'); [p,xval,exitflag] = fsolve( pfunc,0.707,opt,e,k,L) thetaC = 2*asin(sqrt(1/p^2-e^2*k^2/4));
I know that for sufficiently large values of e, I should get . A trial value for such case is e = 137, k=0.01, L=100. The numerical computation for finding p fails to converge after values of e that should result in . What's the reason? Does it have to do with the way asin and sin are defined in matlab? What's the way out? I'm doing this to calculate elastica, and I know that after a particular value of e, it will start making a loop, forcing . How can I do this calculation? deeptrivia ( talk) 18:37, 13 March 2006 (UTC)
Is there any easy explanation (one that I can understand) of how Euclid's parallel postulate is false?.-- Cosmic girl 18:39, 13 March 2006 (UTC)
Wow! :O ...thanks! I understood but I'll read the articles too.-- Cosmic girl 20:29, 14 March 2006 (UTC)
This is Pi Day. But when, in history, was the best approximation to pi equal to 3,14 ?
How was the forumla for the surface area of a sphere derived? Are there any good sites with information about this? 64.198.112.210 16:41, 14 March 2006 (UTC)
Find all n such that (20n+2) divides evenly into (2003n+2002)
L33th4x0r 05:46, 15 March 2006 (UTC)
I've got this strange theory that I conjured out of thin air som 15 years ago, have there been anybody else than me thinking about this stuff.
I postulate hereby that C a 2D creature's fastest way (like in shortest/less resource expenditure) of traveling (in an XY plane) from point A to point B would be to travel in one direction (X or Y) (not distance AB) until it would be at the distance AB - (A - (X or Y)) = B and then the distance B.
This way the creature C would only have to change direction of travel (90 degree change) once.
Try to think about this and and tell me how much further would 2 D creature have to travel compared to a 3D (capable) creature, my answer is squareroot 2 (appr. : 1.4) times more.
Reason: while the 2D creature could change direction of travel (X or Y) for every second or mm (or whatnot) that it went, this would take even more time/resources ..stop/change direction etc.... than it would to just travl the distance in the X direction and then after that in the Y direction....one start/stop/start/stop
Relate this to a 3D creature like us in a 4D world....and the answer would be 0.5 times the value of pi.....and bring in the double slith photon/electron experiments and other relativistic points... anybody got any thoughts about this...?
Could this be elaborated a bit more? [Azalin1999]
Hi again I'm the one who phrased the question. A little note about myself. Never did score high in maths and equations but I'm really curious about this 'theory'. Much thanks for the link to the 'manhattan distance' article, I think I remember reading about it some years ago. My native tongue is Danish so that's my excuse for the inaccurate phrasing.
I originally made some drawings on a XY crossed paper to illustrate the theory. And I had a really hard time to explain my arguments for those I presented it to (mostly indifferent friends). And I still have difficulties atm. because the thing I would like to verify is that it would be possible to apply something like this 'manhattan distance' to distances in a 3D world seen from the perspective of a fourth dimension. Which should be possible. Basically like -- BluePlatypus went about distances in an euclidian plane...
The distance 1/2 Pi was derived from projecting a imaginary path (distance traveled) through 4D space compared to what a 3D creature would have go by not using the 4th dimenson...like a 2D creature can't (see, thus) travel the path that a 3D creature can. In regards to the 'Manhattan Distance' this would be akin to a race between a cab an a helicopter going over the cityblocks.
You're Chuck making some good points. But what if we assume that in our (unlimited) reference 3D space we are looking down on the 2 plane (which could be from any arbitrary reference point/perspective) let's say head on, straight down.
Let's assume some more - Our little 2D creature can only observe (look) through either the X or the Y, and thus only observe it's destination when its in line with either the x axis of the destination or th Y axis, whichever comes first, depending on which route it took.
From the 3D POV this would satisfy my squareroot 2 clause about a 3D being would be able to go the shorter distance right? Because it can sort of observe the direct line of vision...X & Y combined.
Now if the 2D creature were able to in some way observe the destination it could of course just travel the direct route. But this would only happen after it had moved all the way along either the X or Y axis to be in line with the destination. If this 2D thing were sentinent the perceived distance the 2D being traveled would be? the squared X+Y which is less than the distance it really took if a 3D being measured...also there are 2 routes that are the same distance but starting with etiher going out of the X or the Y axis...
Relate this to a 3D world...(damn crunching)hmm non-euclidian geometry..........Spherical trigonometry
As I see it - Going from A to B in 3D is just (always) a straight line. But this C cannot see that so it has to travel from the perspective of the 3D creature in X + Y ie. at the point where it needs to change direction is where the 2D creature actually has traveled the least distance in the X distance (or Y) and then changes direction 90 degrees to be 'the fastest' without changing directions every x/Y mm (or whatever).
So the 3D viewer would, if seeing the 2D creature move along the xy points, percieve the path at some fractional degree from the perfect - Squareroot 2 path - which means the 3D viewer would be able to see the 2D creature's energy expenditure adhere to my postulation.... 2D travelers always expend square root 2 times more energy when the 3D viewer multiply this with hmmm is it cosinus or sinus ? (Perfect angle view that makes a straight line away from the XY plane) That's the hint for ½ PI value. To elaborate : A photon is emitted from somewhere..... this photon is measured at some point and only there you can make the mark that you measured a photon (in whereever space) how it got there (Cab or Taxi) you don't know - you can just measure the time difference between you emtting the photon - and collecting information about when it hit 'point B' 85.81.121.107 ( talk) 19:59, 7 October 2011 (UTC)
Hi, I'm working with gradients at the moment but can't for the life of me rember if you count the squares (i.e. measure) or use the unit values for the graph. To see an example of what I mean: Click here is the gradient 3 over 6 (as attained by counting squares) or 15 over 12 (as attained by using the unit values). If it helps I'm dealing with "real life" data here. Thanks! -- Christopher Denman 17:50, 15 March 2006 (UTC)
On right is a plot of x-, y-, and z- coordinates of two ropes on which some forces are acting. I made this using the plot3 command in matlab. Now I want to remove the axis labels, and marks. In that case, this will look like 2d. How can I make it look 3d? Some kind of shading/lighting/perspective tricks? I need to do this in MATLAB. Thanks! deeptrivia ( talk) 21:39, 15 March 2006 (UTC)
Thanks for your answers. I tried shadows and it helps a bit. I have no choice but to use matlab because this will be a part of a GUI I'm making in Matlab. I think I can manage if I get a solution to the problem regarding cylindrical surfaces below. Cheers, and I appreciate it highly. deeptrivia ( talk) 01:30, 16 March 2006 (UTC)
I need the definition in mathematical terms for manipulatives
This is a follow up question from above (3D effects without axes). Suppose we have a spatial curve defined by x = f(s), y = g(s) and z = h(s). What equations will describe a cylindrical surface of radius r which has this curve as its axis? I can do real neat 3D things in matlab if I plot this surface. Will post the results here, of course. deeptrivia ( talk) 01:28, 16 March 2006 (UTC)
For everyone's benefit. I got a readymade solution based on
Melchoir's answer. See
[1]
deeptrivia (
talk)
03:08, 16 March 2006 (UTC)
I am writing this as an AP Calculus BC student. Assume f(x) describes a continuous, differentiable curve, such as
I want to find the surface area of the solid that results from a rotation of part of the curve, say 0 to 4. For this example, let's assume I'm rotating about the x axis. I know the correct method to solve this problem (surface areas of cone frustrums). However, why can't it be found as a summation of the surface areas of right circular cylinders (excluding the bases)? Thus, my presumed integral would be
Obviously, it is wrong. However, why is it wrong? My textbook helpfully includes the formula above (though I found it myself before seeing this). It then says it can not be used because it has "no predictive value and almost never gives results consistent with other calculations." However, I find this somewhat disappointing, as there is no explanation of why the formula is flawed. Please do not simply show me the right way to do it, and explain that this is therefore the wrong way; that is unhelpful Superm401 - Talk 01:58, 16 March 2006 (UTC)
When calculating the area under a curve, one can approximate either by rectangles, or by trapezoids bounded by some "diagonal segments" on top. I think the second approximation is called the trapezoid method, and it's better than the rectangle method, but both work in the limit. Both converge to the Riemann integral.
On the other hand, when calculating the length of that same curve, you have to approximate the curve by diagonal chords. If you approximate the curve with rectangles, the sum of the rectangles will always add up to b–a (where the domain of the curve is the interval [a,b]).
The technical reason behind this is that the form which gives you the length is not a linear differential form. In other words, the Pythagorean equation is not linear, and that's needed to calculate length. The form that gives you the area is linear, and therefore any sum will do. Stated even more simply, the triangle inequality tells you that the hypotenuse of a triangle is greater than the leg. Rectangles get you the leg of the triangle, and never approximate the length, though they do approximate the area. Calculating surface area is just calculating length and throwing in a 2πr, so the same issues apply to volume versus surface area. - lethe talk + 03:31, 16 March 2006 Th(UTC)
To illustrate the problem somewhat differently, consider a cone obtained by rotation of "y=ax" around the x-axis. The area and the volume are given by integrals
You can see that omitting dl/dx will lead to a wrong result. For the curve , dl/dx varies with x. Another example is the surface area of a unit circle
( Igny 13:04, 16 March 2006 (UTC))
can anyone give the derivation for this?
how do you find the determinant of a parabola?? please help
On page 74, L. Schwartz, Mathematics for the Physical Sciences,Hermann
Quote: The existence of linear functionals which are discontinuous on $\script D$ may be demonstrated mathematically using the axiom of choice. UN-Quote.
Question: Where can I actually find a proof for the existence of a discontinuous linear functional on test spaces?
Be more grateful if you could send your answer directly to me by visiting http://www.maths.uwa.edu.au/~twma/mathematics/index.htm Thank you in advance. twma
Dear Lethe, Thank you for your quick response. Because you did me a favor to visit my page above, I was alert immediately without having to wait until tomorrow.
On page 73 of the same book above, a sequence of test functions f_n tends to 0 if
(a) the supports of f_n are contained in the same bounded set and
(b) for each fixed m, the m-th derivative of f_n tends to 0 uniformly.
\sin n^2x/n could not satisfy the above conditions.
I multiplied \sin n^2x/n with a test function g satisfying g(0)=1. Could not get any further. STILL NEED HELP. twma
To find, explicitly by displaying formulas or implicitly by axiom of choice, a counter example that a linear functional T is not continuous, we need to find a sequence of test functions f_n satisfying both conditions (a) and (b) and in addition T(f_n) fails tending to 0 as n tends to infinity. The sequence \sin n^2x/n does not satisfy (a) and not (b).
Distribution theory is well established nowadays. There are many good books on the subject. For example,
Page 222, F. Treves, Topological vector spaces, distributions and Kernels, Academic.
Pages 28, 26, M.A. Al-Gwaiz, Theory of distributions, Monographs and textbooks in pure and applied mathematics, vol 159.
I quote L. Schwartz because the book was written by the creator. I even looked up the French version of the same book with disappointment. My next possible step is to look up the original paper. Twma 18:52, 17 March 2006 (UTC)twma
You people have something like --- 17 March 2006 (UTC) but I do not have it. Am I overlooking some rules and regulations of this site? If so, apologize and please tell me what to do in order to CONFORM.
I wrongly thought that four tildes are examples of letters of a signature. I am able to conform now. Thank you. My identity is twma in lower case but this site changed it by default to Twma in order to conform.
To save the room, I shall delete part of this section if I have no objection in 24 hours. Twma 18:52, 17 March 2006 (UTC)twma
All right! People want the complete record even full of irrelevant junk such as part of mine. Good to consult first and take action later. No action in this case. Twma 22:57, 18 March 2006 (UTC)
OK, twma, now I think I see what you were trying to do. You want a sequence of functions fn and a linear functional T such that fn → 0 but T(fn) does not → 0. But you chose a sequence of functions which does not converge, so clearly that is not going to show anything (your sequence doesn't satisfy your (a) and (b)). Now, the article discontinuous linear functional teaches us that on a complete vector space, all examples are nonconstructive, so you can't just look for a sequence and a functional, you have to invoke the axiom of choice. The vector space you have chosen is complete (though not in the uniform norm). The examples look like the one you find in that article. Let fn be a sequence of linearly independent functions. Denote by ||g||m,K the seminorm supK Dm|g|. If {Ki}i is any countable collection of compact sets which cover the real line, then ||*||Ki,m is a countable sequence of seminorms. Create a directed countable family of seminorms, and denote the kth seminorm by ||*||k. Then define a linear functional T such that T(fn) = n||fn||n. Then we have for any k, I can choose an fn so that |T(fn)| is greater than any ||fn||m (or even any finite linear combination thereof). Thus T is unbounded. Now use the axiom of choice to find a basis of the space which contains the fn, and define T to be 0 on the rest of the vectors. Any unbounded linear map is discontinuous.
Now, this example is the same in essence as the one at discontinuous linear functional, except that I had to get involved with families of seminorms, since the vector space in question is not a Banach space. This makes the details of the proof a little more involved, but doesn't change the idea behind it. Nevertheless, I found it quite confusing dealing with those seminorms, I wonder if you'll find it just as confusing when trying to read it as I did trying to write it. - lethe talk + 21:39, 17 March 2006 (UTC)
I do NOT know how to produce nice looking mathematical stuff on this page. Be grateful if SOMEBODY could REPLACE this and next paragraph with something equivalent. It compiles well before I pasted here. Thank you in advance. PS: Somebody has done this. Thanks from twma.
Here is an example of a discontinuous linear form on the test space D(R) on the real line R. For every compact subset K of R, D(K) is the vector space of all test functions with support contained in K. The topology of D(K) defined by the seminorms for all integers α ≥ 0 coincides with the subspace topology induced by the test space D(R) equipped with the locally convex inductive topology induced by D(K) for all compact subsets K of R.
Let ρ be a test function with ρ(0) = 1 and ρ(x) = 0 for all |x|>1. Choose 0<an+1<bn+1<an<bn ≤ 1 for all n ≥ 0, for example recursively by b0=1, an=bn/2 and bn+1=an/2. Let cn=(bn+an)/2 and rn=(bn – an)/2. For gn(x)=ρ[(x – cn)/rn], we have |gn|0 ≥ gn(cn) = 1. Then each is a test function with support contained in [an,bn] ⊆ K=[-1,1]. For each α and all n > α, we have ||fn||α ≤ 1/n → 0. Now fn → 0 in D(K) and hence also in D(R). Next because all intervals [an,bn] are disjoint, the sequence {fn} is linearly independent and hence it can be extended to an algebraic basis B of D(R). Define T(φ)=1 for all φ in B and extend T to a required linear form on D(R).
Thanks to the enthusiasm of people of this group that provides encouragement to me in sharp contrast to DingoBabyAffair. Twma 08:24, 19 March 2006 (UTC)
Let ρ be a test function with ρ(0) = 1 and ρ(x) = 0 for all |x|>1 (typo corrected). Movie: Lost in translation. Hope it should be all right now (waiting for your approval). In order to make life easier for myself, I only look at the positive side but rarely at the ugly part of the world until I HAVE TO face it NOW. I agree that based on one example, we can find many more without any difficulty but we DO need one example for a copycat. ONCE AGAIN, THANKS TO THE HELPING HANDS OF THIS GROUP. DingoBabyAffair appeared on the front page of many Australian newspapers for several years in early seventies. A baby had been severely hurt continuously but nobody wanted to help while the politicians argued whether the surrounding dingoes or the mother should be responsible. In SHARP CONTRAST, this group helps without any argument. After more than 30 years of protracted war, this baby grew up as a lost child of cold war. Now he/she is rising like a fabulous phoenix from the ash, new and fresh and young. Saving the Private Ben happened only in the movie while the politicians argued once again whether it did happen recently in reality. Perhaps I should claim copyright for another movie. Am I violating the rules and regulations of this site by comparison in my thank-you-note and by answering query about something irrelevant to Mathematics? Any way, I do not think it will drag on. Twma 00:51, 20 March 2006 (UTC)
How would one solve the equation 3^x = x^2? Is there a rule which specfies which explains the solvability of equations? -- Alexs letterbox 05:35, 17 March 2006 (UTC)
(Title was changed to actually say something useful. StuRat 16:01, 17 March 2006 (UTC))
I know this might be a simple question but can someone please explain to me what Perpendicular mean? And the angle of Depression and Elevation mean ? Thankz
I need to know the growth rate of Primorials(for factorials it is X!=O(e^(x*ln(X)) using Big O notation.) I also need to know how fast you can calculate primorials, is it polylogarithmic? For factorials it is not. Ozone 23:12, 17 March 2006 (UTC)
As for primorials,
suggests, (using some manipulations I am unable to generate here, because I can't figure out how to get the "#" symbol within a <math></math> equation)
— Arthur Rubin | (talk) 22:44, 18 March 2006 (UTC)
http://en.wikipedia.org/wiki/Exact_functor
this article defines left exact functor
Suppose 0→A→B→C is an exact sequence
I am having difficulty to see that the hom(M,-) is a left exact covariant functor. Why is it left exact? Somehow it seems to me that that means proving that if Y is a submodule of X, and alpha is a module morphism of Y to Z, it can be extended to the full X?
Thanks,
Evilbu 16:48, 18 March 2006 (UTC)
How would you solve this equation:
for P? (So that P is only on one side.)
Thanks for any help.
65.31.80.100 19:12, 18 March 2006 (UTC)
I know all about integration by parts, but is there any one integral formula that can find the integral of (a^nxn + a^(n−1)x(n−1) + ... + a2x^2 + a1x + a0) / (b^nxn + b^(n−1)x(n−1) + ... + b2x^2 + b1x + b0). This is clearly the classic definition of a polynomial divided by a polynomial. Is there an integral formula that uses similar notation to account for all possible terms? -- Chris 03:24, 19 March 2006 (UTC)
Chebyshev's theorem says that
has an elementary antiderivative if and only if one of (p+1)/r, q, or (p+1)/r + q is an integer. But I guess q is always an integer for rational functions, so this doesn't answer your question. Probably the answer is: perform synthetic division, factor the denumerator, and integrate by partial fractions. I think you can write a general formula this way. - lethe talk + 04:40, 19 March 2006 (UTC)
So like, assume you're working over the complexes, so that your polynomial can be factored. And assume that the denominator has greater degree than the numerator; you can always make it so by synthetic division. Then you're left with an integral of the form
with
so there are q distinct roots, and the ith root has multiplicity mi. You find the integral of this bad boy by partial fractions. The partial fraction method gives you a general formula for the coefficients. The article on partial fractions gives you this formula for the case that all the roots are distinct (have multiplicity 1). I don't know about the general case. Then you perform the integration. For the distinct root case, you're left with
For the general case, once you have the coefficients, the integrals are equally easy.
Note that you can't write the entire thing in one formula in terms of the coefficients of the polynomials, because by a result of Abel, there is no formula (in terms of finitely many radicals) for the roots of a polynomial. - lethe talk + 05:05, 19 March 2006 (UTC)
There's something basic I don't understand about probability. It isn't the manipulation of the numbers (which has never been a problem for me), it's why the whole thing's possible. What about a natural series of events causes them to fall, given a large sample size, so perfectly into a particular arrangement like 50/50 or 16.7/16.7/16.7/16.7/16.7/16.7? This might be a better question for the science desk, but it seems to fit here too, and most people work both. Black Carrot 22:05, 19 March 2006 (UTC)
If you accept that the chances of a combination of random (equally weighted) events occurring is 1/c, where c is the total possible combinations of events, then you could demonstrate it yourself. This is because the more tosses of a coin, say, you do, the more combinations of all tosses will end up in any given range about the predicted average, say the 0.4 - 0.6 range. However, the chances of getting exactly 0.5 will actually go down (and of course that probability is zero for an odd number of tosses).
As the number of tosses of a coin goes up, the chances of having all heads or all tails goes down. In the case of a single toss, you get either all heads or all tails (H or T) 100% of the time, while with two tosses, you get all heads or all tails (HH or TT) only 50% of the time, and with 3 tosses (HHH or TTT), only 25% of the time. The probability of getting a head/tail ratio somewhere in the middle goes up as a result, particularly as you get closer to half heads and half tails, because a larger percentage of combinations works out to be near half heads and half tails when you have more tosses. You can see this trend with Pascal's triangle (which models coin toss behavior as well as many other things), where the numbers in the center of each row continue to get larger relative to the edges of the row as you move further down the rows. StuRat 16:36, 20 March 2006 (UTC)
Total Rolls Odds ===== ======================= ==== 2 -> 1:1 1/36 3 -> 1:2,2:1 2/36 4 -> 1:3,3:1,2:2 3/36 5 -> 1:4,4:1,2:3,3:2 4/36 6 -> 1:5,5:1,2:4,4:2,3:3 5/36 7 -> 1:6,6:1,2:5,5:2,3:4,4:3 6/36 8 -> 2:6,6:2,3:5,5:3,4:4 5/36 9 -> 3:6,6:3,4:5,5:4 4/36 10 -> 4:6,6:4,5:5 3/36 11 -> 5:6,6:5 2/36 12 -> 6:6 1/36
I mean, why do the individual trials scatter so perfectly along that original curve in the first place? Or do they?
You are trying to over-interpret probabilities. Probability theory (PT) provides a mathematically rigorous logical framework to fit a rule on the occurrence of some phenomenon. It cannot and does not deal with explaining the phenomenon. Say in the case of a biased dice---on the basis of given observations---all that PT tells you is the preference of the dice towards some of the possibilites (for example, say p(1),p(3),p(4)=0.2 and p(2),p(5),p(6)=0.4/3). PT never claims to explain the reason for that bias (you can analyze the reason of that bias by going in details of the geometric shape of the dice etc., but you are not concerned with such details, when you are simpling fitting a rule over the observations). The same reasoning applies reverse: when the events scatter along the proability distribution, in no single trial, the dice is making a conscious or deterministic choice, and even if say, it is making a conscious choice---All in all, PT provided you was the aggregate characteristic or rule about how trials would turn out on an average (in expectation). This is "the" subtlity of probability theory, and many greats have erred when they tried to over-interpret probabilities. The famous debate between Bohr and Eeinstein about correctness of Quantum mechanics is, in fact, centered around this understanding. Of course, both these greats understood PT perfectly and their argument was mainly concerned about whether it is worth to go in additional details,which---at least right now---seems impossible to verify, when PT explains pretty much everything about the world that we could verify experimentally. Check out the article "Probability Theory as Logic" by late Edwin Jaynes at
[2].
--
35.9.136.15
18:49, 23 March 2006 (UTC)Keyur Desai
Black Carrot, perhaps you are also making a logic error, in thinking that if heads comes up the first time a fair coin is flipped, that makes it more likely that tails will come up the next time "to even out the probabilities". This is not the case. It's has a 50:50 probability each time it's flipped, regardless of past flips. StuRat 19:18, 23 March 2006 (UTC)
Hi all, sorry, but if I understand Black Carrot's original question, that user is asking something much more simple: why is it that when you throw a die a bunch of times, it lands on each of the 6 sides about 1/6th of the time? Am I right? If I'm wrong, sorry.
If so, the short answer is, of course, Why not? The longer answer is that we are using, as a mathematical model of the physical situation, the assumption that the die does this. This would be true for a "fair" die. This, of course, would not be true for a loaded one. One could build a die so that it was much more likely to land as a 1 than anything else. Then, of course, this 1/6 model wouldn't be a good model. The probability of landing on different sides would change because of this, and you'd have to build that into your model. Of course, mathematicians have worked this out as well: see Bernoulli trials for a start.
Let's say you're taking the line integral ( path integral) along four straight lines C1, C2, C3, and C4, where C1 is y=-2, C2 is x=2, C3 is y=2, and C4 is x=-2, so you're integrating along a closed curve C, where C is a 4x4 square centered at the origin. (The lines C1-C4 are segmented so that they only go from x=-2 to 2 and y=-2 to 2; the lines are oriented counterclockwise, therefore positive.) Then, let's say you're taking the integral of -ydx/(x^2+y^2)+ xdy/(x^2+y^2) along the curve.
Now, dP/dy equals dQ/dx, so the differential is exact, so the integral is path-independent. Because the curve is closed, this would make the integral equal to zero, because you can choose any path you want, and you could choose a path that remains at the starting point and not go anywhere. All path-independent integrals over closed curves are equal to zero, right? (Right?)
But then my textbook (this is an example from my textbook) shows how one can use Green's theorem here. Generally, one wouldn't be able to use Green's theorem because the denominator in the integral makes the integral undefined at (0,0). But one could draw a circle C', x^2 + y^2 = 1, around the hole, and the textbook shows how the line integral along C (the square) is equivalent to the line integral along C' (the circle). Evaluating this integral quickly gets the answer of 2pi.
My question is this: aren't all path-independent integrals over closed curves 0? What's different here? I'm not so concerned with the specific example - it doesn't have to be that initial curve C. When there's a hole in the region bounded by C, and C is path-independent (b/c the differential is exact), why does a discrepancy arise between a) assuming the integral is 0 because, being closed, the start point is the endpoint, and b) encircling the hole and using Green's? zafiroblue05 | Talk 19:31, 20 March 2006 (UTC)
Thank you all, that explains it perfectly. :) zafiroblue05 | Talk 22:32, 20 March 2006 (UTC)
This one should be easy for you guys. Suppose I have a set of 100 points defined by P[i] = X[i]i + Y[i]j + Z[i]k , i = 1..100 . How can I test whether these points lie in a plane or not? I can think of choosing any three points and finding the normal vector of the plane defined by them, and then taking the dot product of all P[i] - P[0] with that normal and checking if it is zero. Is this the best way of going about it, or is there something more elegant? How can I find the normal vector of the plane defined by 3 points. Sorry for asking such elementary questions, but I'm kinda retarded on this. deeptrivia ( talk) 21:19, 20 March 2006 (UTC)
Okay, there's a slight problem with this method in my case. Since these arrays X[i] etc are floating point numbers, the points can be very slightly out of plane (deviations such as 1e-10.) I want the algorithm to somehow ignore these small deviations. How do I manage that? The rank of the above matrix might come out to be 4 even if practically the points are coplanar. How do I increase the tolerance value for calculation of rank. Thanks! -- deeptrivia ( talk)
A high-math question:
a * x + b ----------- z + y * x
This reads "a * x + b over z + y * x". But what is the English name of this little line betveen the numerator and denominator? It is not "over", not "fraction line". Sign of division? Sounds funny. Can't find anything in relevant Wikis, not in Math books. In Math you can go without mentioning it, if you do some typesetting, you have to name it somehow :-)
Miklos Somogyi
Thank you, I've got a few good-sounding names. It was not more difficult than Fredholm integral equations with a double-layer Cauchy-Kolmogorov kernel of the Third Kind, after all :-) Thanks, MS
I think this is also called a Vinculum. J. LaRue 01:58, 22 March 2006 (UTC)
This one is not right. Vinculum is on top of things (plural), to show that they are in some kind of a group. MS
Yes, I may use the term "vinculum". If I want to join the Borg Collective, I even must. I suspect that mathematicians would suspect what I am talking about re vinculum but actually, do they USE the term themselves? Thanks, MS
If kernel sanders really makes real mathematically accurate chicken, shouldn't the kernel's chicken have no calories? hence be = to the 0 vector? serious responses only please- Kolin farrellovsky 18:04, 21 March 2006 (UTC)
If I travel 10km North, then 10km East and then 10km South and find myself back where I started where am I?
I prefer this version:
If you leave home, then travel 1000 km south, then travel 1000 km east, then see a bear, then travel 1000 km north, and end up back home, what color was the bear ?
StuRat 18:37, 21 March 2006 (UTC)
How is math used in a beautician job, or better yet, what kind of math do beauticians use?
Here's an interesting function:
With:
Anyone seen it before, and does it have a closed form? Fredrik Johansson 17:26, 23 March 2006 (UTC)
Choose a random integer with n decimal digits. I want to be reasonably certain that I can factor it using publically available software on a modern PC within, say, 24 hours. How large can n be? - Alecmconroy 22:32, 23 March 2006 (UTC)
The OP said "Choose a random integer...". If this is really what was meant, then factorisation is probably much easier than these worst case examples. There is a better than 6 in 7 chance that a random integer is divisible by a prime under 50. Of course, this doesn't help if the problem is really related to cryptography, for example, where key numbers are definitely not random, but are deliberately chosen to be hard to factor. Gandalf61 09:56, 24 March 2006 (UTC)
let R be a ring, M a right R module, N a left R module
a balanced product (P,f) consists of an abelian group, a map f from to P, such that f(u+v,w)=f(u,w)+f(v,w) f(u,v+w)=f(u,v)+f(u,w) f(va, w)=f(v,a w)
Is this a general definition? It is used in my course before introducing tensor products? Why can't I find balanced products anywhere else, wikipedia and the rest of the internet included? Evilbu 15:16, 24 March 2006 (UTC)
Thanks, after we define balanced product, we define morphisms between two of them (P1,f1) and (P2,f2)
it has to be a group morphism g of P1 to P2 and for all m, n in M and N
g(f1(m,n))=f2(m,n)
a tensor product is then a balanced product such that there is a unique morphism to each balanced product
Now it is supposed to be obvious (without even proving existence of one) that the elements f(m,n) if (P,f) is a tensor product, generate the abelian group P now why is that? Evilbu 17:56, 24 March 2006 (UTC)
thanks but as i understand you used universal property
what actually did you use then
as i understand, you do not think this is such a trivial question( my syllabus works that way :balanced product, then morphisms between them, then tensor product, then this exercise)
forgive me for insisting but I am quite interested
allow me to continue for a moment with my not so general terminology
if (Z,f) is a tensor product , let P be the subgroup of Z generated by the image of f ( in general, you can't say the image is a group right?)
now (P,f) will be a balanced product as well
so according to my definition of tensor product there is a unique morphisms p from Z to P such that
p(f(x,y))=f(x,y)
this is all correct right? so how exactly should I proceed now?
If 45^x = 1 (mod 56), what does x equal? Is it
?
Please, how do I go about this question? Thanks Reffies. -- Dangherous 17:58, 24 March 2006 (UTC)
i think the point is that you have to Chinese remainder theorem
45^x=1 mod 56 is equivalent with the set of equations
{45^x=1 mod 8, 45^x=1 mod 7} or {5^x=1 mod 8,3^x=1 mod 7} now you see immediately this can only happen if x is true without calculations that require computers
let G be a strongly regular graph. assume nontriviality : do not allow it to be disconnected or to have a disconnected complemenent it has k as eigenvalue once then, and two other eigenvalues
when all eigenvalues are integers
apparently the conference graphs , those are graphs of this form
, are the only ones that don't have integer eigenvalues
but how to see this , essentially there are four parameters here that are restricted by two equations
and (this holds for all strongly regular graphs)
So where does the third restriction come from, as I see only one parameter in a conference graph?
I already requested a conference graph page on wikipedia
The problem is that on the internet, google etc. think you talk about conferences ON graphs :)
Evilbu 23:37, 24 March 2006 (UTC)
Lets say a circle, with diameter D was placed on the corner of a wall. Obviously, there would be a gap between the wall and the circle. The question is what is the diameter of the largest possible circle that can fit in this gap. Using Pythagorean Theorem, I found that the length of the gap would be . However, I have to contend with the gap between this hypothetical circle and its gap between the wall. The length of this gap I called x. I wrote the diameter of the second circle as . However, I cannot solve for x. I realised that the new gap would follow the same rule (). So the new equation would be:
With that, I was hoping to bring all the x's to one side. However, this proved troublesome. Can you help. Thanks.
********************************************************** * * * + * * * + * * * + * + ** * + * + ** * + * + * * *+ * * * * * * * * + * + * + * * + * * + * * * +
IF I AM PAYING A MORTGAGE OF $225.00 PER MONTH FOR 15 YRS ,,HOW MUCH MONEY SHOULD I PUT IN THE BANK TO HAVE THE BANK PAY OUT THE PAYMENTS?ASSUMING I'M GETTING 3% INTEREST WHILE MY MONEY IS IN THE BANK,,,AT THE END OF 15 YEARS MY ACCOUNT SHOULD BE ZERO..
CAN YOU CALCULATE THIS???
THANK YOU,,,JAMES
F = $32,580 dollars
8. The family court orders you to give your former wife a payment of $500
made at the end of each year for 3 years. The interest is 6.7% per year.
You would like to buy out the obligation by paying her a lump sum
instead. How much should you pay in the lump sum?
Interest I = 0.067 per year
Term T = 3 years
Payment Y = $500
Solution:
Y * ( 1 - 1/(1+I)^T )
F = ----------------------
I
$500 ( 1 - 1/1.067^3 )
= ----------------------
0.067
$500 ( 1 - 1/1.21477 )
= ----------------------
0.067
$500 * 0.17680
= ---------------
0.067
= $1319.38
Proof:
The amount you need to pay is equivalent to an amount which you put
into an interest account which your wife can withdraw the payment
at the end of each year. The account should be empty when she made
the last payment withdraw.
Since she makes 3 withdraws, assume the amount needed at the start of
the period to pay for each withdraw are F1,F2 and F3.
Thus we have
let x = (1 + I)
F1 * x = Y
F1 = Y / x
F2 * x^2 = Y
F2 = Y / x^2
F3 * x^3 = Y
F3 = Y / x^3
Therefore the amount you need to put into the interest account at the
start of the period is
F = F1 + F2 + F3
= Y ( 1/x + 1/x^2 + 1/x^3 )
let r = (1/x)
= Y ( r + r^2 + r^3)
in general
F = Y * ( r^1 + r^2 + ... + r^T )
Y * ( r - r^(T+1) )
= -------------------
1 - r
Y * ( 1/x - 1/x^(T+1) )
= -----------------------
1 - 1/x
Y * ( 1 - 1/x^T )
= -----------------
x - 1
Y * ( 1 - 1/(1+I)^T )
= ---------------------
(1+I) - 1
Y * ( 1 - 1/(1+I)^T )
= ----------------------
I
Ohanian
09:53, 27 March 2006 (UTC)
Let's say that:
>> Lane 256 Alley 34 House 7 means approximately: >> we travel 256 units and turn right on to Lane 265; then >> we travel 34 units and turn right on to Alley 34; then >> we travel 7 units and there is the house, on the left. >> >> Telephone pole 22 L 33 R 6 means >> we travel to pole 22, follow the left fork wire 33 poles, then fork >> right for 6 poles and arrive at our goal pole. >> >> ( jidanni.org/geo/house_numbering/ ) P> What is your question? Do you want to assign house numbers? Do you P> want to build a cross references from those numbers to spatial P> location? Do you want to compute the distance from one to another? P> Do you want to uniformly store house numbers like that in a software P> data structure?
I guess I just want to find which part of graph theory deals with naming points and segments on graphs the closest.
e.g., http://en.wikipedia.org/wiki/Glossary_of_graph_theory doesn't ever mention (systematic) ways to name each segment and point... That's what I want: what's the branch of math that deals with names for points in twisty graphs... maybe they have a better way of naming the two houses on the image on jidanni.org/geo/house_numbering/mountain_en.html
I want to know if there are even smarter ways of naming such points, or how folks go about naming points on graphs.
Yes, we would use nice grid coordinates if we were in a flat city, but we have twisty hilly roads.
--Dan Jacobson, jidanni.org
prove or disprove:A and B are path connected subsets of a space X and intersection of A and B closure is non-empty.A union B is path connected.
It's damn obvious, but I can't remember how to prove that the tail of an l2 sequence goes to zero.
That is, given where , to show that . Confusing Manifestation 11:04, 27 March 2006 (UTC)
Thanks for both answers. I knew it was so obvious as to practically follow from the definition, but for some reason the actual steps eluded me. Confusing Manifestation 00:12, 28 March 2006 (UTC)
I am working on producing a spreadsheet and have hit a road block in some geometry. I am trying to upload my diagram but something isn't working right so I'll need to explain it verbally first.
I have a parallelogram, with theta in the lower left hand corner, by starting at theta and traveling clockwise I have B and then the horizontal leg A. Theta and A are my inputs. I can also even determine F, which is perpendicular to B and terminates at angle BA, but I don't really see a way that it helps me out. On lower leg A, if we go to it's far right end and draw a verticle line we get a right triangle with leg d, B, and H. I had a hunch that the quantity (A-d) relates to theta. So in AutoCAD I set A = 1 and varied theta from 0-90 in increments of 10 degrees, converted into radians and plotted the values against (A-d). Found using linear regression with a third polynomial equation, [-0.0698(theta)^3 + 0.3564(theta)^2 - 0.031(theta) + 0.44 = (A-d) ] resulted in a R^2 = 1, so someone please set me straight if I am way off target here but I assumed I since the R^2 = 1 everything was fine and I would be able to multiply the equation by left hand said of the equation by A and I would be able to get (A-d) do some geometry and have the Height pop out. (This part may get confusing and I can set up a junk hotmail account, post it, and if anyone is interested in seeing how I did this in excel email me and I'll send it to you). But I took two arbitrary values of A varied theta, got more equations by from trend lines, divided each term by A and compared the terms to the first equation and they came out reasonably the same......I thought I was good to go but when I do it in AutoCAD....it doesn't really work......don't know if I'm just spinning my wheels or if there really is a way to determine the height of a parallelogram from by given input. But doesn't there just seem a way that theta can be a direct function of (A-d)???
##### A # # ########## A# # ########## # # ########## θ##### θ##########
I do Independent Study math, so it's not graded - I make up my own assignments. Anyway, here's a problem I can't quite figure out:
Find the local max/min values and saddle points of the function:
I take the first partial derivatives and equate them to 0 (I can do that part ;):
Then I can find one set of points, (2, −4): x=2 (from ) → y=−4 (plugged into the other partial derivative)... but then I'm stuck. It's a tiny roadblock but I can't seem to figure it out -_-
Thanks. – ugen64 22:44, 27 March 2006 (UTC)
(Not sure where to ask Macroeconomics question, so I will try here.) I read in The Economist that China has >$800 billion in reserves. Why doesn't China spend this money on sorely needed infrastructure projects, rather than saving it? I.e., what marginal benefit exists for such savings? Lokiloki 02:23, 28 March 2006 (UTC)
Optimal expander graphs are known as Ramanujan Graphs. Explicit constructions for them is given in the Ramanujan Graphs by LPS. I have a doubt in the construction of them. While using PSL or PGL, how they are different from SL and GL. It has been said that PSL is quotient group with out zero transform. Can any one explain me more about how to construct them? Any full example available with any one? -- Guru 03:45, 28 March 2006 (UTC)
A giant lamington cake in the shape of a cube.How many small lamingtons have 0,1,2 or 3 sides iced if the cake was cut into 64 and 125 cubes?
A recent study indicated the total cost of the war is 1 to 2 trillion dollars depending on how long it lasts. Going with the 1 trillion figure and figuring that the US population is close to 300 milllion--how much would the cost be per person?
Looking at this from a logical perspective, it is obvious that the human and financial costs would have been lower if America had dropped an atomic bomb in 2003. It is just that the word "nuclear bomb" makes everyone shout and become emotional. These people are essentially saying that killing people a few at time is preferable to massive deaths even if the number of massive deaths can be fewer. -- Patchouli 01:15, 3 April 2006 (UTC)
Kudos to Harry Truman for saving American and ultimately Japanese lives.-- Patchouli 01:18, 3 April 2006 (UTC)
Hi,I am a new person to this website and i am getting a lot of information from you guys.
I am an IGCSE student that studies in Britain and am studying at grade 10.
I have 4 question to ask you about from the IGCSE.
First question is that you give me brief information about the sine and cosine rule. Secondly, What is factoization of expression, and also it's definition. Thirdly, The simplification of long expressions with exponents. Last question is that can you give me information about the sets.
Thank you very much for your help and i hope that it will come back to you one day.
How would I figure this out 1−1. I can't remember how to figure the answer if if the power is negative. Thank you for the help. I Lov E Plankton 16:36, 28 March 2006 (UTC)
I did a little experiment. I tested the Combination and Permutation functions.
P(n, r) = n! / (n - r)!
C(n, r) = n! / ((n - r)!r!)
Let's say that for each one I'm using 4 (n) items in set of 3 (r).
P(4, 3) = 4! / 1! = 4! = 24
C(4, 3) = 4! / (1! * 3!) = 4
Well everywhere I go, it says that the Combination returns the number of combinations of items in which the order does not matter. Well tell this to the following sets.
(1 2 3), (1 2 4), (1 3 4), (2 3 4)
Notice that it only has 4 items (n), sets of 3 items (r), 4 sets (C), and it IS ordered.
Thats not all though. They always say that Permutation returns the number of ordered pairs, but I found that I can get the same number of unordered sets with all the same variables.
(1 2 3), (1 2 4), (1 3 2), (1 3 4), (1 4 2), (1 4 3), (2 1 3), (2 1 4), (2 3 1), (2 3 4), (2 4 1), (2 4 3), (3 1 2), (3 1 4), (3 2 1), (3 2 4), (3 4 1), (3 4 2), (4 1 2), (4 1 3), (4 2 1), (4 2 3), (4 3 1), (4 3 2)
Again notice that it only has 4 items (n), sets of 3 items (r), 24 sets (C), and it IS NOT ordered.
You think it stops there? Wrong. It is the same for the functions with repetition. I'm not going to go into detail about them though. I have already talked long enough.
I was just wondering about this, and though somewhat might look into it.
Matt DeKok
Does the inequality: (x^(t))(y^(1-t))<=(t)(x)+(1-t)(x) hold? with 0<=t<=1 and x,y > 1 Also any proof? Oh and by "<=" I mean less than or equal to. Thanks Qeee1 17:24, 28 March 2006 (UTC)
Hi there,
I am looking for a good freeware software to plot graphs. I looked through the Graph-Plotting Software Page but was very unsure...does anyone of you know a good programme. I do need it for school calculus, so it should be able to do soem analysis.
Thank you -- 165.165.228.18 19:16, 28 March 2006 (UTC)
I have no experience to use any packages on computer graphic. Only Maple and Matlab are available to me paid by my University but I never try them. My simple question is how do I produce a JPG-file, say sample.jpg of the function joining (-1,0) to (0,1), from (0,1) to (1,0) and set all other values to be zero. Can I use formula such as \sin nx/(\pi x) for n=1,5,10 on the same output? I can start Maple on MacIntosh with a double click, then what? How do I draw a circle inscribed in a triangle? Do I have to study a lot from their users' manual (RTFM) before I can use Maple or Matlab? If successful, I can use TEX-graphicx to paste this file as part of a PDF-file. Thank you in advance. Twma 02:03, 29 March 2006 (UTC)
a radius of a circle is 15cm. find the length of the arc of the circl intercepted by a central angle of 3pie/4radians. (leave in terms of pie)
=degree measure of the arc
=arc leangth
there is an algebraic way, but I find this way easier. (updated by myself
schyler
00:01, 29 March 2006 (UTC))
On a disk the same radius as the observable universe what is the minimum number of digits to describe an arc the length of a ... pick something interesting. The width of a finger, a human hair, a hydrogen atom. I was just reading the Pi article and thought this might be good to add. Trieste 14:57, 29 March 2006 (UTC)
Hi guys,
is there any packet for LaTeX to draw and display functions in a LaTeX Document, such that u enter a formula and parameters and it will draw it into the document.
Thank you -- Da legend 15:54, 29 March 2006 (UTC)
I have been trying to learn "how the $11,000+" amount is calculated. I have looked up the 30 stocks and added the stock price but doesn't come close to $11,000. How is this number derived on a daily basis?
Thanks, Bill
When I was studying the problem of induction at University the lecturer wrote '1,2,3,4,5,6' on the board, and asked what number came next. The general consensus was '7'. He then wrote out a simple function that, when we worked out the next number, it turned out to be something in the hundreds. Depending on a certain variable in the function, it would give a series of successive integers followed by any number you specify. Does anyone know what this function is? Purely out of interest, no hurry. Phileas 04:40, 30 March 2006 (UTC)
I'd be more impressed if someone could write a recursive sequence whose first 6 terms were one through six and whose seventh was anything. OEIS has nothing of the like. - lethe talk + 06:03, 30 March 2006 (UTC)
In the 1952 story Back to the Klondike, Uncle Scrooge claims that he has 3 cubic acres of cash in his Money Bin. "Cubic acres" is an unusual measurement for volumes so I need to ask: How much is 3 cubic acres in cubic metres?
Also, the depth gauge in the bin shows a depth of 99 feet. Is that reasonable? Thuresson 16:27, 30 March 2006 (UTC)
How many suns would it take to fill the sky,I know the size of the sun is about 1/2degree, and the sky is basically half a sphere.But what is the formula to work it out step by step. Looking at the sky I tryed to visalize how suns it would take,the answer must be quiet large,but it is the maths that I have find hard.
It is well known that for every m-times continuously differentiable real function f on R^n, every compact subset K of R^n, and every e>0, there is a polynomial p on R^n such that for every multi-index with and every x in K, we have .
On page 155 of Topological vector spaces, distributions and kernels by F. Treves, Academic 1967, there is a proof using extension of f to a complex entire function on C^n.
Most of the standard undergraduate textbooks in numerical analysis AVAILABLE to me do not deal with this specialized topic.
Question: Is there any proof which is internal to real analysis? Any references?
Thank you in advance. Twma 07:18, 31 March 2006 (UTC)
I visited Shadrin's notes and checked out Powell's book (waiting for 4 days from our Library). It appears that we do not have any alternative proof in our archives. Thanks. Twma 07:39, 5 April 2006 (UTC)
Suppose an event e has two equally likely outcomes, x or y. Suppose e has occurred k=5 times in succession, each with outcome x. What is that probability that the 6th outcome of event e will be x? -- Simian1k 18:37, 31 March 2006 (UTC)
What is the value of the series: ? Thanks in advance, Mickey 195.93.60.7 19:30, 31 March 2006 (UTC)
In the article on the brachystochrone Snell's law is given as sin theta divided by velocity equals Cste. What is Cste ? -- 204.69.190.14 19:38, 31 March 2006 (UTC)
I have to solve the following set of differential equations numerically:
Boundary conditions:
I have three 2nd order equations, and 6 boundary conditions, so I should be able to solve this. The derivatives are with respect to s. Functions f1, f2, f3 are a bit complicated. How can I find solutions to this problem numerically to find ψ(s), θ(s) and φ(s)? I have Matlab at my disposal. Any help will be greatly appreciated. deeptrivia ( talk) 19:55, 31 March 2006 (UTC)
Can anyone give me a clear definition of a third order covariance matrix? The only thing I can find on the net is at mathworld but it is not clear to me what is meant by the superscript notation mn --Will
If I know that Wikipedia reached 500,000 articles on March 17 2005, 666,666 articles on August 4 2005, and 1,000,000 articles on March 2, 2006, and I know that Wikipedia "currently" has x articles, then how can I make this into a third-degree polynomial approximating Wikipedia's growth and solve it to get the time Wikipedia will reach a given milestone? JIP | Talk 08:17, 2 March 2006 (UTC)
Simplify, and solve using
Newton's method. --
Meni Rosenfeld (
talk)
08:31, 2 March 2006 (UTC)
Wait, you got me mixed up. With 3 points of data you only get a quadratic polynomial. So you can solve it directly. -- Meni Rosenfeld ( talk) 08:34, 2 March 2006 (UTC)
Or perhaps you meant there's an additional point, the current time x0 and the current articles y0? Stick it to the formula and you get
And see also Lagrange polynomial. -- Meni Rosenfeld ( talk) 08:40, 2 March 2006 (UTC)
This isn't my best day. You can also solve a third-degree polynomial directly, but I guess Newton's method is simpler. -- Meni Rosenfeld ( talk) 08:42, 2 March 2006 (UTC)
Under which additional conditions (on the function f(x)) is the Fourier transform of a real, positive semidefinite function f(x), defined for the whole real axis, again real and positive semidefinite? --CA
(Please sign your questions.) The Fourier transform is a change of basis. Contemplate the definition of positive semidefinite. -- KSmrq T 13:06, 2 March 2006 (UTC)
(I have signed and made slightly more specific the question.) I do not understand your answer. If you want to insinuate that the Fourier transform F(k) of every real, positive semidefinite function f(x) is again real and positive semidefinite, then this is not correct. First of all, f(x) has to obey f(x) = f(-x) in order to have F(k) real. Within this class of functions, a simple counterexample is the symmetric, rectangular pulse. Indeed, if f(x) is
f(x) = 1 for -a <= x <= a f(x) = 0 for |x| > a
(here a is a positive, real constant and <= means "less or equal") then its Fourier transform F(k) is (up to a factor)
F(k) = sin(ak)/k
which certainly is not positive semidefinite. --CA
I need to prove that the area bounded by a unit hyperbola and a line from the origin to the hyperbola is equal to twice the angle of that line.
I know that the point where the line and the hyperbola meet is (cosht, sinht). Using that, I was able to find the equation of the line: y = xtanht. Im running into trouble with the integral. I think I did it right. I wish I could show it better, but I can't get the syntax of the math language to work: I figured I have to integrate along the y axis, from sinht to 0, because sinht is the y value of the intercection. Assuming I did it right, I got an integral of sqrt(y^2+1) - y/tanht. Please let me know if I am on the right track, and if you can help me out with the math formatting, that would help too. Thanks a lot. -- Chris 17:07, 2 March 2006 (UTC)
I've been told that the Riemann hypothesis has many broad implications, if only it were proven, but what are those implications? And why should I, a person who has an interest in math but doesn't spend all day looking at numbers (though I read quite a bit about philosophy, science and computers) care about it?
(Also, couldn't we construct a statement along the lines of "X is true iff the Riemann hypothesis is true." And then see if X is true or not, and use that information to either prove or disprove the Riemann hypothesis?) - 86.138.233.25 20:09, 2 March 2006 (UTC)
Suppose you were to define an arbitrary operator, Û, in 3-space, using cartesian coordinates, as
Would it reduce all linear functions it was applied to, to 0?-- 64.12.116.11 01:43, 4 March 2006 (UTC)
What command should I use in TeX to get double contour integral?
So, I'm looking up information on logarithms, and it says that Briggs and Napier decided that the log of 10 shuld be one, and the log of 1 should be zero, and that at first they thought log 10 should be 10^10 to avoid fractions. Was there some mathematical basis for this that someone would be willing to explain to me, or were they just making it all up for fun? Ductape Daredevil 17:06, 6 March 2006 (UTC)
Hello, I have already seen in the article about plus and minus signs that the Jewish usually do not use the plus sign. However, they use an inverted T. I am interested if Arab countries use the usual symbol or another (as + may resemble a Christian cross). Thank you. -- 84.21.200.224 18:38, 6 March 2006 (UTC)
I am calculating average values in a database of a few million records. It takes a very long time to scan each record and decide if it should be included in the running average. So, I'd like to do standard deviation on the fly rather than go through all the records once to get the mean and then go through them all to get the standard deviation. Is that possible? -- Kainaw (talk) 16:00, 7 March 2006 (UTC)
If there are only a few million of them, why not make one pass in which you decide whether a record should be included and cache the value on which you want the statistics? Then make a second pass through those values and get your s.d. It should all fit in physical memory so it will be very fast, and you won't have to worry about the roundoff-error problem. -- Trovatore 18:23, 7 March 2006 (UTC)
SELECT ave(SALARY) FROM EMPLOYEE_TABLE WHERE STATUS != "TERMINATED" AND SALARY > 0.00 AND SALARY < 99999999999.99;
SELECT ave(SALARY),stdev(SALARY) FROM EMPLOYEE_TABLE WHERE STATUS != "TERMINATED" AND SALARY > 0.00 AND SALARY < 99999999999.99;
This question shouldn't be too hard, which is good, since I need this done tonight. I have managed to be pretty ignorant in probability to this point in my life, which is very sad. I should be able to get this from the article, but it's very technical and I'm having trouble reading it.
How do I get the cumulative distribution function for the log-normal distribution? Let's say I have a silly program which will give me the CDF of the normal distribution, but not the lognormal. I know the values , which isn't a mean but kinda looks like one, and .
So if z is a random variable with the lognormal distribution with that and , what exactly is the probability that where X is some number I also have? moink 10:12, 8 March 2006 (UTC)
hi, please i would like to know the difference between exponential distance and linear distance? i would also like to know if the impact of distance on the visibility of an object is either exponential or linear...thanks
Three cake boxes are stacked. Find the surface area of the entire stack if all the prism bases are squares. Top Box: L=12 W=12 H=6 Middle Box: L=26 W=26 H=6 Bottom Box: L=36 W=36 H=6
It seems that some assumptions must be made. These would be my assumptions:
1) The area each box has in contact with another box is not counted as surface area for either box.
2) The area the bottom box has in contact with the table is not counted.
3) The boxes are stacked such that the largest possible area is in contact with the table or box underneath it. That is, none are lying on their sides or hanging over the edge of the table or box underneath. StuRat 21:21, 13 March 2006 (UTC)
We do not need to know the table area.
How did 'Renee' prove that '1=0'? ( If she ever existed and what I read isn't just part of a novel).-- Cosmic girl 19:20, 8 March 2006 (UTC)
thanks :D.-- Cosmic girl 20:54, 8 March 2006 (UTC)
do my homework-- Gefploxer 21:56, 8 March 2006 (UTC)
What is infinity divided by infinity? —The preceding unsigned comment was added by Biofireball ( talk • contribs) .
Isn't infinity/infinity = 0 or 1?.-- Cosmic girl 23:55, 8 March 2006 (UTC)
Long time ago I remember reading a problem and solution which I can no longer recall. Problem is to cut and distribute a completely homogeneous cake into n pieces among n people such that each person perceives that he received fair share of cake. Note that it is not important whether it is fair share or not, but all must believe that it is. For n=2, solution is one person cuts the cake and another choses his piece. Thus person cutting the cake will know that both pieces are equal since he cut it (and took atmost care on his behalf) and person picking will get to pick whichever he thinks is bigger share. I remember that solution exists for n=3 or more, but I don't know what. Can someone help me here? Again, cake is plain, no fancy icing, and all participants have no preference over piece except its size/volume. Thanks. AshishG ( talk · contribs)
Actually this page has some information, including solution for n=3 which is different & much complex then one proposed above. And it says that n=4 or more is just too difficult. So I take back my question. By the way, this reference desk is great place for fun! AshishG ( talk · contribs)
Suppose X has a normal distribution with expected value 0 and variance 1. Let
Y = -X if -C<=X<=C or Y=X if |X|>c,
where c is a positive number to be specified below. If c is very small, then the correlation corr(X, Y) is near 1; if c is very large, then corr(X, Y) is near -1. Since the correlation is a continuous function of c, the intermediate value theorem implies there is some particular value of c that makes the correlation 0. That value is approximately 1.54. In that case, X and Y are uncorrelated, but they are clearly not independent, since X completely determines Y.
So, I've been told that the square root of -1 is i. I've looked at the square root article but it doesn't say anything about this. I understand sqrt(-1) has no integer number, so why i? Any help would be greatly appreciated :) -Benbread 20:08, 10 March 2006 (UTC)
arch z = -i cos^-1 z = -i arccos z. But |z| < 1. So let's say M * arch 0,11 = 1000 * -i * 1,46057328 = -1460i. Another question please. -- DLL 11:23, 11 March 2006 (UTC)
the question comes along a story one person in SriLanka rented out a room for 3 persons,each one must pay him ten rupees as key money and he will get totally 30rupees.When he collected 30rupees and returned home his wife said that the 10 rupees for each one is too much and return them 5 rupees,so owner called his servant and gave him a 5 rupee coin and ordered him to handover it to the new boardes,servant took it and walked .While the way he think to buy a toffee for him and bought one spending 2 rupees.Finally he return only three rps to boarders.Only now the question begins,when the servant returned the 3rps each boarder gets 1 rupee.So actually each one have spent only 9rps for the room.Finally if we see through the account, the boarders spent money=9+9+9=27rps.the servant spent for toffee=2rps.so the total money spent in this story is 29rps.But initially we got 30 rupees,so where is that one rupee? -- 222.165.169.196 12:09, 11 March 2006 (UTC)
Earlier this week while discussing a question regarding the angles between clock hands with some of my friends, I posed them a question of my own: assuming a clock with second, minute and hour hands, in which all hands move continuously (ie. the minute hand doesn't wait until the second hand reaches 12 to move), at what time(s) will the angle between each pair of hand be 120 degrees? I figured, while it might take some figuring out, it wouldn't be that difficult.
Not knowing the answer myself, I've spent the week trying to figure it out to no avail. I've tried doing some series of equations to express the angle of each in terms of hour, minutes and seconds, but that hasn't worked. I've tried doing it simply in seconds, but dealing with the number of complete rotations of the second hand has proved troublesome. My friends are equally stumped. Any suggestions on how to go about solving such a problem would be much appreciated.
-- Elzaban 16:22, 11 March 2006 (UTC)
I have these two equations:
The two unknowns are and Xmax. How can I solve this. I'm not even sure if I have sufficient information to solve, since one of the unknowns is a function. Help would be highly appreciated. deeptrivia ( talk) 02:15, 12 March 2006 (UTC)
Thanks! I found a missing equation. I still don't know how to solve it, but I haven't tried much. It's not a design problem, and there has to be a unique solution. Thanks for your help :) deeptrivia ( talk) 18:16, 13 March 2006 (UTC)
Yes, this is homework, but I have done most of the work. We have been given the function y=exp(-x2). We are asked: What are the dimensions and area of the largest rectangle that fits into the curve and the x axis, as shown on the below:
Let x equal the distance between one of the vertical sides of the rectangle and the y-axis. The area of the rectangle is therefore 2x(exp(-x2)-x) (length times breadth). I call this function A(x), and it has a maximum when I graph it on my calculator. To find the maximum, I use calculus, letting the derivative of A(x) equal zero:
How on earth would I solve the last equation for x? The closest I can get to is:
Taking natural logs will get rid of the exponential expression on the left, but leave a log on the right. I'm sure I haven't been taught the tools to deal with equations like this. (Year 12 Specialist Mathematics, Victoria, Australia).
Did I miss an easier way? Can the above be solved using high-school mathematics? -- Alexs letterbox 04:58, 12 March 2006 (UTC)
I changed the format of the first two equations and another, just for legibility, in case anyone else had trouble reading it. D. F. Schmidt 02:39, 18 March 2006 (UTC)
I ran into a problem recently while trying to solve a pair of equations that appeared to be fairly easy, but had me stumped when I actually tried to do them. It was part of my maths work at school, and the thing that had me most puzzled was that it was only the lead-in part to the harder part of the question which was on some basic integration.
The specific question asked for the points of intersection of and . I couldn't do it at all, so I'd appreciate it if anyone could demonstrate a reasonably simple method, because it should be doable with fairly basic maths. I'm fine with manipulating them around and so forth, it's just I can't work towards something with less than two unknowns, for instance.
I can solve most simultaneous equations but when it came to this I wasn't sure how to communicate a decent proof on paper. In connection with solving this I decided to see if I could solve which I can easily see answers to in my head. I couldn't, however, prove my answers elegantly on paper. So it would appear that my problem lies in not being able to get down to one unknown when I'm restricted by the sine function, and if anyone could offer any general help on that it'd be most welcome. 81.157.152.22 19:44, 12 March 2006 (UTC)
I got this question as a homework assignment and i just can't figure it out. Here's the question: What is the least value of N such that N! is greater than a googol?
I have to solve the equations:
and
for . Here, F is the incomplete elliptic integral of the first kind. e, k and L are known.
I am doing this in MATLAB as follows:
opt = optimset('Display','notify','TolFun',1e-8,'TolX',1e-8,'MaxFunEvals',10000); pfunc=inline('L - (mfun(''EllipticF'',sqrt(1/p^2-e^2*k^2/4),p)-mfun(''EllipticF'',sin(pi/4),p))*p/k','p','e','k','L'); [p,xval,exitflag] = fsolve( pfunc,0.707,opt,e,k,L) thetaC = 2*asin(sqrt(1/p^2-e^2*k^2/4));
I know that for sufficiently large values of e, I should get . A trial value for such case is e = 137, k=0.01, L=100. The numerical computation for finding p fails to converge after values of e that should result in . What's the reason? Does it have to do with the way asin and sin are defined in matlab? What's the way out? I'm doing this to calculate elastica, and I know that after a particular value of e, it will start making a loop, forcing . How can I do this calculation? deeptrivia ( talk) 18:37, 13 March 2006 (UTC)
Is there any easy explanation (one that I can understand) of how Euclid's parallel postulate is false?.-- Cosmic girl 18:39, 13 March 2006 (UTC)
Wow! :O ...thanks! I understood but I'll read the articles too.-- Cosmic girl 20:29, 14 March 2006 (UTC)
This is Pi Day. But when, in history, was the best approximation to pi equal to 3,14 ?
How was the forumla for the surface area of a sphere derived? Are there any good sites with information about this? 64.198.112.210 16:41, 14 March 2006 (UTC)
Find all n such that (20n+2) divides evenly into (2003n+2002)
L33th4x0r 05:46, 15 March 2006 (UTC)
I've got this strange theory that I conjured out of thin air som 15 years ago, have there been anybody else than me thinking about this stuff.
I postulate hereby that C a 2D creature's fastest way (like in shortest/less resource expenditure) of traveling (in an XY plane) from point A to point B would be to travel in one direction (X or Y) (not distance AB) until it would be at the distance AB - (A - (X or Y)) = B and then the distance B.
This way the creature C would only have to change direction of travel (90 degree change) once.
Try to think about this and and tell me how much further would 2 D creature have to travel compared to a 3D (capable) creature, my answer is squareroot 2 (appr. : 1.4) times more.
Reason: while the 2D creature could change direction of travel (X or Y) for every second or mm (or whatnot) that it went, this would take even more time/resources ..stop/change direction etc.... than it would to just travl the distance in the X direction and then after that in the Y direction....one start/stop/start/stop
Relate this to a 3D creature like us in a 4D world....and the answer would be 0.5 times the value of pi.....and bring in the double slith photon/electron experiments and other relativistic points... anybody got any thoughts about this...?
Could this be elaborated a bit more? [Azalin1999]
Hi again I'm the one who phrased the question. A little note about myself. Never did score high in maths and equations but I'm really curious about this 'theory'. Much thanks for the link to the 'manhattan distance' article, I think I remember reading about it some years ago. My native tongue is Danish so that's my excuse for the inaccurate phrasing.
I originally made some drawings on a XY crossed paper to illustrate the theory. And I had a really hard time to explain my arguments for those I presented it to (mostly indifferent friends). And I still have difficulties atm. because the thing I would like to verify is that it would be possible to apply something like this 'manhattan distance' to distances in a 3D world seen from the perspective of a fourth dimension. Which should be possible. Basically like -- BluePlatypus went about distances in an euclidian plane...
The distance 1/2 Pi was derived from projecting a imaginary path (distance traveled) through 4D space compared to what a 3D creature would have go by not using the 4th dimenson...like a 2D creature can't (see, thus) travel the path that a 3D creature can. In regards to the 'Manhattan Distance' this would be akin to a race between a cab an a helicopter going over the cityblocks.
You're Chuck making some good points. But what if we assume that in our (unlimited) reference 3D space we are looking down on the 2 plane (which could be from any arbitrary reference point/perspective) let's say head on, straight down.
Let's assume some more - Our little 2D creature can only observe (look) through either the X or the Y, and thus only observe it's destination when its in line with either the x axis of the destination or th Y axis, whichever comes first, depending on which route it took.
From the 3D POV this would satisfy my squareroot 2 clause about a 3D being would be able to go the shorter distance right? Because it can sort of observe the direct line of vision...X & Y combined.
Now if the 2D creature were able to in some way observe the destination it could of course just travel the direct route. But this would only happen after it had moved all the way along either the X or Y axis to be in line with the destination. If this 2D thing were sentinent the perceived distance the 2D being traveled would be? the squared X+Y which is less than the distance it really took if a 3D being measured...also there are 2 routes that are the same distance but starting with etiher going out of the X or the Y axis...
Relate this to a 3D world...(damn crunching)hmm non-euclidian geometry..........Spherical trigonometry
As I see it - Going from A to B in 3D is just (always) a straight line. But this C cannot see that so it has to travel from the perspective of the 3D creature in X + Y ie. at the point where it needs to change direction is where the 2D creature actually has traveled the least distance in the X distance (or Y) and then changes direction 90 degrees to be 'the fastest' without changing directions every x/Y mm (or whatever).
So the 3D viewer would, if seeing the 2D creature move along the xy points, percieve the path at some fractional degree from the perfect - Squareroot 2 path - which means the 3D viewer would be able to see the 2D creature's energy expenditure adhere to my postulation.... 2D travelers always expend square root 2 times more energy when the 3D viewer multiply this with hmmm is it cosinus or sinus ? (Perfect angle view that makes a straight line away from the XY plane) That's the hint for ½ PI value. To elaborate : A photon is emitted from somewhere..... this photon is measured at some point and only there you can make the mark that you measured a photon (in whereever space) how it got there (Cab or Taxi) you don't know - you can just measure the time difference between you emtting the photon - and collecting information about when it hit 'point B' 85.81.121.107 ( talk) 19:59, 7 October 2011 (UTC)
Hi, I'm working with gradients at the moment but can't for the life of me rember if you count the squares (i.e. measure) or use the unit values for the graph. To see an example of what I mean: Click here is the gradient 3 over 6 (as attained by counting squares) or 15 over 12 (as attained by using the unit values). If it helps I'm dealing with "real life" data here. Thanks! -- Christopher Denman 17:50, 15 March 2006 (UTC)
On right is a plot of x-, y-, and z- coordinates of two ropes on which some forces are acting. I made this using the plot3 command in matlab. Now I want to remove the axis labels, and marks. In that case, this will look like 2d. How can I make it look 3d? Some kind of shading/lighting/perspective tricks? I need to do this in MATLAB. Thanks! deeptrivia ( talk) 21:39, 15 March 2006 (UTC)
Thanks for your answers. I tried shadows and it helps a bit. I have no choice but to use matlab because this will be a part of a GUI I'm making in Matlab. I think I can manage if I get a solution to the problem regarding cylindrical surfaces below. Cheers, and I appreciate it highly. deeptrivia ( talk) 01:30, 16 March 2006 (UTC)
I need the definition in mathematical terms for manipulatives
This is a follow up question from above (3D effects without axes). Suppose we have a spatial curve defined by x = f(s), y = g(s) and z = h(s). What equations will describe a cylindrical surface of radius r which has this curve as its axis? I can do real neat 3D things in matlab if I plot this surface. Will post the results here, of course. deeptrivia ( talk) 01:28, 16 March 2006 (UTC)
For everyone's benefit. I got a readymade solution based on
Melchoir's answer. See
[1]
deeptrivia (
talk)
03:08, 16 March 2006 (UTC)
I am writing this as an AP Calculus BC student. Assume f(x) describes a continuous, differentiable curve, such as
I want to find the surface area of the solid that results from a rotation of part of the curve, say 0 to 4. For this example, let's assume I'm rotating about the x axis. I know the correct method to solve this problem (surface areas of cone frustrums). However, why can't it be found as a summation of the surface areas of right circular cylinders (excluding the bases)? Thus, my presumed integral would be
Obviously, it is wrong. However, why is it wrong? My textbook helpfully includes the formula above (though I found it myself before seeing this). It then says it can not be used because it has "no predictive value and almost never gives results consistent with other calculations." However, I find this somewhat disappointing, as there is no explanation of why the formula is flawed. Please do not simply show me the right way to do it, and explain that this is therefore the wrong way; that is unhelpful Superm401 - Talk 01:58, 16 March 2006 (UTC)
When calculating the area under a curve, one can approximate either by rectangles, or by trapezoids bounded by some "diagonal segments" on top. I think the second approximation is called the trapezoid method, and it's better than the rectangle method, but both work in the limit. Both converge to the Riemann integral.
On the other hand, when calculating the length of that same curve, you have to approximate the curve by diagonal chords. If you approximate the curve with rectangles, the sum of the rectangles will always add up to b–a (where the domain of the curve is the interval [a,b]).
The technical reason behind this is that the form which gives you the length is not a linear differential form. In other words, the Pythagorean equation is not linear, and that's needed to calculate length. The form that gives you the area is linear, and therefore any sum will do. Stated even more simply, the triangle inequality tells you that the hypotenuse of a triangle is greater than the leg. Rectangles get you the leg of the triangle, and never approximate the length, though they do approximate the area. Calculating surface area is just calculating length and throwing in a 2πr, so the same issues apply to volume versus surface area. - lethe talk + 03:31, 16 March 2006 Th(UTC)
To illustrate the problem somewhat differently, consider a cone obtained by rotation of "y=ax" around the x-axis. The area and the volume are given by integrals
You can see that omitting dl/dx will lead to a wrong result. For the curve , dl/dx varies with x. Another example is the surface area of a unit circle
( Igny 13:04, 16 March 2006 (UTC))
can anyone give the derivation for this?
how do you find the determinant of a parabola?? please help
On page 74, L. Schwartz, Mathematics for the Physical Sciences,Hermann
Quote: The existence of linear functionals which are discontinuous on $\script D$ may be demonstrated mathematically using the axiom of choice. UN-Quote.
Question: Where can I actually find a proof for the existence of a discontinuous linear functional on test spaces?
Be more grateful if you could send your answer directly to me by visiting http://www.maths.uwa.edu.au/~twma/mathematics/index.htm Thank you in advance. twma
Dear Lethe, Thank you for your quick response. Because you did me a favor to visit my page above, I was alert immediately without having to wait until tomorrow.
On page 73 of the same book above, a sequence of test functions f_n tends to 0 if
(a) the supports of f_n are contained in the same bounded set and
(b) for each fixed m, the m-th derivative of f_n tends to 0 uniformly.
\sin n^2x/n could not satisfy the above conditions.
I multiplied \sin n^2x/n with a test function g satisfying g(0)=1. Could not get any further. STILL NEED HELP. twma
To find, explicitly by displaying formulas or implicitly by axiom of choice, a counter example that a linear functional T is not continuous, we need to find a sequence of test functions f_n satisfying both conditions (a) and (b) and in addition T(f_n) fails tending to 0 as n tends to infinity. The sequence \sin n^2x/n does not satisfy (a) and not (b).
Distribution theory is well established nowadays. There are many good books on the subject. For example,
Page 222, F. Treves, Topological vector spaces, distributions and Kernels, Academic.
Pages 28, 26, M.A. Al-Gwaiz, Theory of distributions, Monographs and textbooks in pure and applied mathematics, vol 159.
I quote L. Schwartz because the book was written by the creator. I even looked up the French version of the same book with disappointment. My next possible step is to look up the original paper. Twma 18:52, 17 March 2006 (UTC)twma
You people have something like --- 17 March 2006 (UTC) but I do not have it. Am I overlooking some rules and regulations of this site? If so, apologize and please tell me what to do in order to CONFORM.
I wrongly thought that four tildes are examples of letters of a signature. I am able to conform now. Thank you. My identity is twma in lower case but this site changed it by default to Twma in order to conform.
To save the room, I shall delete part of this section if I have no objection in 24 hours. Twma 18:52, 17 March 2006 (UTC)twma
All right! People want the complete record even full of irrelevant junk such as part of mine. Good to consult first and take action later. No action in this case. Twma 22:57, 18 March 2006 (UTC)
OK, twma, now I think I see what you were trying to do. You want a sequence of functions fn and a linear functional T such that fn → 0 but T(fn) does not → 0. But you chose a sequence of functions which does not converge, so clearly that is not going to show anything (your sequence doesn't satisfy your (a) and (b)). Now, the article discontinuous linear functional teaches us that on a complete vector space, all examples are nonconstructive, so you can't just look for a sequence and a functional, you have to invoke the axiom of choice. The vector space you have chosen is complete (though not in the uniform norm). The examples look like the one you find in that article. Let fn be a sequence of linearly independent functions. Denote by ||g||m,K the seminorm supK Dm|g|. If {Ki}i is any countable collection of compact sets which cover the real line, then ||*||Ki,m is a countable sequence of seminorms. Create a directed countable family of seminorms, and denote the kth seminorm by ||*||k. Then define a linear functional T such that T(fn) = n||fn||n. Then we have for any k, I can choose an fn so that |T(fn)| is greater than any ||fn||m (or even any finite linear combination thereof). Thus T is unbounded. Now use the axiom of choice to find a basis of the space which contains the fn, and define T to be 0 on the rest of the vectors. Any unbounded linear map is discontinuous.
Now, this example is the same in essence as the one at discontinuous linear functional, except that I had to get involved with families of seminorms, since the vector space in question is not a Banach space. This makes the details of the proof a little more involved, but doesn't change the idea behind it. Nevertheless, I found it quite confusing dealing with those seminorms, I wonder if you'll find it just as confusing when trying to read it as I did trying to write it. - lethe talk + 21:39, 17 March 2006 (UTC)
I do NOT know how to produce nice looking mathematical stuff on this page. Be grateful if SOMEBODY could REPLACE this and next paragraph with something equivalent. It compiles well before I pasted here. Thank you in advance. PS: Somebody has done this. Thanks from twma.
Here is an example of a discontinuous linear form on the test space D(R) on the real line R. For every compact subset K of R, D(K) is the vector space of all test functions with support contained in K. The topology of D(K) defined by the seminorms for all integers α ≥ 0 coincides with the subspace topology induced by the test space D(R) equipped with the locally convex inductive topology induced by D(K) for all compact subsets K of R.
Let ρ be a test function with ρ(0) = 1 and ρ(x) = 0 for all |x|>1. Choose 0<an+1<bn+1<an<bn ≤ 1 for all n ≥ 0, for example recursively by b0=1, an=bn/2 and bn+1=an/2. Let cn=(bn+an)/2 and rn=(bn – an)/2. For gn(x)=ρ[(x – cn)/rn], we have |gn|0 ≥ gn(cn) = 1. Then each is a test function with support contained in [an,bn] ⊆ K=[-1,1]. For each α and all n > α, we have ||fn||α ≤ 1/n → 0. Now fn → 0 in D(K) and hence also in D(R). Next because all intervals [an,bn] are disjoint, the sequence {fn} is linearly independent and hence it can be extended to an algebraic basis B of D(R). Define T(φ)=1 for all φ in B and extend T to a required linear form on D(R).
Thanks to the enthusiasm of people of this group that provides encouragement to me in sharp contrast to DingoBabyAffair. Twma 08:24, 19 March 2006 (UTC)
Let ρ be a test function with ρ(0) = 1 and ρ(x) = 0 for all |x|>1 (typo corrected). Movie: Lost in translation. Hope it should be all right now (waiting for your approval). In order to make life easier for myself, I only look at the positive side but rarely at the ugly part of the world until I HAVE TO face it NOW. I agree that based on one example, we can find many more without any difficulty but we DO need one example for a copycat. ONCE AGAIN, THANKS TO THE HELPING HANDS OF THIS GROUP. DingoBabyAffair appeared on the front page of many Australian newspapers for several years in early seventies. A baby had been severely hurt continuously but nobody wanted to help while the politicians argued whether the surrounding dingoes or the mother should be responsible. In SHARP CONTRAST, this group helps without any argument. After more than 30 years of protracted war, this baby grew up as a lost child of cold war. Now he/she is rising like a fabulous phoenix from the ash, new and fresh and young. Saving the Private Ben happened only in the movie while the politicians argued once again whether it did happen recently in reality. Perhaps I should claim copyright for another movie. Am I violating the rules and regulations of this site by comparison in my thank-you-note and by answering query about something irrelevant to Mathematics? Any way, I do not think it will drag on. Twma 00:51, 20 March 2006 (UTC)
How would one solve the equation 3^x = x^2? Is there a rule which specfies which explains the solvability of equations? -- Alexs letterbox 05:35, 17 March 2006 (UTC)
(Title was changed to actually say something useful. StuRat 16:01, 17 March 2006 (UTC))
I know this might be a simple question but can someone please explain to me what Perpendicular mean? And the angle of Depression and Elevation mean ? Thankz
I need to know the growth rate of Primorials(for factorials it is X!=O(e^(x*ln(X)) using Big O notation.) I also need to know how fast you can calculate primorials, is it polylogarithmic? For factorials it is not. Ozone 23:12, 17 March 2006 (UTC)
As for primorials,
suggests, (using some manipulations I am unable to generate here, because I can't figure out how to get the "#" symbol within a <math></math> equation)
— Arthur Rubin | (talk) 22:44, 18 March 2006 (UTC)
http://en.wikipedia.org/wiki/Exact_functor
this article defines left exact functor
Suppose 0→A→B→C is an exact sequence
I am having difficulty to see that the hom(M,-) is a left exact covariant functor. Why is it left exact? Somehow it seems to me that that means proving that if Y is a submodule of X, and alpha is a module morphism of Y to Z, it can be extended to the full X?
Thanks,
Evilbu 16:48, 18 March 2006 (UTC)
How would you solve this equation:
for P? (So that P is only on one side.)
Thanks for any help.
65.31.80.100 19:12, 18 March 2006 (UTC)
I know all about integration by parts, but is there any one integral formula that can find the integral of (a^nxn + a^(n−1)x(n−1) + ... + a2x^2 + a1x + a0) / (b^nxn + b^(n−1)x(n−1) + ... + b2x^2 + b1x + b0). This is clearly the classic definition of a polynomial divided by a polynomial. Is there an integral formula that uses similar notation to account for all possible terms? -- Chris 03:24, 19 March 2006 (UTC)
Chebyshev's theorem says that
has an elementary antiderivative if and only if one of (p+1)/r, q, or (p+1)/r + q is an integer. But I guess q is always an integer for rational functions, so this doesn't answer your question. Probably the answer is: perform synthetic division, factor the denumerator, and integrate by partial fractions. I think you can write a general formula this way. - lethe talk + 04:40, 19 March 2006 (UTC)
So like, assume you're working over the complexes, so that your polynomial can be factored. And assume that the denominator has greater degree than the numerator; you can always make it so by synthetic division. Then you're left with an integral of the form
with
so there are q distinct roots, and the ith root has multiplicity mi. You find the integral of this bad boy by partial fractions. The partial fraction method gives you a general formula for the coefficients. The article on partial fractions gives you this formula for the case that all the roots are distinct (have multiplicity 1). I don't know about the general case. Then you perform the integration. For the distinct root case, you're left with
For the general case, once you have the coefficients, the integrals are equally easy.
Note that you can't write the entire thing in one formula in terms of the coefficients of the polynomials, because by a result of Abel, there is no formula (in terms of finitely many radicals) for the roots of a polynomial. - lethe talk + 05:05, 19 March 2006 (UTC)
There's something basic I don't understand about probability. It isn't the manipulation of the numbers (which has never been a problem for me), it's why the whole thing's possible. What about a natural series of events causes them to fall, given a large sample size, so perfectly into a particular arrangement like 50/50 or 16.7/16.7/16.7/16.7/16.7/16.7? This might be a better question for the science desk, but it seems to fit here too, and most people work both. Black Carrot 22:05, 19 March 2006 (UTC)
If you accept that the chances of a combination of random (equally weighted) events occurring is 1/c, where c is the total possible combinations of events, then you could demonstrate it yourself. This is because the more tosses of a coin, say, you do, the more combinations of all tosses will end up in any given range about the predicted average, say the 0.4 - 0.6 range. However, the chances of getting exactly 0.5 will actually go down (and of course that probability is zero for an odd number of tosses).
As the number of tosses of a coin goes up, the chances of having all heads or all tails goes down. In the case of a single toss, you get either all heads or all tails (H or T) 100% of the time, while with two tosses, you get all heads or all tails (HH or TT) only 50% of the time, and with 3 tosses (HHH or TTT), only 25% of the time. The probability of getting a head/tail ratio somewhere in the middle goes up as a result, particularly as you get closer to half heads and half tails, because a larger percentage of combinations works out to be near half heads and half tails when you have more tosses. You can see this trend with Pascal's triangle (which models coin toss behavior as well as many other things), where the numbers in the center of each row continue to get larger relative to the edges of the row as you move further down the rows. StuRat 16:36, 20 March 2006 (UTC)
Total Rolls Odds ===== ======================= ==== 2 -> 1:1 1/36 3 -> 1:2,2:1 2/36 4 -> 1:3,3:1,2:2 3/36 5 -> 1:4,4:1,2:3,3:2 4/36 6 -> 1:5,5:1,2:4,4:2,3:3 5/36 7 -> 1:6,6:1,2:5,5:2,3:4,4:3 6/36 8 -> 2:6,6:2,3:5,5:3,4:4 5/36 9 -> 3:6,6:3,4:5,5:4 4/36 10 -> 4:6,6:4,5:5 3/36 11 -> 5:6,6:5 2/36 12 -> 6:6 1/36
I mean, why do the individual trials scatter so perfectly along that original curve in the first place? Or do they?
You are trying to over-interpret probabilities. Probability theory (PT) provides a mathematically rigorous logical framework to fit a rule on the occurrence of some phenomenon. It cannot and does not deal with explaining the phenomenon. Say in the case of a biased dice---on the basis of given observations---all that PT tells you is the preference of the dice towards some of the possibilites (for example, say p(1),p(3),p(4)=0.2 and p(2),p(5),p(6)=0.4/3). PT never claims to explain the reason for that bias (you can analyze the reason of that bias by going in details of the geometric shape of the dice etc., but you are not concerned with such details, when you are simpling fitting a rule over the observations). The same reasoning applies reverse: when the events scatter along the proability distribution, in no single trial, the dice is making a conscious or deterministic choice, and even if say, it is making a conscious choice---All in all, PT provided you was the aggregate characteristic or rule about how trials would turn out on an average (in expectation). This is "the" subtlity of probability theory, and many greats have erred when they tried to over-interpret probabilities. The famous debate between Bohr and Eeinstein about correctness of Quantum mechanics is, in fact, centered around this understanding. Of course, both these greats understood PT perfectly and their argument was mainly concerned about whether it is worth to go in additional details,which---at least right now---seems impossible to verify, when PT explains pretty much everything about the world that we could verify experimentally. Check out the article "Probability Theory as Logic" by late Edwin Jaynes at
[2].
--
35.9.136.15
18:49, 23 March 2006 (UTC)Keyur Desai
Black Carrot, perhaps you are also making a logic error, in thinking that if heads comes up the first time a fair coin is flipped, that makes it more likely that tails will come up the next time "to even out the probabilities". This is not the case. It's has a 50:50 probability each time it's flipped, regardless of past flips. StuRat 19:18, 23 March 2006 (UTC)
Hi all, sorry, but if I understand Black Carrot's original question, that user is asking something much more simple: why is it that when you throw a die a bunch of times, it lands on each of the 6 sides about 1/6th of the time? Am I right? If I'm wrong, sorry.
If so, the short answer is, of course, Why not? The longer answer is that we are using, as a mathematical model of the physical situation, the assumption that the die does this. This would be true for a "fair" die. This, of course, would not be true for a loaded one. One could build a die so that it was much more likely to land as a 1 than anything else. Then, of course, this 1/6 model wouldn't be a good model. The probability of landing on different sides would change because of this, and you'd have to build that into your model. Of course, mathematicians have worked this out as well: see Bernoulli trials for a start.
Let's say you're taking the line integral ( path integral) along four straight lines C1, C2, C3, and C4, where C1 is y=-2, C2 is x=2, C3 is y=2, and C4 is x=-2, so you're integrating along a closed curve C, where C is a 4x4 square centered at the origin. (The lines C1-C4 are segmented so that they only go from x=-2 to 2 and y=-2 to 2; the lines are oriented counterclockwise, therefore positive.) Then, let's say you're taking the integral of -ydx/(x^2+y^2)+ xdy/(x^2+y^2) along the curve.
Now, dP/dy equals dQ/dx, so the differential is exact, so the integral is path-independent. Because the curve is closed, this would make the integral equal to zero, because you can choose any path you want, and you could choose a path that remains at the starting point and not go anywhere. All path-independent integrals over closed curves are equal to zero, right? (Right?)
But then my textbook (this is an example from my textbook) shows how one can use Green's theorem here. Generally, one wouldn't be able to use Green's theorem because the denominator in the integral makes the integral undefined at (0,0). But one could draw a circle C', x^2 + y^2 = 1, around the hole, and the textbook shows how the line integral along C (the square) is equivalent to the line integral along C' (the circle). Evaluating this integral quickly gets the answer of 2pi.
My question is this: aren't all path-independent integrals over closed curves 0? What's different here? I'm not so concerned with the specific example - it doesn't have to be that initial curve C. When there's a hole in the region bounded by C, and C is path-independent (b/c the differential is exact), why does a discrepancy arise between a) assuming the integral is 0 because, being closed, the start point is the endpoint, and b) encircling the hole and using Green's? zafiroblue05 | Talk 19:31, 20 March 2006 (UTC)
Thank you all, that explains it perfectly. :) zafiroblue05 | Talk 22:32, 20 March 2006 (UTC)
This one should be easy for you guys. Suppose I have a set of 100 points defined by P[i] = X[i]i + Y[i]j + Z[i]k , i = 1..100 . How can I test whether these points lie in a plane or not? I can think of choosing any three points and finding the normal vector of the plane defined by them, and then taking the dot product of all P[i] - P[0] with that normal and checking if it is zero. Is this the best way of going about it, or is there something more elegant? How can I find the normal vector of the plane defined by 3 points. Sorry for asking such elementary questions, but I'm kinda retarded on this. deeptrivia ( talk) 21:19, 20 March 2006 (UTC)
Okay, there's a slight problem with this method in my case. Since these arrays X[i] etc are floating point numbers, the points can be very slightly out of plane (deviations such as 1e-10.) I want the algorithm to somehow ignore these small deviations. How do I manage that? The rank of the above matrix might come out to be 4 even if practically the points are coplanar. How do I increase the tolerance value for calculation of rank. Thanks! -- deeptrivia ( talk)
A high-math question:
a * x + b ----------- z + y * x
This reads "a * x + b over z + y * x". But what is the English name of this little line betveen the numerator and denominator? It is not "over", not "fraction line". Sign of division? Sounds funny. Can't find anything in relevant Wikis, not in Math books. In Math you can go without mentioning it, if you do some typesetting, you have to name it somehow :-)
Miklos Somogyi
Thank you, I've got a few good-sounding names. It was not more difficult than Fredholm integral equations with a double-layer Cauchy-Kolmogorov kernel of the Third Kind, after all :-) Thanks, MS
I think this is also called a Vinculum. J. LaRue 01:58, 22 March 2006 (UTC)
This one is not right. Vinculum is on top of things (plural), to show that they are in some kind of a group. MS
Yes, I may use the term "vinculum". If I want to join the Borg Collective, I even must. I suspect that mathematicians would suspect what I am talking about re vinculum but actually, do they USE the term themselves? Thanks, MS
If kernel sanders really makes real mathematically accurate chicken, shouldn't the kernel's chicken have no calories? hence be = to the 0 vector? serious responses only please- Kolin farrellovsky 18:04, 21 March 2006 (UTC)
If I travel 10km North, then 10km East and then 10km South and find myself back where I started where am I?
I prefer this version:
If you leave home, then travel 1000 km south, then travel 1000 km east, then see a bear, then travel 1000 km north, and end up back home, what color was the bear ?
StuRat 18:37, 21 March 2006 (UTC)
How is math used in a beautician job, or better yet, what kind of math do beauticians use?
Here's an interesting function:
With:
Anyone seen it before, and does it have a closed form? Fredrik Johansson 17:26, 23 March 2006 (UTC)
Choose a random integer with n decimal digits. I want to be reasonably certain that I can factor it using publically available software on a modern PC within, say, 24 hours. How large can n be? - Alecmconroy 22:32, 23 March 2006 (UTC)
The OP said "Choose a random integer...". If this is really what was meant, then factorisation is probably much easier than these worst case examples. There is a better than 6 in 7 chance that a random integer is divisible by a prime under 50. Of course, this doesn't help if the problem is really related to cryptography, for example, where key numbers are definitely not random, but are deliberately chosen to be hard to factor. Gandalf61 09:56, 24 March 2006 (UTC)
let R be a ring, M a right R module, N a left R module
a balanced product (P,f) consists of an abelian group, a map f from to P, such that f(u+v,w)=f(u,w)+f(v,w) f(u,v+w)=f(u,v)+f(u,w) f(va, w)=f(v,a w)
Is this a general definition? It is used in my course before introducing tensor products? Why can't I find balanced products anywhere else, wikipedia and the rest of the internet included? Evilbu 15:16, 24 March 2006 (UTC)
Thanks, after we define balanced product, we define morphisms between two of them (P1,f1) and (P2,f2)
it has to be a group morphism g of P1 to P2 and for all m, n in M and N
g(f1(m,n))=f2(m,n)
a tensor product is then a balanced product such that there is a unique morphism to each balanced product
Now it is supposed to be obvious (without even proving existence of one) that the elements f(m,n) if (P,f) is a tensor product, generate the abelian group P now why is that? Evilbu 17:56, 24 March 2006 (UTC)
thanks but as i understand you used universal property
what actually did you use then
as i understand, you do not think this is such a trivial question( my syllabus works that way :balanced product, then morphisms between them, then tensor product, then this exercise)
forgive me for insisting but I am quite interested
allow me to continue for a moment with my not so general terminology
if (Z,f) is a tensor product , let P be the subgroup of Z generated by the image of f ( in general, you can't say the image is a group right?)
now (P,f) will be a balanced product as well
so according to my definition of tensor product there is a unique morphisms p from Z to P such that
p(f(x,y))=f(x,y)
this is all correct right? so how exactly should I proceed now?
If 45^x = 1 (mod 56), what does x equal? Is it
?
Please, how do I go about this question? Thanks Reffies. -- Dangherous 17:58, 24 March 2006 (UTC)
i think the point is that you have to Chinese remainder theorem
45^x=1 mod 56 is equivalent with the set of equations
{45^x=1 mod 8, 45^x=1 mod 7} or {5^x=1 mod 8,3^x=1 mod 7} now you see immediately this can only happen if x is true without calculations that require computers
let G be a strongly regular graph. assume nontriviality : do not allow it to be disconnected or to have a disconnected complemenent it has k as eigenvalue once then, and two other eigenvalues
when all eigenvalues are integers
apparently the conference graphs , those are graphs of this form
, are the only ones that don't have integer eigenvalues
but how to see this , essentially there are four parameters here that are restricted by two equations
and (this holds for all strongly regular graphs)
So where does the third restriction come from, as I see only one parameter in a conference graph?
I already requested a conference graph page on wikipedia
The problem is that on the internet, google etc. think you talk about conferences ON graphs :)
Evilbu 23:37, 24 March 2006 (UTC)
Lets say a circle, with diameter D was placed on the corner of a wall. Obviously, there would be a gap between the wall and the circle. The question is what is the diameter of the largest possible circle that can fit in this gap. Using Pythagorean Theorem, I found that the length of the gap would be . However, I have to contend with the gap between this hypothetical circle and its gap between the wall. The length of this gap I called x. I wrote the diameter of the second circle as . However, I cannot solve for x. I realised that the new gap would follow the same rule (). So the new equation would be:
With that, I was hoping to bring all the x's to one side. However, this proved troublesome. Can you help. Thanks.
********************************************************** * * * + * * * + * * * + * + ** * + * + ** * + * + * * *+ * * * * * * * * + * + * + * * + * * + * * * +
IF I AM PAYING A MORTGAGE OF $225.00 PER MONTH FOR 15 YRS ,,HOW MUCH MONEY SHOULD I PUT IN THE BANK TO HAVE THE BANK PAY OUT THE PAYMENTS?ASSUMING I'M GETTING 3% INTEREST WHILE MY MONEY IS IN THE BANK,,,AT THE END OF 15 YEARS MY ACCOUNT SHOULD BE ZERO..
CAN YOU CALCULATE THIS???
THANK YOU,,,JAMES
F = $32,580 dollars
8. The family court orders you to give your former wife a payment of $500
made at the end of each year for 3 years. The interest is 6.7% per year.
You would like to buy out the obligation by paying her a lump sum
instead. How much should you pay in the lump sum?
Interest I = 0.067 per year
Term T = 3 years
Payment Y = $500
Solution:
Y * ( 1 - 1/(1+I)^T )
F = ----------------------
I
$500 ( 1 - 1/1.067^3 )
= ----------------------
0.067
$500 ( 1 - 1/1.21477 )
= ----------------------
0.067
$500 * 0.17680
= ---------------
0.067
= $1319.38
Proof:
The amount you need to pay is equivalent to an amount which you put
into an interest account which your wife can withdraw the payment
at the end of each year. The account should be empty when she made
the last payment withdraw.
Since she makes 3 withdraws, assume the amount needed at the start of
the period to pay for each withdraw are F1,F2 and F3.
Thus we have
let x = (1 + I)
F1 * x = Y
F1 = Y / x
F2 * x^2 = Y
F2 = Y / x^2
F3 * x^3 = Y
F3 = Y / x^3
Therefore the amount you need to put into the interest account at the
start of the period is
F = F1 + F2 + F3
= Y ( 1/x + 1/x^2 + 1/x^3 )
let r = (1/x)
= Y ( r + r^2 + r^3)
in general
F = Y * ( r^1 + r^2 + ... + r^T )
Y * ( r - r^(T+1) )
= -------------------
1 - r
Y * ( 1/x - 1/x^(T+1) )
= -----------------------
1 - 1/x
Y * ( 1 - 1/x^T )
= -----------------
x - 1
Y * ( 1 - 1/(1+I)^T )
= ---------------------
(1+I) - 1
Y * ( 1 - 1/(1+I)^T )
= ----------------------
I
Ohanian
09:53, 27 March 2006 (UTC)
Let's say that:
>> Lane 256 Alley 34 House 7 means approximately: >> we travel 256 units and turn right on to Lane 265; then >> we travel 34 units and turn right on to Alley 34; then >> we travel 7 units and there is the house, on the left. >> >> Telephone pole 22 L 33 R 6 means >> we travel to pole 22, follow the left fork wire 33 poles, then fork >> right for 6 poles and arrive at our goal pole. >> >> ( jidanni.org/geo/house_numbering/ ) P> What is your question? Do you want to assign house numbers? Do you P> want to build a cross references from those numbers to spatial P> location? Do you want to compute the distance from one to another? P> Do you want to uniformly store house numbers like that in a software P> data structure?
I guess I just want to find which part of graph theory deals with naming points and segments on graphs the closest.
e.g., http://en.wikipedia.org/wiki/Glossary_of_graph_theory doesn't ever mention (systematic) ways to name each segment and point... That's what I want: what's the branch of math that deals with names for points in twisty graphs... maybe they have a better way of naming the two houses on the image on jidanni.org/geo/house_numbering/mountain_en.html
I want to know if there are even smarter ways of naming such points, or how folks go about naming points on graphs.
Yes, we would use nice grid coordinates if we were in a flat city, but we have twisty hilly roads.
--Dan Jacobson, jidanni.org
prove or disprove:A and B are path connected subsets of a space X and intersection of A and B closure is non-empty.A union B is path connected.
It's damn obvious, but I can't remember how to prove that the tail of an l2 sequence goes to zero.
That is, given where , to show that . Confusing Manifestation 11:04, 27 March 2006 (UTC)
Thanks for both answers. I knew it was so obvious as to practically follow from the definition, but for some reason the actual steps eluded me. Confusing Manifestation 00:12, 28 March 2006 (UTC)
I am working on producing a spreadsheet and have hit a road block in some geometry. I am trying to upload my diagram but something isn't working right so I'll need to explain it verbally first.
I have a parallelogram, with theta in the lower left hand corner, by starting at theta and traveling clockwise I have B and then the horizontal leg A. Theta and A are my inputs. I can also even determine F, which is perpendicular to B and terminates at angle BA, but I don't really see a way that it helps me out. On lower leg A, if we go to it's far right end and draw a verticle line we get a right triangle with leg d, B, and H. I had a hunch that the quantity (A-d) relates to theta. So in AutoCAD I set A = 1 and varied theta from 0-90 in increments of 10 degrees, converted into radians and plotted the values against (A-d). Found using linear regression with a third polynomial equation, [-0.0698(theta)^3 + 0.3564(theta)^2 - 0.031(theta) + 0.44 = (A-d) ] resulted in a R^2 = 1, so someone please set me straight if I am way off target here but I assumed I since the R^2 = 1 everything was fine and I would be able to multiply the equation by left hand said of the equation by A and I would be able to get (A-d) do some geometry and have the Height pop out. (This part may get confusing and I can set up a junk hotmail account, post it, and if anyone is interested in seeing how I did this in excel email me and I'll send it to you). But I took two arbitrary values of A varied theta, got more equations by from trend lines, divided each term by A and compared the terms to the first equation and they came out reasonably the same......I thought I was good to go but when I do it in AutoCAD....it doesn't really work......don't know if I'm just spinning my wheels or if there really is a way to determine the height of a parallelogram from by given input. But doesn't there just seem a way that theta can be a direct function of (A-d)???
##### A # # ########## A# # ########## # # ########## θ##### θ##########
I do Independent Study math, so it's not graded - I make up my own assignments. Anyway, here's a problem I can't quite figure out:
Find the local max/min values and saddle points of the function:
I take the first partial derivatives and equate them to 0 (I can do that part ;):
Then I can find one set of points, (2, −4): x=2 (from ) → y=−4 (plugged into the other partial derivative)... but then I'm stuck. It's a tiny roadblock but I can't seem to figure it out -_-
Thanks. – ugen64 22:44, 27 March 2006 (UTC)
(Not sure where to ask Macroeconomics question, so I will try here.) I read in The Economist that China has >$800 billion in reserves. Why doesn't China spend this money on sorely needed infrastructure projects, rather than saving it? I.e., what marginal benefit exists for such savings? Lokiloki 02:23, 28 March 2006 (UTC)
Optimal expander graphs are known as Ramanujan Graphs. Explicit constructions for them is given in the Ramanujan Graphs by LPS. I have a doubt in the construction of them. While using PSL or PGL, how they are different from SL and GL. It has been said that PSL is quotient group with out zero transform. Can any one explain me more about how to construct them? Any full example available with any one? -- Guru 03:45, 28 March 2006 (UTC)
A giant lamington cake in the shape of a cube.How many small lamingtons have 0,1,2 or 3 sides iced if the cake was cut into 64 and 125 cubes?
A recent study indicated the total cost of the war is 1 to 2 trillion dollars depending on how long it lasts. Going with the 1 trillion figure and figuring that the US population is close to 300 milllion--how much would the cost be per person?
Looking at this from a logical perspective, it is obvious that the human and financial costs would have been lower if America had dropped an atomic bomb in 2003. It is just that the word "nuclear bomb" makes everyone shout and become emotional. These people are essentially saying that killing people a few at time is preferable to massive deaths even if the number of massive deaths can be fewer. -- Patchouli 01:15, 3 April 2006 (UTC)
Kudos to Harry Truman for saving American and ultimately Japanese lives.-- Patchouli 01:18, 3 April 2006 (UTC)
Hi,I am a new person to this website and i am getting a lot of information from you guys.
I am an IGCSE student that studies in Britain and am studying at grade 10.
I have 4 question to ask you about from the IGCSE.
First question is that you give me brief information about the sine and cosine rule. Secondly, What is factoization of expression, and also it's definition. Thirdly, The simplification of long expressions with exponents. Last question is that can you give me information about the sets.
Thank you very much for your help and i hope that it will come back to you one day.
How would I figure this out 1−1. I can't remember how to figure the answer if if the power is negative. Thank you for the help. I Lov E Plankton 16:36, 28 March 2006 (UTC)
I did a little experiment. I tested the Combination and Permutation functions.
P(n, r) = n! / (n - r)!
C(n, r) = n! / ((n - r)!r!)
Let's say that for each one I'm using 4 (n) items in set of 3 (r).
P(4, 3) = 4! / 1! = 4! = 24
C(4, 3) = 4! / (1! * 3!) = 4
Well everywhere I go, it says that the Combination returns the number of combinations of items in which the order does not matter. Well tell this to the following sets.
(1 2 3), (1 2 4), (1 3 4), (2 3 4)
Notice that it only has 4 items (n), sets of 3 items (r), 4 sets (C), and it IS ordered.
Thats not all though. They always say that Permutation returns the number of ordered pairs, but I found that I can get the same number of unordered sets with all the same variables.
(1 2 3), (1 2 4), (1 3 2), (1 3 4), (1 4 2), (1 4 3), (2 1 3), (2 1 4), (2 3 1), (2 3 4), (2 4 1), (2 4 3), (3 1 2), (3 1 4), (3 2 1), (3 2 4), (3 4 1), (3 4 2), (4 1 2), (4 1 3), (4 2 1), (4 2 3), (4 3 1), (4 3 2)
Again notice that it only has 4 items (n), sets of 3 items (r), 24 sets (C), and it IS NOT ordered.
You think it stops there? Wrong. It is the same for the functions with repetition. I'm not going to go into detail about them though. I have already talked long enough.
I was just wondering about this, and though somewhat might look into it.
Matt DeKok
Does the inequality: (x^(t))(y^(1-t))<=(t)(x)+(1-t)(x) hold? with 0<=t<=1 and x,y > 1 Also any proof? Oh and by "<=" I mean less than or equal to. Thanks Qeee1 17:24, 28 March 2006 (UTC)
Hi there,
I am looking for a good freeware software to plot graphs. I looked through the Graph-Plotting Software Page but was very unsure...does anyone of you know a good programme. I do need it for school calculus, so it should be able to do soem analysis.
Thank you -- 165.165.228.18 19:16, 28 March 2006 (UTC)
I have no experience to use any packages on computer graphic. Only Maple and Matlab are available to me paid by my University but I never try them. My simple question is how do I produce a JPG-file, say sample.jpg of the function joining (-1,0) to (0,1), from (0,1) to (1,0) and set all other values to be zero. Can I use formula such as \sin nx/(\pi x) for n=1,5,10 on the same output? I can start Maple on MacIntosh with a double click, then what? How do I draw a circle inscribed in a triangle? Do I have to study a lot from their users' manual (RTFM) before I can use Maple or Matlab? If successful, I can use TEX-graphicx to paste this file as part of a PDF-file. Thank you in advance. Twma 02:03, 29 March 2006 (UTC)
a radius of a circle is 15cm. find the length of the arc of the circl intercepted by a central angle of 3pie/4radians. (leave in terms of pie)
=degree measure of the arc
=arc leangth
there is an algebraic way, but I find this way easier. (updated by myself
schyler
00:01, 29 March 2006 (UTC))
On a disk the same radius as the observable universe what is the minimum number of digits to describe an arc the length of a ... pick something interesting. The width of a finger, a human hair, a hydrogen atom. I was just reading the Pi article and thought this might be good to add. Trieste 14:57, 29 March 2006 (UTC)
Hi guys,
is there any packet for LaTeX to draw and display functions in a LaTeX Document, such that u enter a formula and parameters and it will draw it into the document.
Thank you -- Da legend 15:54, 29 March 2006 (UTC)
I have been trying to learn "how the $11,000+" amount is calculated. I have looked up the 30 stocks and added the stock price but doesn't come close to $11,000. How is this number derived on a daily basis?
Thanks, Bill
When I was studying the problem of induction at University the lecturer wrote '1,2,3,4,5,6' on the board, and asked what number came next. The general consensus was '7'. He then wrote out a simple function that, when we worked out the next number, it turned out to be something in the hundreds. Depending on a certain variable in the function, it would give a series of successive integers followed by any number you specify. Does anyone know what this function is? Purely out of interest, no hurry. Phileas 04:40, 30 March 2006 (UTC)
I'd be more impressed if someone could write a recursive sequence whose first 6 terms were one through six and whose seventh was anything. OEIS has nothing of the like. - lethe talk + 06:03, 30 March 2006 (UTC)
In the 1952 story Back to the Klondike, Uncle Scrooge claims that he has 3 cubic acres of cash in his Money Bin. "Cubic acres" is an unusual measurement for volumes so I need to ask: How much is 3 cubic acres in cubic metres?
Also, the depth gauge in the bin shows a depth of 99 feet. Is that reasonable? Thuresson 16:27, 30 March 2006 (UTC)
How many suns would it take to fill the sky,I know the size of the sun is about 1/2degree, and the sky is basically half a sphere.But what is the formula to work it out step by step. Looking at the sky I tryed to visalize how suns it would take,the answer must be quiet large,but it is the maths that I have find hard.
It is well known that for every m-times continuously differentiable real function f on R^n, every compact subset K of R^n, and every e>0, there is a polynomial p on R^n such that for every multi-index with and every x in K, we have .
On page 155 of Topological vector spaces, distributions and kernels by F. Treves, Academic 1967, there is a proof using extension of f to a complex entire function on C^n.
Most of the standard undergraduate textbooks in numerical analysis AVAILABLE to me do not deal with this specialized topic.
Question: Is there any proof which is internal to real analysis? Any references?
Thank you in advance. Twma 07:18, 31 March 2006 (UTC)
I visited Shadrin's notes and checked out Powell's book (waiting for 4 days from our Library). It appears that we do not have any alternative proof in our archives. Thanks. Twma 07:39, 5 April 2006 (UTC)
Suppose an event e has two equally likely outcomes, x or y. Suppose e has occurred k=5 times in succession, each with outcome x. What is that probability that the 6th outcome of event e will be x? -- Simian1k 18:37, 31 March 2006 (UTC)
What is the value of the series: ? Thanks in advance, Mickey 195.93.60.7 19:30, 31 March 2006 (UTC)
In the article on the brachystochrone Snell's law is given as sin theta divided by velocity equals Cste. What is Cste ? -- 204.69.190.14 19:38, 31 March 2006 (UTC)
I have to solve the following set of differential equations numerically:
Boundary conditions:
I have three 2nd order equations, and 6 boundary conditions, so I should be able to solve this. The derivatives are with respect to s. Functions f1, f2, f3 are a bit complicated. How can I find solutions to this problem numerically to find ψ(s), θ(s) and φ(s)? I have Matlab at my disposal. Any help will be greatly appreciated. deeptrivia ( talk) 19:55, 31 March 2006 (UTC)