Problem: A line of light emanating from a lighthouse makes one revolution every 10 seconds. The lighthouse is located 4km off a straight shoreline. How fast does the light move along the shoreline when it forms a 45 degree angle to a line from the lighthouse perpendicular to the shoreline?
It basically boils down to this equation, and we are trying to find dx/dt when θ = 45 degrees
tan(θ) = x/4km
(differentiate)
sec²(θ) dθ/dt = (1/4km) dx/dt
(plug 45 degrees in)
2 dθ/dt = 1/4km dx/dt
(isolate dx/dt)
dx/dt = 8km dθ/dt
Now is where I am confused. The resultant answer is supposed to be in km, so we can't put in 45 degrees, since that has a unit of degrees. We are supposed to put in π/5s (the radian equivalent of 1rev/10 sec) and get
8πkm/5s
because radians are "unitless," being the ratio of the arc swept over the radius. However, why radians? I could easily invent another measure that is "unitless" but would have a different numerical value. For example, I could I could use "diams" (named after diameter), that would equal the ratio of the arc over the diameter. It would effectively equal half of the radian value, so the answer given would be half of the correct answer that putting in radians would give me (and would therefore be incorrect). -- JianLi 01:21, 1 February 2006 (UTC)
Is there a good free software that can make good looking fractals, phase portraits of chaotic attractors, etc at a good resolution. The only tool I have is matlab, but using it I can't make good looking high resolution plots. Thanks! deeptrivia ( talk) 01:27, 1 February 2006 (UTC)
Based on the following equations:
File:Nlmodel.png
deeptrivia (
talk)
02:07, 7 February 2006 (UTC)
Hi,
Is there anyone can show me the method on how to proof the below number theory's problem:
For any interger n there are always n consecutive integers that all of which are not primes.
Thank you very much
EX
Many people say the Pythogoras' Theorem was not given by Phytogoras. So my question is who gave the Pythogoras' Theorem?(was it Phytogoras or someone else?) It was most defiantly Pytogoras.
I wonder if there is a reference in the literature for this operator?
And of course, is there a witty proof that lim p -> 1 is rigorously the normal differential operator? -- HappyCamper 07:09, 1 February 2006 (UTC)
After much searching, I have found the parametric equations that describe harmonographs such as the ones at Questacon and the Wollongong Science Centres in Australia. They are:
Where Ax and Ay are the amplitudes, px and py are the phase shifts, wx and wy are the period setters and d_x is the decay factor. The site I visited here says that As, ps and ws are all to do with the rotation.
Does anybody have or know of graphing software that can graph a parametric equation with a decaying function incorporated?
Also, does anybody know the fractal formed on the complex plane, which is the set of points z such that z2 is a real number?
-- Alexs letterbox 10:46, 1 February 2006 (UTC)
Eh... This looked so simple, so trivial, but it's being terrible. I created a cube on POV-Ray, <1,1,1>/2 to -<1,1,1>/2 (side = 1). Well, I want to rotate it and then use the difference command to remove everything below 0y, creating then a tetrahedron with sides = and height . Cutting is easy, but the rotation has been an issue. I made an animation to help you guys understand what I'm trying to do. Here, x = red, y = green, z = blue.
First thing, I rotate 45° on the z axis. Then, I have to find the angle of rotation on the x axis to make the three vertices lie on the xz plane. Well, I first tried 45°. It didn't work, and I figured why. Well, I then did some math and came with the angle . This almost works, but something is wrong and I can't figure what. Can't be that I need to rotate the other axis, because rotating on the y axis won't change anything. As you can see, the top vertice matches the z axis perfecly, but the other three just don't.
Worth noting, POV-Ray treats rotate <1,1,0> (two axis in one command) differently than rotate <1,0,0> and then rotate <0,1,0> (one axis per command). Not a clue why, though. Anyone can clear this out?
So, anyway, how do I do this? ☢ Ҡieff⌇ ↯ 01:38, 2 February 2006 (UTC)
In a very amateur way I have enjoyed working through books on elementary, classical number theory. I am of course aware that there is a huge field of analytic number theory, but I have no insight into this area at all (and only first year undergraduate knowledge of analysis). Is anyone aware of a textbook that might introduce me to some of the main techniques and results of analytic number theory without assuming that I am a mathematical genius or throwing me right in at the deep end? Thanks for any help you can give. Maid Marion 13:50, 2 February 2006 (UTC)
Does anyone here know where I can get the solutions to the International Mathematical Talent Search. I found the questions at http://www.math.ca/Competitions/IMTS/. I've searched a while on google, and didnt get any, so if you dont get the solutions, I might have to post the questions which I find difficult here again ;-) ! -- Rohit 17:37, 2 February 2006 (UTC)
(no questions today)
I have to draw a phase portrait of a dynamical system given by the following equation.
Since the x-axis is angle, the manifold is . I want to draw the phase portrait on the surface of a cylinder so that and 0 coincide. How can I do this in Matlab/Maple ? On the right is an example of a similar situation. deeptrivia ( talk) 02:16, 4 February 2006 (UTC)
I want to map it on the surface of the cylinder, so that 0 and 2π on the theta axis coincide, rather than being on opposite sides. This is somewhat like saying that I want to represent it as a globe (only one dimension is curved though, making it a cylinder instead of a sphere) as opposed to a map. I want to keep this cylinder transparent (probably not 100% transparent) so that things on the far side can be seen. deeptrivia ( talk) 05:31, 4 February 2006 (UTC)
I have a question on [1] Anyone please help me.
-- HydrogenSu 12:16, 4 February 2006 (UTC)
your question seems to be unclear. I think perhaps you want to ask why
equals 0. I think the explanation is supposed to go like this: a function f is odd if for all x, f(x)=f(–x). Odd functions satisfy
since the positive area on one side of the y-axis cancels out with the negative area on the other side. With some care, this result can be extended to improper integrals. For even functions, you can't cancel out the area, but you can say that the total area from –∞ to +∞ is twice the area from 0 to +∞. This is used in the subsequent step, and accounts for the 2 in front of the cosine.
The sine function is indeed an odd function, and the cosine function is indeed even. However, the integrand above is not the sine function, but rather the product of a sine and an exponential. As far as I can see, the integrand is not odd, and therefore this step of the calculation is an error. Nor is the 2 in front of the cosine correct.
This calculation seems to be proceding with a Fourier transform, which isn't really appropriate for doing a Laplace transform.
What I would suggest instead would be to start with the identity
then square it, and integrate the resulting exponentials. - lethe talk + 13:10, 4 February 2006 (UTC)
After trying it myself, I think that the above suggestion isn't so great, and you'd be better served with the identity
- lethe talk + 14:10, 4 February 2006 (UTC)
Dear all:
Does anyone know what the following combinatorial expression sums up to?
Thanks
206.172.66.136 01:59, 5 February 2006 (UTC)
—The preceding unsigned header was added by 152.163.100.11 ( talk • contribs) . probably meaning integer
Is 2.54? How to do? Thanks.-- HydrogenSu 13:17, 7 February 2006 (UTC)
It's , according to the second formula given in
Riemann_zeta_function#The_Riemann_zeta_function_as_a_Mellin_transform.--
gwaihir
21:31, 9 February 2006 (UTC)
We're at point (x1, y1, z1) looking at angle . We want to face point (x2, y2, z2). I know that to face a new angle in two dimmensions, we could rotate by the arctan((y2-y1)/(x2-x1)). But how do I do this in three dimensions? 216.158.57.50 18:07, 7 February 2006 (UTC)
can you do all my math homework for me, it's hard Maths are for kids 18:48, 8 February 2006 (UTC)
Why do Brits call it "maths" instead of "math" ? Do you also study "Englishes", "histories", and "governments" ? StuRat 20:02, 8 February 2006 (UTC)
French men (and women) say Maths, referring to "MathématiqueS"...Spanish people say "Matemáticas", so as Portuguese do. Everyone uses the plural but American. For once we agree with the "Rosbiffs", the "Ricains" nous cassent les couilles.
"I love you=ㄨㄛˇ ㄞˋ ㄋ一ˇ"
where was the first math instrument found?
The density of the primes are 1/ln(P), is there a similar result for semiprimes? Can this result be edited to only include square free numbers?
How to derive this? -- HydrogenSu 14:37, 9 February 2006 (UTC)
Typed the above by JAVA,also contribute them to other users!
According to the Wikipedia articles, the Toroid is a solid while the Torus is its surface. According to the American Heritage Dictionary,
a toroid is
a A surface generated by a closed curve rotating about, but not intersecting or containing, an axis in its own plane. b. A solid having such a surface.
and a torus is
A toroid generated by a circle; a surface having the shape of a doughnut. In this sense, also called tore2
Which definitions are right? I'm confused -- JianLi 03:10, 10 February 2006 (UTC)
Actually, I did make an effort to use only the mathematical definitions. For the full definitions, see torus and toroid and look under the definitions labeled "Mathematics" -- JianLi 21:05, 10 February 2006 (UTC) In any case, if the terms are used interchangeably (as StuRat said), or Torus is a surface while Toroid may be either (as Chan-Ho said), why do we have separate articles? Does anybody think a merge is in order? -- JianLi 21:05, 10 February 2006 (UTC)
In addition to the surface/solid confusion, note that the dictionary allows a toroid to be made by any closed curve, not just a circle. How do you reconcile that? Are dictionary definitions just unreliable for mathematics, even if it was listed as a "mathematics" definition? -- JianLi 21:08, 10 February 2006 (UTC)
<post removed> - Relegated to talk pages. See BluePlatypus and HydrogenSu. Thank you. -- HappyCamper 13:26, 10 February 2006 (UTC)
Since too many questions are being answered too quickly, I thought I'd ask if anybody has heard of the homotopy lambda-calculus talked of by Vladimir Voevodsky (2002 Fields medal) in this lecture, or can guess what it's about? Is it something to do with motivic cohomology? --- Charles Stewart (talk) 19:14, 10 February 2006 (UTC)
I went to this lecture. He didn't get to the "homotopy" part of it... it's a four lecture series. He pretty much outlined plain vanilla lambda calculus. That's it.
The Regular polygon article says the following gives the area of a regular polygon:
What does t stand for?
My friend and I deduced an alternate formula, is it correct?
Where s is the side length, n is the number of sides, and i is the angle measure of an interior angle. — Ilyan e p (Talk) 18:46, 11 February 2006 (UTC)
These will solve Topic:Infinite Sums.
That's what my high school teachers taught. I learned.-- HydrogenSu 23:01, 12 February 2006 (UTC)
Sorry,nobody told people that . For my solutions above,which was according to the asker's . And then started to derive it.
However,I don't know why you had to say that strange words. That was off topic-- HydrogenSu 13:20, 17 February 2006 (UTC)
I know that:
How do I prove that? I just figured it out by putting it into a calculator (and knowing that math club questions like this always add up to a nice round whole number) — Ilyan e p (Talk) 19:01, 11 February 2006 (UTC)
Well now this is just degrading into vandalism. Changing other people's comments is a serious breech of
Wikiquette. —
Keenan Pepper
22:37, 12 February 2006 (UTC)
-- HydrogenSu 16:48, 15 February 2006 (UTC)
We recently went over this in economics class, but our professor didn't tell us how it was calculated; I imagined it was because it was beyond the scope of the class, and it was good enough to know that it was a measure of inequality. For example, he gave us Brazil's Lorenz value as .68, and the U.S.'s as .46. How did they arrive at those values? From the looks of it, it has something to do with the area enclosed by a graph representing a country's income quintiles divided by itself and the area that would be covered by a line representing perfect equality. Please correct any of the above if it's incorect. -- Impaciente 01:41, 12 February 2006 (UTC)
How, exactly, is the covariant derivative defined? Of corse, I've read the article, but I'm still not sure what the domain and the range of the covariant derivative is. Probably I'm missing something that is really trivial.
Let M be a Riemannian manifold of dimension m and any point of the manifold. In the tangent space there are vectors u,v. I understand the covariant derivative is a map (depending on the point p) , where with being the tangent space of a point .
That's my understanding so far. If this was correct, there would be some mentioning of the point q in the article, so I guess p=q, and the connection with other points is by local charts? The Infidel 11:43, 12 February 2006 (UTC)
If My living is 24 feet long by 20 feet wide. How much carpet must I buy to cover the entire floor? (how much is that in square feet?)
Dont joke thats the easiest question or is it a trick?
Anyway if its not a trick the answer is 480 square feet
61.17.48.173
09:35, 14 February 2006 (UTC)
My son wants to know the name of a number with 98 zeroes. For example, a 6 followed by 98 zeroes.
Thanks, Dan—The preceding unsigned comment was added by 66.19.241.133 ( talk • contribs) 23:42, 13 February 2006 (UTC)
: ( — Ilyan e p (Talk) 00:34, 14 February 2006 (UTC) (carry on and ignore this)
O...K... I'll just ignore that above section Ilyanep ;) Anyway, my question relates to something I was thinking about recently. , right? Now reverse the digits of the numbers on both sides of this statement to get , a statement which is also true. This also works with and . My question is if there is a mathematical reason for this or is it just complete coincidence? -- Daverocks ( talk) 11:11, 14 February 2006 (UTC)
At the Wikipedia location "en.wikipedia.org/wiki/10:08" the claim is made that the position of the hands of a clock achieves exact symmetry at 10:09:13.8". The article also claims that "if a rectangle is drawn inside the circle touching where the hands are pointing at 10:08, this will approximate the Golden rectangle...".
Can someone show me the detailed mathematical calculations that would substantiate those claims?
Thanks. Don
Hour hand revolutions = [10 + 9/60 + 13.8/3600 ] / 12 = 0.84615277777777 revolutions
Minute hand revolutions = [ 9 + 13.8/60 ] / 60 = 0.15383333333333 revolutions
My friend is an alien who crash-landed on this boring planet. Being no scientist-alien, he needs help reprograming the hyperdrive. Unfortunately, math on his planet is in base-6, so I need to know pi for the hyper-dimensional geometery warping. Please help!!! I don't want my alien friend to materialize inside of a neutron star!
How does one calculate the curve length of a sine curve? That is, if you used a string to trace the sine curve, say, from 0 to 2π, what would the length of the string be when you stretched it out? And would there be any practical use, in physics for example, for this length function? -- JianLi 20:35, 15 February 2006 (UTC)
To estimate the area under a curve, one may use the trapezoidal method or the midpoint method. And since the trapezoidal method has twice as much error as the midpoint method (or maybe it was the other way around, I forget), to find the exact area under the curve, this method: (Trapezoidal Area) + 2(Midpoint Area) / 3 What is the name of this method?
I heard that this method only works for polynomial functions below a certain power (6, I think). Why is that? -- JianLi 20:53, 15 February 2006 (UTC)
I have to design a hole-in-one using a bank shot at several angles. I know that angle of incidence = angle of reflection, but is that true when the obstacle is at an angle besides 90 degrees to the horizontal, such as 60, 45,30, 50,etc.
Here's a simple diagram:
\ ( Angle of Reflection) \ \ / \ / (Obstacle- 45 degrees to parallel wall) \ / \ / \ / \ /
--------------------------/----------------------------------------------------(Imaginary Horizontal Parallel to Wall)
/ / (Angle of Incidence) / / / / (Start)
Thank you for your help! Please answer if possible as soon as possible?! Go Wikipedia!!!!!!! You may have to use physics, geometry,etc. For the purposes of a middle/ high school project for now I'm assuming under my teacher's directions that there isn't friction and no energy is lost. Signed, Sarepr91
-sarepr91: my teacher says that the angle between the obstacle and the wall matters and i have to state the theory behind that! please help tell me some resources!! Thanx for your answers by the way.
+---------------------------------------------------+ | | + /\ | o < > O | + \/ | | | +---------------------------------------------------+
why multiplication of two negative integers is positive?
for example -2*-2 = 4.
mani
The multiplication section of the negative number article has just been rewritten to help people understand this question, so you might want to re-read that section to see if it helps now. - R. S. Shaw 22:00, 20 February 2006 (UTC)
Hello Ref desk! I am going to do a calculus test tomorrow, and I am having trouble understanding one of the exercise questions that have been handed out to help us prepare for the test. I guess it's a bit late, but could you help me how to solve it? The problem is:
Decide the general solution to the partial differential equation
by introducing the variables s = x2 + y2, t = x2 - y2.
I guess I shouldn't have skipped so many lectures...
/ 130.238.41.167 09:08, 16 February 2006 (UTC)
I already asked this on the humanities section on a question about Hume, but I wanted to ask a mathematician if our math does indeed 'break down' seconds after the BB, during it and 'before' it. ...does it fail? break down, or just don't make sense?.and is it known what kind of math is there then? or is there no math? or is there some 'irrational' math?.-- Cosmic girl 16:48, 16 February 2006 (UTC)
thanks :) ..Kainaw told me they do break down though.-- Cosmic girl 17:49, 16 February 2006 (UTC)
cool, thanks :) ...hey, sorry to be so annoying...but is there any possibility that our MATH (meaning our inbedded human logic...since I believe we can't know if math has any meaning beyond our minds) can be different or not exist or be 'irrational' (for us) beyond or 'outside' the Big Bang? there IS a possibility , right? (a really wacky, useless and absurd possibility but a possibility still)
Oh and also! (I'm annoying I know...but I've nowhere else to ask)WHY do physics 'fail' when 'explaining infinity' or when aproaching infinity?( I read it somewhere but I don't get it)-- Cosmic girl 17:19, 17 February 2006 (UTC)
I didn't mean that math 'vanishes' when noone is thinking... I asked IF it's possible that math can be different from the math we have in the reality beyond the BB(if there is such a thing) but I know the difficulty of this question so I'll just stop asking it. =P. -- Cosmic girl 21:39, 17 February 2006 (UTC)
Ok, I see your point, but what I meant to ask was more like is 1=1, 2=2 ... (meaning 'rational') beyond our existence...It may seem obvious that it is so, even beyond the big bang, but I'm asking if I'm the only one that sees the possibility of math being irrational (meaning 3=10 or something)beyond the BB...I know it's crazy,and there's no way of knowing it but what does the philosophy of mathematics say about this?does it admit the probability? I don't understand the article very well, it's too technical.-- Cosmic girl 23:21, 17 February 2006 (UTC)
Exaclty! it wouldnt be 'math' anymore since math is rational...agree, and you rephrased me better, I meant to ask if there can be some sort of 'logic' that would be ilogic for us, or inconcievalbe. thanx...I wasn't aware that that's how I should've phrased the question...maybe at the humanities reference desk.-- Cosmic girl 19:11, 18 February 2006 (UTC)
Actually I agree with the latter...but maybe the former are right...that's the nice thing, whatever. =P-- Cosmic girl 19:11, 18 February 2006 (UTC)
How can it be consistent if it doesn't explain reality?-- Cosmic girl 18:26, 20 February 2006 (UTC)
Stupid question: when something says 2,553 (amount in millions), what does that mean? 2,553,000,000 or 2,553,000?
In the USA, it means 2,553,000,000. In other countries, including the UK, it may mean 2,553,000. Please tell us what country you are asking this question from. zappa 16:41, 22 February 2006 (UTC)
Please kindly tell me the precise interval of time between two samkrantis of various months in indian solar calendar (exactly the Vikram Sambat).What is the phylosophy behind the mathematics of Vikram sambat.
someone is going to probably ask a question about a triple integral later today-- 205.188.116.136 20:21, 17 February 2006 (UTC)
The probability that a number is prime is 1/ln(P), is there a similar result for semiprimes, what if we only allow square free numbers. Can this be extended to 3-almost, 4-almost..... Ozone 05:49, 18 February 2006 (UTC)
What is the length of a curve when the metric is not positive semidefinite? I suppose it's
but I can't find any source for this definition. The Infidel 11:45, 19 February 2006 (UTC)
Find the sum of all such that
where
I am wondering if there is a way of solving the problem above without enumerating all possible Pythagorean triples in the range, since this problem was taken out of a math competition.
Thanks.
206.172.66.43 17:34, 19 February 2006 (UTC)
15, 30, 45, 60, 75, 90 | for the (3, 4, 5) case |
65 | for the (5, 12, 13) case |
I knew I shouldn't have decided to major in a degree that requires a statistics class. I acutally have two questions.
Thanks, H e rmione 1980 18:32, 19 February 2006 (UTC)
Powerball says that the odds of matching just the last number, the Powerball, is 1 in 68.96. The article also says that the Powerball goes from the number 1 to 42. So shouldn't the chance of matching the powerball be around 1 in 42? What explains the discrepancy? zafiroblue05 | Talk 00:57, 20 February 2006 (UTC)
I want to write a program for a robot. One thing I need is something that allows my robot to move to any given location from its current location. Now, I know how to calculate the distance (difference between x and y coordinates each squared and added then the square root of that number) but I don't know how I would calculate the angle. Taking the arctan of the change in y over x won't always work because arctan (-1/1) /= arctan (1/-1). Is there any way around this?
FUNCTION Atan2 (Y, X) hpi = 1.570796326794897# pi = 2 * hpi IF ABS(Y) < ABS(X) THEN IF X > 0 THEN Atan2 = ATN(Y / X) ELSE Atan2 = ATN(Y / X) + pi END IF ELSE IF Y > 0 THEN Atan2 = ATN(-X / Y) + hpi ELSE Atan2 = ATN(-X / Y) - hpi END IF END IF END FUNCTION
In some Wikipedia articles I've seen the statement that the most "efficient" (in some unstated way) number base is e (2.718...). This raises some questions:
Thanks. - R. S. Shaw 04:30, 20 February 2006 (UTC)
Thanks for the link to the Hayes essay in American Scientist; it is very helpful wrt question 5. (The "efficiency" is an optimum of a measure of little or no practical significance.) The golden ratio base article answers 1 & 2. Q 3 has been clarified (most integers have only infinite expressions in transcendental bases). And yes, counting in base e would be horrible; the "carry" in the addition 2 + 1 would not only affect the position to the left of the units position, but also an infinite number of places to the right. - R. S. Shaw 22:22, 21 February 2006 (UTC)
Despite the heading, this isn't a question in physics since I'm actually interested in the solution of a specific (type of) set of differential equations. Suppose a projectile is moving in the x-y plane, experiencing a constant gravitational acceleration of magnitude g in the negative direction of the y axis, and air drag proportional to the square of its velocity. This gives rise to the equations:
As far as I know, these equations have no (non-trivial) elementary solution. However, does anyone know a way to represent its solution in some other way, perhaps using non-elementary functions or power series? Since this motion has a singularity point, I think there should be some sort of power series involving t, the time since the point of singularity, and , the angle to which the direction of velocity converges in the singularity. Perhaps an expansion in ? How about a way to express a solution in terms of the boundary conditions of location and velocity at a specific time? Any help in the matter would be appreciated. -- Meni Rosenfeld ( talk) 16:12, 20 February 2006 (UTC)
I don't agree that |x'| reaches 0. It does converge to 0, and the solution in the case x'=0 is indeed simple, but alas, I am looking for an exact solution, so this does not solve the problem. As I said, what I am looking for is a way to represent the exact solution in the entire region, in terms of either non-elementary functions, or an infinite series (preferrably a rapidly converging one). -- Meni Rosenfeld ( talk) 06:21, 24 February 2006 (UTC)
If you know an algorithm that can produce arbitarily many terms of the exact power series, that would be great. I doubt there is a closed form for the nth term, but I could be mistaken. What series do you have in mind? Laurent? -- Meni Rosenfeld ( talk) 08:21, 24 February 2006 (UTC)
Arthur Rubin | (talk) 18:43, 24 February 2006 (UTC) and 20:13, 24 February 2006 (UTC)
There seems to be little talk about ovals , ovoids and ovaloids on this page. Now before I can help make some pages, I would like to clear something up :
an ovaloid is a set of points, no three collinear, in PG(3,q) that is maximal with this property. Now, when one says maximal, do they mean :no set with this property and more points can be found, or do they mean : it cannpot be extended to a bigger set such that no three are collinear.
There is a subtle difference in definition there am I not right?
Thanks,
evilbu
How many minutes is one billion seconds?
I have normally distributed observations xi, with i from 1 to N, with a known mean m and standard deviation s, and I would like to compute the upper and lower values of the confidence interval at a parameter p (typically 0.05 for 95% confidence intervals.) What are the formulas for the upper and lower bounds? -- James S. 20:30, 21 February 2006 (UTC)
I found http://mathworld.wolfram.com/ConfidenceInterval.html but I don't like the integrals, and what is equation diamond? Apparently the inverse error function is required. Gnuplot has:
inverf(x) inverse error function of x
-- James S. 22:00, 21 February 2006 (UTC)
Perl5's Statistics::Distributions module has source code for
$u=Statistics::Distributions::udistr (.05); print "u-crit (95th percentile = 0.05 sig_level) = $u\n";
...from which I paraphase this...
x = -ln(4 * significance_level * (1 - significance_level)); critval = sqrt( x * ( 1.57079628800 + x * ( 0.03706987906 + x * (-0.8364353589E-03 + x * (-0.2250947176E-03 + x * ( 0.6841218299E-05 + x * ( 0.5824238515E-05 + x * (-0.1045274970E-05 + x * ( 0.8360937017E-07 + x * (-0.3231081277E-08 + x * ( 0.3657763036E-10 + x * 0.6936233982E-12))))))))))); if (significance_level > 0.5) then {critval = -critval}; ci_top = mean + (standard_deviation/sqrt(N_obs)) * critval/2; ci_bot = mean - (standard_deviation/sqrt(N_obs)) * critval/2;
Where significance_level is, e.g., 0.05 for 95% confidence.
-- James S. 07:30, 24 February 2006 (UTC)
Please see Talk:Confidence interval. -- James S. 08:07, 27 February 2006 (UTC)
Suppose we have a smooth function f(.) - is it possible to write this operator A = f(X) B f(-X) for operators B and X in terms of a bunch of commutators, like the Campbell Baker Hausdoff formulas? -- HappyCamper 05:05, 22 February 2006 (UTC)
What are the philosophical implications of this theorem?...If there are any...I'm not sure, I'm just wondering.-- Cosmic girl 19:29, 22 February 2006 (UTC)
Yes, I've read it completely! :S..but from what I understood, even if my understanding of it is consistent, I will nevcer find a proof that it is...haha (lame joke).-- Cosmic girl 21:16, 22 February 2006 (UTC)
I thought so, Hamlet...did you really know I was gonna ask this? hahaha...creepy.-- Cosmic girl 21:18, 22 February 2006 (UTC)
Why chomksy?...isn't he just a lingüist who talks about politics?...what are his thoughts on 'truth' for example, or on 'god'...I thought Chomsky was only a communist linguüist who has strong opinions when it comes to politics...but I've never encountered any original or interesting philosophical propositions of his...and also...what does karma and hindi philosophy have to do with the theorem? I don't see the conection...I thougt this theorem was about undertinty or something like that.-- Cosmic girl 19:18, 23 February 2006 (UTC)
How can it be used against ID and Theism?-- Cosmic girl 21:18, 22 February 2006 (UTC)
By the way, no one has really said much about Cosmic Girl's original question. The theorems are of great philosophical importance in the philosophy of mathematics; applications to philosophy outside phil of math are much dicier.
Even within philosophy of mathematics, while almost everyone agrees the theorems are important, precisely in what way they're important remains contested. My take on it would be something like this: They made it more difficult to give a "formalist" or "logicist" account of mathematics and why it works. Since they didn't make it any more difficult to give a Platonist/realist account, they somewhat enhanced the position of the Platonist viewpoint with respect to its competitors (though without in any way helping to explain "where" or "how" mathematical entities exist independently of our reasoning about them). -- Trovatore 22:17, 22 February 2006 (UTC)
I'm kind of lost now...what does the theorem have to say about whether mathematical entities exist independently of our reasoning about them?..does it have to say anything in the 1st place? I don't want to sound patronizing because I'm really stupid when it comes to math... but I believe that there's no possible way of knowing without a doubt, EVER, that mathematical entities exist appart from our reasoning about them.-- Cosmic girl 02:01, 23 February 2006 (UTC)
What did Gödel find so unconfortable about this that he went crazy? I'm not disturbed by this theorem, maybe I'm not getting something...haha... ( I hope I'm not punished by some power from beyond for this joke).oh and also...what does the mystery of the Aleph have to do with this?.-- Cosmic girl 20:45, 23 February 2006 (UTC)
Are you sure mathematicians have 'accepted' there are things they can never prove true or false? like what things? and can they 'prove' anything true in the first place? if so, what can they prove?.-- Cosmic girl 17:39, 24 February 2006 (UTC)
wow...I'm so lost now, so you are saying that Gödel meant that say axiom A and axiom B can't prove such and such? what I meant by the question was that IF the theorem meant that we can't know if axiom A and axiom B are 'true' in the first place...well of course they are true, because they are axioms...but I thought that the theorem meant that while axioms can appear to be automatically true to us, they may not be so. and the rest of the stuff I don't get. :| -- Cosmic girl 17:37, 24 February 2006 (UTC)
You are right, sorry for all the nonsense...=P.-- Cosmic girl 03:11, 25 February 2006 (UTC)
Thank you, your answer was the simplest one,and I will read the articles above.-- Cosmic girl 03:11, 25 February 2006 (UTC)
Hi everyone... am having trouble with a specific aspect of first-order autocorrelation.
The setup is y_t=B*y_(t-1)+u_t ; u_t=p*u_(t-1)+e_t ... y_t and u_t are covariance-stationary processes.
I'm supposed to eventually find cov(y_(t-1), u_t) and I've started off by breaking the covariance into cov(y_t/B , u_t) and cov (-u_t/B , u_t). I'm not sure this is the right approach, am becoming convinced it probably isn't. Anyways, continuing from there I've got the second covariance (with the u's) solved, but the first one, no matter how I break it down, still comes back to something in the form of cov(y_t , u_t).
Any ideas of how to get around this? Thanks very much for any thoughts. rabbit 84.92.181.246 00:44, 23 February 2006 (UTC)
is .999... repeating to infinity equal to 1?
In the quadratic equation article, it says an alternate form of the quadratic formula is:
Am I correct in saying that this would not work where c is equal to zero, e.g. in the case "x2 - 5x = 0"? That formula would return zero, but the actual answer would be 0 or 5. -- 210.246.30.87 07:35, 23 February 2006 (UTC)
if (b > 0)
then q := -0.5 * (b + sqrt(d))
else q := -0.5 * (b - sqrt(d))
r1 := q / a
r2 := c / q
copysign
function could be used instead of the test, for languages that adequately support IEEE floating point. --
KSmrq
T
18:52, 25 February 2006 (UTC)This is not a factual question, it is a request. Can anyone generate an animation of the 3-torus? I was thinking something similar to the pentatope one you can see at the right, where each frame is a 3D slice of it. ☢ Ҡi∊ff⌇ ↯ 10:20, 23 February 2006 (UTC)
Uh... The 3-Torus is a 4-D object, so an animation would be adequate. I can imagine a 4-D sphere, but a 4-D torus clogs my imagination. ☢ Ҡi∊ff⌇ ↯ 13:06, 23 February 2006 (UTC)
In general the n-Torus is just Sn-1 X Sn, where Sn is the n-dimensional sphere. (Basically, you take a (n-1)-sphere and rotate is around an axis... think of 3D case, where you rotate a circle around).
Does there exsist any non-trival subgroup of the (real) General linear group that is not a sub-group of the Orthogonal group? Further, does there exsist such a sub-group that doesn't have the Orthogonal group as a sub-group?
(Alternatively: is there a geometry which is an Affine geometry (which deals with invarients under GLn), but not a Euclidean geometry (which deals with invarients under On)? Further, is there such a geometry which does not "contain" Euclidean geometry?) Tompw 13:40, 23 February 2006 (UTC)
In doing a mock maths paper, one question asked me to estimate the sum of six four-digit numbers by a)the front-end method and b)the "cluster" method. None of us have any idea of what these terms meant, and after some google search(wikipedia search on both terms failed, returning results on topic of statistics), the results shows that the front-end method is to truncate the number to have only two most significant figures, then add them up as usual.(notice in case some number has three digits only as in my example, like 729, it takes 700, not 720). But unfortunately, I still can't find out what the "cluster" method is. Any helps would be appreciated. Thanks. -- Lemontea 15:18, 23 February 2006 (UTC)
(Transferred from
the French Reference Desk)
I know that
planck's:
mulitiplied by 1/n then do another parts of statics. Then do N*n backing to the original formulas
Same or not between these two cases?
note:for 3D
........then others
Between
.......then others in Math.....
The same or Not?
And setting somewhat numbers does not respect Planck.
The official method, is to be the 2nd I wrote before.-- HydrogenSu 23 février 2006 à 16:34 (CET)
Yes, this is a homework question. Yes, I've put some thought into it myself. I just need some help getting over the last little bit.
Here's the primal problem:
minimize
subject to ,
Ok, so first I make the Lagrangian:
and I can rearrange this so that x & s are separate:
and now I find the dual function
Now, since x is unrestricted, and the dual function can't go off unbounded below, I know that the dual problem must have the constraint which means I can reduce my dual function to
And... now I'm stuck. What, if anything, do I do with the part that's minimized over s? Is there another constraint in the dual problem, or am I stuck with this, or what? moink 02:08, 24 February 2006 (UTC)
Does anybody know of any puzzles or concepts in mathematics that are:
I work at a Science Centre, and am looking for ideas,
Thanks, -- Alexs letterbox 07:56, 24 February 2006 (UTC)
I like "guess the number of jelly beans in the jar". It touches on geometry, sampling, and probability (if asked to also estimate the number of each color). And after the contest you all get to eat the jelly beans ! StuRat 11:18, 24 February 2006 (UTC)
We might need an article on pronumeral — does it differ from variable? Gdr 16:28, 24 February 2006 (UTC)
I saw some beautiful graphical proofs of - 1. sum of cubes, 2.pythogorean theorem, etc...which they didnt teach me at school. I found it very nice and inspiring for thinking problems in a very graphical PoV. I could search it up again if u want. -- Rohit 18:07, 24 February 2006 (UTC)
Without having to relearn statistics, how large of a sample would be required to determine, with a normal degree of certainty, valid results about the distribution of topics in Wikipedia (so from a total population of 1 million)? Rmhermen 19:41, 24 February 2006 (UTC)
1100 is common number used as a minimum, as it gives about a 3% margin of error over a 90% confidence interval, meaning the results will be within 3% of the actual number 90% of the time. Hopefully a statistician here can show the calculations for this and add details. StuRat 22:45, 25 February 2006 (UTC)
Is there a way to prove that there are an infinite number of pythagorian triple families (like 3,4,5 is the family in which 6,8,10 and 9,12,15 belong)? I assume this would involve the proof that there are an infinite number of prime numbers, but you also have to prove that they are in the right proportions. — Ilyan e p (Talk) 04:18, 25 February 2006 (UTC)
It's also probably an indirect proof — Ilyan e p (Talk) 04:19, 25 February 2006 (UTC)
Does anyone have a solution to the following question that would be accessible to an average high school student? "If a rectangle is drawn inside the circle touching where the hands of a clock are pointing, at how many times will the rectangle be 'golden'?" Visit http://en.wikipedia.org/wiki/10:08 for clarification. There is an image at http://en.wikipedia.org/wiki/Talk:10:08 [Don]
Using "SohCahToa" trigonometry, I found that the central angle that intercepts the long side of the embedded golden rectangle is approximately 116.565 degrees. That makes your "x" = 116.565/360 = 0.32379. If we let n=9, the (12/11)(9+x) formula gives 10:10:17.07, one instance of "golden time" that I found earlier by a different means. However, I confess that I do not understand why your formulas work. Please explain how you derived them. Thanks! [Don]
Arthur, I appreciate your interest in my "Golden Time" inquiry. Unfortunately, I don't understand your latest explanation. If I look at 10:10:17.07 = 10.171409246, as an example, what would y/12 mod 1 and y mod 1 produce? [Don]
Arthur Rubin | (talk) 15:43, 27 February 2006 (UTC)
It was good for me to review "clock" or modular arithmetic. I now understand that mod 1 returns the decimal part of a number. In our problem, it is the fraction of a revolution from noon. Please respond to a couple more questions.
1. How does one "Solve θ(y) = x" or "x = 11/12y mod 1"? Is it appropriate to add an integer "n" to x when dropping the "mod 1" since mod 1 only returns the remainder when dividing a number by 1?
2. How did you know that n should be an integer from 0 to 10 rather than from 0 to 11? [Don}
Thanks for your help. (I have learned how to log in!) Don don 15:49, 4 March 2006 (UTC)
A variable to a constant is a parabola, a constant to a variable is exponential, but what is a variable to a variable?
Hi there, I searched for one of the numerous parabola formulas: formula, but got no hits; I also searched the parabola article. Can anyone give me the specific article for this formula? Thanks, KILO-LIMA 22:47, 25 February 2006 (UTC)
I've been interested on mechanisms to aproximate certain functions in the physical world. For example, you can draw a circle by fixing a point somewhere and rotating a fixed length thing around. An ellipse can be drawn with a string with ends fixed on the foci. Sure, easy, because they can be defined like that anyway. But, I'm looking for methods for a few particular functions, not sure if they are even possible, but it's worth asking...
Note that I'm not looking for straight geometric algorithms, like using a ruler\straightedge and compass, or careful measures (except on the case of certain, necessary proportions), but mechanical devices that actually "plot" these curves in their natural movement. Also, they must be table-top gadget things, so saying I could throw a sphere on a plane to plot x² isn't really what I want. These devices can include strings, pulleys, rods, wheels, gears, trails, etc.
Additionally, I'd like to know if there's any interesting, physical method to approximate e, something akin to Buffon's needle?
Well, that'll be all. :P ☢ Ҡi∊ff⌇ ↯ 13:25, 26 February 2006 (UTC)
For x2, would it work to choose the focus and the directrix and attach a string that is fixed to the focus and can move along the directrix, attach your pencil to the midpoint of the string, pull it taut, and trace? I guess this would work for any conic section, so it would do 1/x as well (simply adjust the eccentricity). - lethe talk + 16:18, 26 February 2006 (UTC)
There are three solutions for , x = 2, x = 4 and the other one is negative. I have absolutely no idea how to find this, and I've tried everything I know. How do we solve things like these? ☢ Ҡi∊ff⌇ ↯ 14:47, 26 February 2006 (UTC)
Goedel's incompleteness theorem only applies to first order logic, right? If so, would that mean that it might be possible to create a different form of logic that is sound, complete, etc. AND is capable of doing what Goedel's incompleteness theorem says that first order logic is incapable of (i.e. is also capable of making a complete and consistent system of math)? —The preceding unsigned comment was added by 86.138.233.25 ( talk • contribs) 15:49, 26 February 2006 .
Could someone please explain what the Nine lemma is, and why it is important? Where is this lemma used, and what is it really trying to say in the article? -- HappyCamper 15:58, 26 February 2006 (UTC)
How do I go from to ? I've been staring at problems of this sort for a couple days, and I'm at a complete loss. -- Theshibboleth 20:19, 26 February 2006 (UTC)
Hi, I am aware of the no-homweork questions, but this question is really beginning to annoy me; and I hope you won't be bothered by helping me complete it! It concerns parabolas and straight lines:
Question 9(a) and (b) I have done correctly. However I am having problems with (c). It begins:
- The is from the line. Then, becuase this is a quadratic question, it must equal zero, so: . Then change to a positive term: . This then factorises to . So so and so . Now this is where the problem occurs. Becuase we have the x-coordinate, put it back into the formula to get the y-coordinate. So using : , , and . So the coordinates are —but looking at the graph this is already there.
So, using : , , and therefore . So the coordinates for this one are —but this is clearly not correct by looking at the graph. Does anybody know where I am going wrong? I appreciate to the highest on this question. If you cannot answer, then no problems caused. Thank you very much again. KILO-LIMA 20:33, 27 February 2006 (UTC)
From what I've read, I know that the general consensus among mathematicians is that 'Cantor was right'...and they agree even more because of Quantum Mechanics (I don't know why)... I'm also aware that Cantor was religious and sort of 'prooved' the existence of God with his theory about transfinite numbers and said that God was the 'actual infinite' or 'actus purisimus' or something like that... My question is...If mathematicians accept as truth Cantor's theory, and supposedly it's 'proved' (I don't know how)...then doesn't that mean that all mathematicians are theists?...that would be the logical consecuence...but I'm sure this is not the case...so why...I mean, how do non-theist mathematicians 'escape' Cantor's reasoning?.-- Cosmic girl 02:34, 28 February 2006 (UTC)
Hi Pepper!...why is his Absolute Infinite inconsistent with his mathematical works? I guess I know why, but maybe I'm wrong, can you explain me?.-- Cosmic girl 04:27, 28 February 2006 (UTC)
Nope...I'm not :) lol.thanks for your answers to the Gödel question by the way! XD -- Cosmic girl 04:34, 28 February 2006 (UTC)
Hahaha...okok! you don't have to yell at me! I'll explain myself... first of all, by consensus among mathematicians I meant that Cantor's theory is regarded as 'true' and 'proved' now, and in his time he was criticized...and I made it clear that I didn't know how is it 'proved', since I don't know the math of it in the first place and I admit it. second...by God I mean 'actual infinity' like Cantor did,and by 'escapinc Cantor's reasoning' I mean that since he said he 'prooved the existence of an actual infinite which he equated with God'...I believe there must be detractors...what I asked was if the detractors had consistent arguments and theorems like Cantor's to 'disprove' 'actual infinity' or 'god'.
ps. take it easy KSmrq...I'm dumb.-- Cosmic girl 04:32, 28 February 2006 (UTC)
He did equate the actual infinite with God...and I believe transfinite numbers stand for numbers that are composed of an infinite ammount of numbers that are infinite as well...not something that isn't finite nor infinite...but correct me if I'm wrong.-- Cosmic girl 04:42, 28 February 2006 (UTC)
Are you sure? ok, I bet you are right...but my understanding was that the actual infinite was a 'real infinity' and transfinite numbers where infinite numbers but only potentially... :S. -- Cosmic girl 05:02, 28 February 2006 (UTC)
I see...thanx :).-- Cosmic girl 16:57, 28 February 2006 (UTC)
Hello mathematicians, I've been having fun with Euler's equation and have managed to juggle a homework equation up to the point where I'm left with
, where A is a constant. This looks to me like I should be getting y equal to something with arcsin or arccos, and need a push in the right direction. Sorry this is a homework question guys, but pretend it isn't
(Can someone put this into maths syntax if possible, ;) ): Thanks -- 131.251.0.8 10:02, 28 February 2006 (UTC)
2cos(ci+i) = cos(ci), with c constant and i the sqrt(-1). Surely there's no solution to cos(i) is there? cosine only applies to real numbers surely. -- 131.251.0.7 12:23, 28 February 2006 (UTC)
Richard Feynman once asked if there was a "natural" "square root" of the exponential function - that is, a function f defined on the reals such that
It's "obvious" that there are continuous solutions, and less obviously solutions, and I've been told there are real analytic solutions, but is there a "natural" solution?
One can find all continuous solutions by letting a be an arbitrary real strictly between 0 and 1, and f an arbitrary monotone increasing continuous function from [0,a] onto [a,1]. One can then extend f uniquely to a solution of the specified equation.
It's not too difficult to do the same with solutions -- all you need to do is for the initial f to be and the formal derivatives of f(f(x)) must match the derivatives of ex at x=0.
Also "obviously", if there is a "natural" solution g of
then we could take
Any ideas? Arthur Rubin | (talk) 16:00, 28 February 2006 (UTC)
Arthur Rubin | (talk) 02:49, 1 March 2006 (UTC)
Yes, well, silly me. Where I was trying to go with this was to look at sequences of functions, since "naturalness" often manifests itself in terms of some related sequence which has some particularly nice properties. But I'm taking a naive aproach here, clearly there's a raft of literature, which Kusma references. linas 03:07, 1 March 2006 (UTC)
Problem: A line of light emanating from a lighthouse makes one revolution every 10 seconds. The lighthouse is located 4km off a straight shoreline. How fast does the light move along the shoreline when it forms a 45 degree angle to a line from the lighthouse perpendicular to the shoreline?
It basically boils down to this equation, and we are trying to find dx/dt when θ = 45 degrees
tan(θ) = x/4km
(differentiate)
sec²(θ) dθ/dt = (1/4km) dx/dt
(plug 45 degrees in)
2 dθ/dt = 1/4km dx/dt
(isolate dx/dt)
dx/dt = 8km dθ/dt
Now is where I am confused. The resultant answer is supposed to be in km, so we can't put in 45 degrees, since that has a unit of degrees. We are supposed to put in π/5s (the radian equivalent of 1rev/10 sec) and get
8πkm/5s
because radians are "unitless," being the ratio of the arc swept over the radius. However, why radians? I could easily invent another measure that is "unitless" but would have a different numerical value. For example, I could I could use "diams" (named after diameter), that would equal the ratio of the arc over the diameter. It would effectively equal half of the radian value, so the answer given would be half of the correct answer that putting in radians would give me (and would therefore be incorrect). -- JianLi 01:21, 1 February 2006 (UTC)
Is there a good free software that can make good looking fractals, phase portraits of chaotic attractors, etc at a good resolution. The only tool I have is matlab, but using it I can't make good looking high resolution plots. Thanks! deeptrivia ( talk) 01:27, 1 February 2006 (UTC)
Based on the following equations:
File:Nlmodel.png
deeptrivia (
talk)
02:07, 7 February 2006 (UTC)
Hi,
Is there anyone can show me the method on how to proof the below number theory's problem:
For any interger n there are always n consecutive integers that all of which are not primes.
Thank you very much
EX
Many people say the Pythogoras' Theorem was not given by Phytogoras. So my question is who gave the Pythogoras' Theorem?(was it Phytogoras or someone else?) It was most defiantly Pytogoras.
I wonder if there is a reference in the literature for this operator?
And of course, is there a witty proof that lim p -> 1 is rigorously the normal differential operator? -- HappyCamper 07:09, 1 February 2006 (UTC)
After much searching, I have found the parametric equations that describe harmonographs such as the ones at Questacon and the Wollongong Science Centres in Australia. They are:
Where Ax and Ay are the amplitudes, px and py are the phase shifts, wx and wy are the period setters and d_x is the decay factor. The site I visited here says that As, ps and ws are all to do with the rotation.
Does anybody have or know of graphing software that can graph a parametric equation with a decaying function incorporated?
Also, does anybody know the fractal formed on the complex plane, which is the set of points z such that z2 is a real number?
-- Alexs letterbox 10:46, 1 February 2006 (UTC)
Eh... This looked so simple, so trivial, but it's being terrible. I created a cube on POV-Ray, <1,1,1>/2 to -<1,1,1>/2 (side = 1). Well, I want to rotate it and then use the difference command to remove everything below 0y, creating then a tetrahedron with sides = and height . Cutting is easy, but the rotation has been an issue. I made an animation to help you guys understand what I'm trying to do. Here, x = red, y = green, z = blue.
First thing, I rotate 45° on the z axis. Then, I have to find the angle of rotation on the x axis to make the three vertices lie on the xz plane. Well, I first tried 45°. It didn't work, and I figured why. Well, I then did some math and came with the angle . This almost works, but something is wrong and I can't figure what. Can't be that I need to rotate the other axis, because rotating on the y axis won't change anything. As you can see, the top vertice matches the z axis perfecly, but the other three just don't.
Worth noting, POV-Ray treats rotate <1,1,0> (two axis in one command) differently than rotate <1,0,0> and then rotate <0,1,0> (one axis per command). Not a clue why, though. Anyone can clear this out?
So, anyway, how do I do this? ☢ Ҡieff⌇ ↯ 01:38, 2 February 2006 (UTC)
In a very amateur way I have enjoyed working through books on elementary, classical number theory. I am of course aware that there is a huge field of analytic number theory, but I have no insight into this area at all (and only first year undergraduate knowledge of analysis). Is anyone aware of a textbook that might introduce me to some of the main techniques and results of analytic number theory without assuming that I am a mathematical genius or throwing me right in at the deep end? Thanks for any help you can give. Maid Marion 13:50, 2 February 2006 (UTC)
Does anyone here know where I can get the solutions to the International Mathematical Talent Search. I found the questions at http://www.math.ca/Competitions/IMTS/. I've searched a while on google, and didnt get any, so if you dont get the solutions, I might have to post the questions which I find difficult here again ;-) ! -- Rohit 17:37, 2 February 2006 (UTC)
(no questions today)
I have to draw a phase portrait of a dynamical system given by the following equation.
Since the x-axis is angle, the manifold is . I want to draw the phase portrait on the surface of a cylinder so that and 0 coincide. How can I do this in Matlab/Maple ? On the right is an example of a similar situation. deeptrivia ( talk) 02:16, 4 February 2006 (UTC)
I want to map it on the surface of the cylinder, so that 0 and 2π on the theta axis coincide, rather than being on opposite sides. This is somewhat like saying that I want to represent it as a globe (only one dimension is curved though, making it a cylinder instead of a sphere) as opposed to a map. I want to keep this cylinder transparent (probably not 100% transparent) so that things on the far side can be seen. deeptrivia ( talk) 05:31, 4 February 2006 (UTC)
I have a question on [1] Anyone please help me.
-- HydrogenSu 12:16, 4 February 2006 (UTC)
your question seems to be unclear. I think perhaps you want to ask why
equals 0. I think the explanation is supposed to go like this: a function f is odd if for all x, f(x)=f(–x). Odd functions satisfy
since the positive area on one side of the y-axis cancels out with the negative area on the other side. With some care, this result can be extended to improper integrals. For even functions, you can't cancel out the area, but you can say that the total area from –∞ to +∞ is twice the area from 0 to +∞. This is used in the subsequent step, and accounts for the 2 in front of the cosine.
The sine function is indeed an odd function, and the cosine function is indeed even. However, the integrand above is not the sine function, but rather the product of a sine and an exponential. As far as I can see, the integrand is not odd, and therefore this step of the calculation is an error. Nor is the 2 in front of the cosine correct.
This calculation seems to be proceding with a Fourier transform, which isn't really appropriate for doing a Laplace transform.
What I would suggest instead would be to start with the identity
then square it, and integrate the resulting exponentials. - lethe talk + 13:10, 4 February 2006 (UTC)
After trying it myself, I think that the above suggestion isn't so great, and you'd be better served with the identity
- lethe talk + 14:10, 4 February 2006 (UTC)
Dear all:
Does anyone know what the following combinatorial expression sums up to?
Thanks
206.172.66.136 01:59, 5 February 2006 (UTC)
—The preceding unsigned header was added by 152.163.100.11 ( talk • contribs) . probably meaning integer
Is 2.54? How to do? Thanks.-- HydrogenSu 13:17, 7 February 2006 (UTC)
It's , according to the second formula given in
Riemann_zeta_function#The_Riemann_zeta_function_as_a_Mellin_transform.--
gwaihir
21:31, 9 February 2006 (UTC)
We're at point (x1, y1, z1) looking at angle . We want to face point (x2, y2, z2). I know that to face a new angle in two dimmensions, we could rotate by the arctan((y2-y1)/(x2-x1)). But how do I do this in three dimensions? 216.158.57.50 18:07, 7 February 2006 (UTC)
can you do all my math homework for me, it's hard Maths are for kids 18:48, 8 February 2006 (UTC)
Why do Brits call it "maths" instead of "math" ? Do you also study "Englishes", "histories", and "governments" ? StuRat 20:02, 8 February 2006 (UTC)
French men (and women) say Maths, referring to "MathématiqueS"...Spanish people say "Matemáticas", so as Portuguese do. Everyone uses the plural but American. For once we agree with the "Rosbiffs", the "Ricains" nous cassent les couilles.
"I love you=ㄨㄛˇ ㄞˋ ㄋ一ˇ"
where was the first math instrument found?
The density of the primes are 1/ln(P), is there a similar result for semiprimes? Can this result be edited to only include square free numbers?
How to derive this? -- HydrogenSu 14:37, 9 February 2006 (UTC)
Typed the above by JAVA,also contribute them to other users!
According to the Wikipedia articles, the Toroid is a solid while the Torus is its surface. According to the American Heritage Dictionary,
a toroid is
a A surface generated by a closed curve rotating about, but not intersecting or containing, an axis in its own plane. b. A solid having such a surface.
and a torus is
A toroid generated by a circle; a surface having the shape of a doughnut. In this sense, also called tore2
Which definitions are right? I'm confused -- JianLi 03:10, 10 February 2006 (UTC)
Actually, I did make an effort to use only the mathematical definitions. For the full definitions, see torus and toroid and look under the definitions labeled "Mathematics" -- JianLi 21:05, 10 February 2006 (UTC) In any case, if the terms are used interchangeably (as StuRat said), or Torus is a surface while Toroid may be either (as Chan-Ho said), why do we have separate articles? Does anybody think a merge is in order? -- JianLi 21:05, 10 February 2006 (UTC)
In addition to the surface/solid confusion, note that the dictionary allows a toroid to be made by any closed curve, not just a circle. How do you reconcile that? Are dictionary definitions just unreliable for mathematics, even if it was listed as a "mathematics" definition? -- JianLi 21:08, 10 February 2006 (UTC)
<post removed> - Relegated to talk pages. See BluePlatypus and HydrogenSu. Thank you. -- HappyCamper 13:26, 10 February 2006 (UTC)
Since too many questions are being answered too quickly, I thought I'd ask if anybody has heard of the homotopy lambda-calculus talked of by Vladimir Voevodsky (2002 Fields medal) in this lecture, or can guess what it's about? Is it something to do with motivic cohomology? --- Charles Stewart (talk) 19:14, 10 February 2006 (UTC)
I went to this lecture. He didn't get to the "homotopy" part of it... it's a four lecture series. He pretty much outlined plain vanilla lambda calculus. That's it.
The Regular polygon article says the following gives the area of a regular polygon:
What does t stand for?
My friend and I deduced an alternate formula, is it correct?
Where s is the side length, n is the number of sides, and i is the angle measure of an interior angle. — Ilyan e p (Talk) 18:46, 11 February 2006 (UTC)
These will solve Topic:Infinite Sums.
That's what my high school teachers taught. I learned.-- HydrogenSu 23:01, 12 February 2006 (UTC)
Sorry,nobody told people that . For my solutions above,which was according to the asker's . And then started to derive it.
However,I don't know why you had to say that strange words. That was off topic-- HydrogenSu 13:20, 17 February 2006 (UTC)
I know that:
How do I prove that? I just figured it out by putting it into a calculator (and knowing that math club questions like this always add up to a nice round whole number) — Ilyan e p (Talk) 19:01, 11 February 2006 (UTC)
Well now this is just degrading into vandalism. Changing other people's comments is a serious breech of
Wikiquette. —
Keenan Pepper
22:37, 12 February 2006 (UTC)
-- HydrogenSu 16:48, 15 February 2006 (UTC)
We recently went over this in economics class, but our professor didn't tell us how it was calculated; I imagined it was because it was beyond the scope of the class, and it was good enough to know that it was a measure of inequality. For example, he gave us Brazil's Lorenz value as .68, and the U.S.'s as .46. How did they arrive at those values? From the looks of it, it has something to do with the area enclosed by a graph representing a country's income quintiles divided by itself and the area that would be covered by a line representing perfect equality. Please correct any of the above if it's incorect. -- Impaciente 01:41, 12 February 2006 (UTC)
How, exactly, is the covariant derivative defined? Of corse, I've read the article, but I'm still not sure what the domain and the range of the covariant derivative is. Probably I'm missing something that is really trivial.
Let M be a Riemannian manifold of dimension m and any point of the manifold. In the tangent space there are vectors u,v. I understand the covariant derivative is a map (depending on the point p) , where with being the tangent space of a point .
That's my understanding so far. If this was correct, there would be some mentioning of the point q in the article, so I guess p=q, and the connection with other points is by local charts? The Infidel 11:43, 12 February 2006 (UTC)
If My living is 24 feet long by 20 feet wide. How much carpet must I buy to cover the entire floor? (how much is that in square feet?)
Dont joke thats the easiest question or is it a trick?
Anyway if its not a trick the answer is 480 square feet
61.17.48.173
09:35, 14 February 2006 (UTC)
My son wants to know the name of a number with 98 zeroes. For example, a 6 followed by 98 zeroes.
Thanks, Dan—The preceding unsigned comment was added by 66.19.241.133 ( talk • contribs) 23:42, 13 February 2006 (UTC)
: ( — Ilyan e p (Talk) 00:34, 14 February 2006 (UTC) (carry on and ignore this)
O...K... I'll just ignore that above section Ilyanep ;) Anyway, my question relates to something I was thinking about recently. , right? Now reverse the digits of the numbers on both sides of this statement to get , a statement which is also true. This also works with and . My question is if there is a mathematical reason for this or is it just complete coincidence? -- Daverocks ( talk) 11:11, 14 February 2006 (UTC)
At the Wikipedia location "en.wikipedia.org/wiki/10:08" the claim is made that the position of the hands of a clock achieves exact symmetry at 10:09:13.8". The article also claims that "if a rectangle is drawn inside the circle touching where the hands are pointing at 10:08, this will approximate the Golden rectangle...".
Can someone show me the detailed mathematical calculations that would substantiate those claims?
Thanks. Don
Hour hand revolutions = [10 + 9/60 + 13.8/3600 ] / 12 = 0.84615277777777 revolutions
Minute hand revolutions = [ 9 + 13.8/60 ] / 60 = 0.15383333333333 revolutions
My friend is an alien who crash-landed on this boring planet. Being no scientist-alien, he needs help reprograming the hyperdrive. Unfortunately, math on his planet is in base-6, so I need to know pi for the hyper-dimensional geometery warping. Please help!!! I don't want my alien friend to materialize inside of a neutron star!
How does one calculate the curve length of a sine curve? That is, if you used a string to trace the sine curve, say, from 0 to 2π, what would the length of the string be when you stretched it out? And would there be any practical use, in physics for example, for this length function? -- JianLi 20:35, 15 February 2006 (UTC)
To estimate the area under a curve, one may use the trapezoidal method or the midpoint method. And since the trapezoidal method has twice as much error as the midpoint method (or maybe it was the other way around, I forget), to find the exact area under the curve, this method: (Trapezoidal Area) + 2(Midpoint Area) / 3 What is the name of this method?
I heard that this method only works for polynomial functions below a certain power (6, I think). Why is that? -- JianLi 20:53, 15 February 2006 (UTC)
I have to design a hole-in-one using a bank shot at several angles. I know that angle of incidence = angle of reflection, but is that true when the obstacle is at an angle besides 90 degrees to the horizontal, such as 60, 45,30, 50,etc.
Here's a simple diagram:
\ ( Angle of Reflection) \ \ / \ / (Obstacle- 45 degrees to parallel wall) \ / \ / \ / \ /
--------------------------/----------------------------------------------------(Imaginary Horizontal Parallel to Wall)
/ / (Angle of Incidence) / / / / (Start)
Thank you for your help! Please answer if possible as soon as possible?! Go Wikipedia!!!!!!! You may have to use physics, geometry,etc. For the purposes of a middle/ high school project for now I'm assuming under my teacher's directions that there isn't friction and no energy is lost. Signed, Sarepr91
-sarepr91: my teacher says that the angle between the obstacle and the wall matters and i have to state the theory behind that! please help tell me some resources!! Thanx for your answers by the way.
+---------------------------------------------------+ | | + /\ | o < > O | + \/ | | | +---------------------------------------------------+
why multiplication of two negative integers is positive?
for example -2*-2 = 4.
mani
The multiplication section of the negative number article has just been rewritten to help people understand this question, so you might want to re-read that section to see if it helps now. - R. S. Shaw 22:00, 20 February 2006 (UTC)
Hello Ref desk! I am going to do a calculus test tomorrow, and I am having trouble understanding one of the exercise questions that have been handed out to help us prepare for the test. I guess it's a bit late, but could you help me how to solve it? The problem is:
Decide the general solution to the partial differential equation
by introducing the variables s = x2 + y2, t = x2 - y2.
I guess I shouldn't have skipped so many lectures...
/ 130.238.41.167 09:08, 16 February 2006 (UTC)
I already asked this on the humanities section on a question about Hume, but I wanted to ask a mathematician if our math does indeed 'break down' seconds after the BB, during it and 'before' it. ...does it fail? break down, or just don't make sense?.and is it known what kind of math is there then? or is there no math? or is there some 'irrational' math?.-- Cosmic girl 16:48, 16 February 2006 (UTC)
thanks :) ..Kainaw told me they do break down though.-- Cosmic girl 17:49, 16 February 2006 (UTC)
cool, thanks :) ...hey, sorry to be so annoying...but is there any possibility that our MATH (meaning our inbedded human logic...since I believe we can't know if math has any meaning beyond our minds) can be different or not exist or be 'irrational' (for us) beyond or 'outside' the Big Bang? there IS a possibility , right? (a really wacky, useless and absurd possibility but a possibility still)
Oh and also! (I'm annoying I know...but I've nowhere else to ask)WHY do physics 'fail' when 'explaining infinity' or when aproaching infinity?( I read it somewhere but I don't get it)-- Cosmic girl 17:19, 17 February 2006 (UTC)
I didn't mean that math 'vanishes' when noone is thinking... I asked IF it's possible that math can be different from the math we have in the reality beyond the BB(if there is such a thing) but I know the difficulty of this question so I'll just stop asking it. =P. -- Cosmic girl 21:39, 17 February 2006 (UTC)
Ok, I see your point, but what I meant to ask was more like is 1=1, 2=2 ... (meaning 'rational') beyond our existence...It may seem obvious that it is so, even beyond the big bang, but I'm asking if I'm the only one that sees the possibility of math being irrational (meaning 3=10 or something)beyond the BB...I know it's crazy,and there's no way of knowing it but what does the philosophy of mathematics say about this?does it admit the probability? I don't understand the article very well, it's too technical.-- Cosmic girl 23:21, 17 February 2006 (UTC)
Exaclty! it wouldnt be 'math' anymore since math is rational...agree, and you rephrased me better, I meant to ask if there can be some sort of 'logic' that would be ilogic for us, or inconcievalbe. thanx...I wasn't aware that that's how I should've phrased the question...maybe at the humanities reference desk.-- Cosmic girl 19:11, 18 February 2006 (UTC)
Actually I agree with the latter...but maybe the former are right...that's the nice thing, whatever. =P-- Cosmic girl 19:11, 18 February 2006 (UTC)
How can it be consistent if it doesn't explain reality?-- Cosmic girl 18:26, 20 February 2006 (UTC)
Stupid question: when something says 2,553 (amount in millions), what does that mean? 2,553,000,000 or 2,553,000?
In the USA, it means 2,553,000,000. In other countries, including the UK, it may mean 2,553,000. Please tell us what country you are asking this question from. zappa 16:41, 22 February 2006 (UTC)
Please kindly tell me the precise interval of time between two samkrantis of various months in indian solar calendar (exactly the Vikram Sambat).What is the phylosophy behind the mathematics of Vikram sambat.
someone is going to probably ask a question about a triple integral later today-- 205.188.116.136 20:21, 17 February 2006 (UTC)
The probability that a number is prime is 1/ln(P), is there a similar result for semiprimes, what if we only allow square free numbers. Can this be extended to 3-almost, 4-almost..... Ozone 05:49, 18 February 2006 (UTC)
What is the length of a curve when the metric is not positive semidefinite? I suppose it's
but I can't find any source for this definition. The Infidel 11:45, 19 February 2006 (UTC)
Find the sum of all such that
where
I am wondering if there is a way of solving the problem above without enumerating all possible Pythagorean triples in the range, since this problem was taken out of a math competition.
Thanks.
206.172.66.43 17:34, 19 February 2006 (UTC)
15, 30, 45, 60, 75, 90 | for the (3, 4, 5) case |
65 | for the (5, 12, 13) case |
I knew I shouldn't have decided to major in a degree that requires a statistics class. I acutally have two questions.
Thanks, H e rmione 1980 18:32, 19 February 2006 (UTC)
Powerball says that the odds of matching just the last number, the Powerball, is 1 in 68.96. The article also says that the Powerball goes from the number 1 to 42. So shouldn't the chance of matching the powerball be around 1 in 42? What explains the discrepancy? zafiroblue05 | Talk 00:57, 20 February 2006 (UTC)
I want to write a program for a robot. One thing I need is something that allows my robot to move to any given location from its current location. Now, I know how to calculate the distance (difference between x and y coordinates each squared and added then the square root of that number) but I don't know how I would calculate the angle. Taking the arctan of the change in y over x won't always work because arctan (-1/1) /= arctan (1/-1). Is there any way around this?
FUNCTION Atan2 (Y, X) hpi = 1.570796326794897# pi = 2 * hpi IF ABS(Y) < ABS(X) THEN IF X > 0 THEN Atan2 = ATN(Y / X) ELSE Atan2 = ATN(Y / X) + pi END IF ELSE IF Y > 0 THEN Atan2 = ATN(-X / Y) + hpi ELSE Atan2 = ATN(-X / Y) - hpi END IF END IF END FUNCTION
In some Wikipedia articles I've seen the statement that the most "efficient" (in some unstated way) number base is e (2.718...). This raises some questions:
Thanks. - R. S. Shaw 04:30, 20 February 2006 (UTC)
Thanks for the link to the Hayes essay in American Scientist; it is very helpful wrt question 5. (The "efficiency" is an optimum of a measure of little or no practical significance.) The golden ratio base article answers 1 & 2. Q 3 has been clarified (most integers have only infinite expressions in transcendental bases). And yes, counting in base e would be horrible; the "carry" in the addition 2 + 1 would not only affect the position to the left of the units position, but also an infinite number of places to the right. - R. S. Shaw 22:22, 21 February 2006 (UTC)
Despite the heading, this isn't a question in physics since I'm actually interested in the solution of a specific (type of) set of differential equations. Suppose a projectile is moving in the x-y plane, experiencing a constant gravitational acceleration of magnitude g in the negative direction of the y axis, and air drag proportional to the square of its velocity. This gives rise to the equations:
As far as I know, these equations have no (non-trivial) elementary solution. However, does anyone know a way to represent its solution in some other way, perhaps using non-elementary functions or power series? Since this motion has a singularity point, I think there should be some sort of power series involving t, the time since the point of singularity, and , the angle to which the direction of velocity converges in the singularity. Perhaps an expansion in ? How about a way to express a solution in terms of the boundary conditions of location and velocity at a specific time? Any help in the matter would be appreciated. -- Meni Rosenfeld ( talk) 16:12, 20 February 2006 (UTC)
I don't agree that |x'| reaches 0. It does converge to 0, and the solution in the case x'=0 is indeed simple, but alas, I am looking for an exact solution, so this does not solve the problem. As I said, what I am looking for is a way to represent the exact solution in the entire region, in terms of either non-elementary functions, or an infinite series (preferrably a rapidly converging one). -- Meni Rosenfeld ( talk) 06:21, 24 February 2006 (UTC)
If you know an algorithm that can produce arbitarily many terms of the exact power series, that would be great. I doubt there is a closed form for the nth term, but I could be mistaken. What series do you have in mind? Laurent? -- Meni Rosenfeld ( talk) 08:21, 24 February 2006 (UTC)
Arthur Rubin | (talk) 18:43, 24 February 2006 (UTC) and 20:13, 24 February 2006 (UTC)
There seems to be little talk about ovals , ovoids and ovaloids on this page. Now before I can help make some pages, I would like to clear something up :
an ovaloid is a set of points, no three collinear, in PG(3,q) that is maximal with this property. Now, when one says maximal, do they mean :no set with this property and more points can be found, or do they mean : it cannpot be extended to a bigger set such that no three are collinear.
There is a subtle difference in definition there am I not right?
Thanks,
evilbu
How many minutes is one billion seconds?
I have normally distributed observations xi, with i from 1 to N, with a known mean m and standard deviation s, and I would like to compute the upper and lower values of the confidence interval at a parameter p (typically 0.05 for 95% confidence intervals.) What are the formulas for the upper and lower bounds? -- James S. 20:30, 21 February 2006 (UTC)
I found http://mathworld.wolfram.com/ConfidenceInterval.html but I don't like the integrals, and what is equation diamond? Apparently the inverse error function is required. Gnuplot has:
inverf(x) inverse error function of x
-- James S. 22:00, 21 February 2006 (UTC)
Perl5's Statistics::Distributions module has source code for
$u=Statistics::Distributions::udistr (.05); print "u-crit (95th percentile = 0.05 sig_level) = $u\n";
...from which I paraphase this...
x = -ln(4 * significance_level * (1 - significance_level)); critval = sqrt( x * ( 1.57079628800 + x * ( 0.03706987906 + x * (-0.8364353589E-03 + x * (-0.2250947176E-03 + x * ( 0.6841218299E-05 + x * ( 0.5824238515E-05 + x * (-0.1045274970E-05 + x * ( 0.8360937017E-07 + x * (-0.3231081277E-08 + x * ( 0.3657763036E-10 + x * 0.6936233982E-12))))))))))); if (significance_level > 0.5) then {critval = -critval}; ci_top = mean + (standard_deviation/sqrt(N_obs)) * critval/2; ci_bot = mean - (standard_deviation/sqrt(N_obs)) * critval/2;
Where significance_level is, e.g., 0.05 for 95% confidence.
-- James S. 07:30, 24 February 2006 (UTC)
Please see Talk:Confidence interval. -- James S. 08:07, 27 February 2006 (UTC)
Suppose we have a smooth function f(.) - is it possible to write this operator A = f(X) B f(-X) for operators B and X in terms of a bunch of commutators, like the Campbell Baker Hausdoff formulas? -- HappyCamper 05:05, 22 February 2006 (UTC)
What are the philosophical implications of this theorem?...If there are any...I'm not sure, I'm just wondering.-- Cosmic girl 19:29, 22 February 2006 (UTC)
Yes, I've read it completely! :S..but from what I understood, even if my understanding of it is consistent, I will nevcer find a proof that it is...haha (lame joke).-- Cosmic girl 21:16, 22 February 2006 (UTC)
I thought so, Hamlet...did you really know I was gonna ask this? hahaha...creepy.-- Cosmic girl 21:18, 22 February 2006 (UTC)
Why chomksy?...isn't he just a lingüist who talks about politics?...what are his thoughts on 'truth' for example, or on 'god'...I thought Chomsky was only a communist linguüist who has strong opinions when it comes to politics...but I've never encountered any original or interesting philosophical propositions of his...and also...what does karma and hindi philosophy have to do with the theorem? I don't see the conection...I thougt this theorem was about undertinty or something like that.-- Cosmic girl 19:18, 23 February 2006 (UTC)
How can it be used against ID and Theism?-- Cosmic girl 21:18, 22 February 2006 (UTC)
By the way, no one has really said much about Cosmic Girl's original question. The theorems are of great philosophical importance in the philosophy of mathematics; applications to philosophy outside phil of math are much dicier.
Even within philosophy of mathematics, while almost everyone agrees the theorems are important, precisely in what way they're important remains contested. My take on it would be something like this: They made it more difficult to give a "formalist" or "logicist" account of mathematics and why it works. Since they didn't make it any more difficult to give a Platonist/realist account, they somewhat enhanced the position of the Platonist viewpoint with respect to its competitors (though without in any way helping to explain "where" or "how" mathematical entities exist independently of our reasoning about them). -- Trovatore 22:17, 22 February 2006 (UTC)
I'm kind of lost now...what does the theorem have to say about whether mathematical entities exist independently of our reasoning about them?..does it have to say anything in the 1st place? I don't want to sound patronizing because I'm really stupid when it comes to math... but I believe that there's no possible way of knowing without a doubt, EVER, that mathematical entities exist appart from our reasoning about them.-- Cosmic girl 02:01, 23 February 2006 (UTC)
What did Gödel find so unconfortable about this that he went crazy? I'm not disturbed by this theorem, maybe I'm not getting something...haha... ( I hope I'm not punished by some power from beyond for this joke).oh and also...what does the mystery of the Aleph have to do with this?.-- Cosmic girl 20:45, 23 February 2006 (UTC)
Are you sure mathematicians have 'accepted' there are things they can never prove true or false? like what things? and can they 'prove' anything true in the first place? if so, what can they prove?.-- Cosmic girl 17:39, 24 February 2006 (UTC)
wow...I'm so lost now, so you are saying that Gödel meant that say axiom A and axiom B can't prove such and such? what I meant by the question was that IF the theorem meant that we can't know if axiom A and axiom B are 'true' in the first place...well of course they are true, because they are axioms...but I thought that the theorem meant that while axioms can appear to be automatically true to us, they may not be so. and the rest of the stuff I don't get. :| -- Cosmic girl 17:37, 24 February 2006 (UTC)
You are right, sorry for all the nonsense...=P.-- Cosmic girl 03:11, 25 February 2006 (UTC)
Thank you, your answer was the simplest one,and I will read the articles above.-- Cosmic girl 03:11, 25 February 2006 (UTC)
Hi everyone... am having trouble with a specific aspect of first-order autocorrelation.
The setup is y_t=B*y_(t-1)+u_t ; u_t=p*u_(t-1)+e_t ... y_t and u_t are covariance-stationary processes.
I'm supposed to eventually find cov(y_(t-1), u_t) and I've started off by breaking the covariance into cov(y_t/B , u_t) and cov (-u_t/B , u_t). I'm not sure this is the right approach, am becoming convinced it probably isn't. Anyways, continuing from there I've got the second covariance (with the u's) solved, but the first one, no matter how I break it down, still comes back to something in the form of cov(y_t , u_t).
Any ideas of how to get around this? Thanks very much for any thoughts. rabbit 84.92.181.246 00:44, 23 February 2006 (UTC)
is .999... repeating to infinity equal to 1?
In the quadratic equation article, it says an alternate form of the quadratic formula is:
Am I correct in saying that this would not work where c is equal to zero, e.g. in the case "x2 - 5x = 0"? That formula would return zero, but the actual answer would be 0 or 5. -- 210.246.30.87 07:35, 23 February 2006 (UTC)
if (b > 0)
then q := -0.5 * (b + sqrt(d))
else q := -0.5 * (b - sqrt(d))
r1 := q / a
r2 := c / q
copysign
function could be used instead of the test, for languages that adequately support IEEE floating point. --
KSmrq
T
18:52, 25 February 2006 (UTC)This is not a factual question, it is a request. Can anyone generate an animation of the 3-torus? I was thinking something similar to the pentatope one you can see at the right, where each frame is a 3D slice of it. ☢ Ҡi∊ff⌇ ↯ 10:20, 23 February 2006 (UTC)
Uh... The 3-Torus is a 4-D object, so an animation would be adequate. I can imagine a 4-D sphere, but a 4-D torus clogs my imagination. ☢ Ҡi∊ff⌇ ↯ 13:06, 23 February 2006 (UTC)
In general the n-Torus is just Sn-1 X Sn, where Sn is the n-dimensional sphere. (Basically, you take a (n-1)-sphere and rotate is around an axis... think of 3D case, where you rotate a circle around).
Does there exsist any non-trival subgroup of the (real) General linear group that is not a sub-group of the Orthogonal group? Further, does there exsist such a sub-group that doesn't have the Orthogonal group as a sub-group?
(Alternatively: is there a geometry which is an Affine geometry (which deals with invarients under GLn), but not a Euclidean geometry (which deals with invarients under On)? Further, is there such a geometry which does not "contain" Euclidean geometry?) Tompw 13:40, 23 February 2006 (UTC)
In doing a mock maths paper, one question asked me to estimate the sum of six four-digit numbers by a)the front-end method and b)the "cluster" method. None of us have any idea of what these terms meant, and after some google search(wikipedia search on both terms failed, returning results on topic of statistics), the results shows that the front-end method is to truncate the number to have only two most significant figures, then add them up as usual.(notice in case some number has three digits only as in my example, like 729, it takes 700, not 720). But unfortunately, I still can't find out what the "cluster" method is. Any helps would be appreciated. Thanks. -- Lemontea 15:18, 23 February 2006 (UTC)
(Transferred from
the French Reference Desk)
I know that
planck's:
mulitiplied by 1/n then do another parts of statics. Then do N*n backing to the original formulas
Same or not between these two cases?
note:for 3D
........then others
Between
.......then others in Math.....
The same or Not?
And setting somewhat numbers does not respect Planck.
The official method, is to be the 2nd I wrote before.-- HydrogenSu 23 février 2006 à 16:34 (CET)
Yes, this is a homework question. Yes, I've put some thought into it myself. I just need some help getting over the last little bit.
Here's the primal problem:
minimize
subject to ,
Ok, so first I make the Lagrangian:
and I can rearrange this so that x & s are separate:
and now I find the dual function
Now, since x is unrestricted, and the dual function can't go off unbounded below, I know that the dual problem must have the constraint which means I can reduce my dual function to
And... now I'm stuck. What, if anything, do I do with the part that's minimized over s? Is there another constraint in the dual problem, or am I stuck with this, or what? moink 02:08, 24 February 2006 (UTC)
Does anybody know of any puzzles or concepts in mathematics that are:
I work at a Science Centre, and am looking for ideas,
Thanks, -- Alexs letterbox 07:56, 24 February 2006 (UTC)
I like "guess the number of jelly beans in the jar". It touches on geometry, sampling, and probability (if asked to also estimate the number of each color). And after the contest you all get to eat the jelly beans ! StuRat 11:18, 24 February 2006 (UTC)
We might need an article on pronumeral — does it differ from variable? Gdr 16:28, 24 February 2006 (UTC)
I saw some beautiful graphical proofs of - 1. sum of cubes, 2.pythogorean theorem, etc...which they didnt teach me at school. I found it very nice and inspiring for thinking problems in a very graphical PoV. I could search it up again if u want. -- Rohit 18:07, 24 February 2006 (UTC)
Without having to relearn statistics, how large of a sample would be required to determine, with a normal degree of certainty, valid results about the distribution of topics in Wikipedia (so from a total population of 1 million)? Rmhermen 19:41, 24 February 2006 (UTC)
1100 is common number used as a minimum, as it gives about a 3% margin of error over a 90% confidence interval, meaning the results will be within 3% of the actual number 90% of the time. Hopefully a statistician here can show the calculations for this and add details. StuRat 22:45, 25 February 2006 (UTC)
Is there a way to prove that there are an infinite number of pythagorian triple families (like 3,4,5 is the family in which 6,8,10 and 9,12,15 belong)? I assume this would involve the proof that there are an infinite number of prime numbers, but you also have to prove that they are in the right proportions. — Ilyan e p (Talk) 04:18, 25 February 2006 (UTC)
It's also probably an indirect proof — Ilyan e p (Talk) 04:19, 25 February 2006 (UTC)
Does anyone have a solution to the following question that would be accessible to an average high school student? "If a rectangle is drawn inside the circle touching where the hands of a clock are pointing, at how many times will the rectangle be 'golden'?" Visit http://en.wikipedia.org/wiki/10:08 for clarification. There is an image at http://en.wikipedia.org/wiki/Talk:10:08 [Don]
Using "SohCahToa" trigonometry, I found that the central angle that intercepts the long side of the embedded golden rectangle is approximately 116.565 degrees. That makes your "x" = 116.565/360 = 0.32379. If we let n=9, the (12/11)(9+x) formula gives 10:10:17.07, one instance of "golden time" that I found earlier by a different means. However, I confess that I do not understand why your formulas work. Please explain how you derived them. Thanks! [Don]
Arthur, I appreciate your interest in my "Golden Time" inquiry. Unfortunately, I don't understand your latest explanation. If I look at 10:10:17.07 = 10.171409246, as an example, what would y/12 mod 1 and y mod 1 produce? [Don]
Arthur Rubin | (talk) 15:43, 27 February 2006 (UTC)
It was good for me to review "clock" or modular arithmetic. I now understand that mod 1 returns the decimal part of a number. In our problem, it is the fraction of a revolution from noon. Please respond to a couple more questions.
1. How does one "Solve θ(y) = x" or "x = 11/12y mod 1"? Is it appropriate to add an integer "n" to x when dropping the "mod 1" since mod 1 only returns the remainder when dividing a number by 1?
2. How did you know that n should be an integer from 0 to 10 rather than from 0 to 11? [Don}
Thanks for your help. (I have learned how to log in!) Don don 15:49, 4 March 2006 (UTC)
A variable to a constant is a parabola, a constant to a variable is exponential, but what is a variable to a variable?
Hi there, I searched for one of the numerous parabola formulas: formula, but got no hits; I also searched the parabola article. Can anyone give me the specific article for this formula? Thanks, KILO-LIMA 22:47, 25 February 2006 (UTC)
I've been interested on mechanisms to aproximate certain functions in the physical world. For example, you can draw a circle by fixing a point somewhere and rotating a fixed length thing around. An ellipse can be drawn with a string with ends fixed on the foci. Sure, easy, because they can be defined like that anyway. But, I'm looking for methods for a few particular functions, not sure if they are even possible, but it's worth asking...
Note that I'm not looking for straight geometric algorithms, like using a ruler\straightedge and compass, or careful measures (except on the case of certain, necessary proportions), but mechanical devices that actually "plot" these curves in their natural movement. Also, they must be table-top gadget things, so saying I could throw a sphere on a plane to plot x² isn't really what I want. These devices can include strings, pulleys, rods, wheels, gears, trails, etc.
Additionally, I'd like to know if there's any interesting, physical method to approximate e, something akin to Buffon's needle?
Well, that'll be all. :P ☢ Ҡi∊ff⌇ ↯ 13:25, 26 February 2006 (UTC)
For x2, would it work to choose the focus and the directrix and attach a string that is fixed to the focus and can move along the directrix, attach your pencil to the midpoint of the string, pull it taut, and trace? I guess this would work for any conic section, so it would do 1/x as well (simply adjust the eccentricity). - lethe talk + 16:18, 26 February 2006 (UTC)
There are three solutions for , x = 2, x = 4 and the other one is negative. I have absolutely no idea how to find this, and I've tried everything I know. How do we solve things like these? ☢ Ҡi∊ff⌇ ↯ 14:47, 26 February 2006 (UTC)
Goedel's incompleteness theorem only applies to first order logic, right? If so, would that mean that it might be possible to create a different form of logic that is sound, complete, etc. AND is capable of doing what Goedel's incompleteness theorem says that first order logic is incapable of (i.e. is also capable of making a complete and consistent system of math)? —The preceding unsigned comment was added by 86.138.233.25 ( talk • contribs) 15:49, 26 February 2006 .
Could someone please explain what the Nine lemma is, and why it is important? Where is this lemma used, and what is it really trying to say in the article? -- HappyCamper 15:58, 26 February 2006 (UTC)
How do I go from to ? I've been staring at problems of this sort for a couple days, and I'm at a complete loss. -- Theshibboleth 20:19, 26 February 2006 (UTC)
Hi, I am aware of the no-homweork questions, but this question is really beginning to annoy me; and I hope you won't be bothered by helping me complete it! It concerns parabolas and straight lines:
Question 9(a) and (b) I have done correctly. However I am having problems with (c). It begins:
- The is from the line. Then, becuase this is a quadratic question, it must equal zero, so: . Then change to a positive term: . This then factorises to . So so and so . Now this is where the problem occurs. Becuase we have the x-coordinate, put it back into the formula to get the y-coordinate. So using : , , and . So the coordinates are —but looking at the graph this is already there.
So, using : , , and therefore . So the coordinates for this one are —but this is clearly not correct by looking at the graph. Does anybody know where I am going wrong? I appreciate to the highest on this question. If you cannot answer, then no problems caused. Thank you very much again. KILO-LIMA 20:33, 27 February 2006 (UTC)
From what I've read, I know that the general consensus among mathematicians is that 'Cantor was right'...and they agree even more because of Quantum Mechanics (I don't know why)... I'm also aware that Cantor was religious and sort of 'prooved' the existence of God with his theory about transfinite numbers and said that God was the 'actual infinite' or 'actus purisimus' or something like that... My question is...If mathematicians accept as truth Cantor's theory, and supposedly it's 'proved' (I don't know how)...then doesn't that mean that all mathematicians are theists?...that would be the logical consecuence...but I'm sure this is not the case...so why...I mean, how do non-theist mathematicians 'escape' Cantor's reasoning?.-- Cosmic girl 02:34, 28 February 2006 (UTC)
Hi Pepper!...why is his Absolute Infinite inconsistent with his mathematical works? I guess I know why, but maybe I'm wrong, can you explain me?.-- Cosmic girl 04:27, 28 February 2006 (UTC)
Nope...I'm not :) lol.thanks for your answers to the Gödel question by the way! XD -- Cosmic girl 04:34, 28 February 2006 (UTC)
Hahaha...okok! you don't have to yell at me! I'll explain myself... first of all, by consensus among mathematicians I meant that Cantor's theory is regarded as 'true' and 'proved' now, and in his time he was criticized...and I made it clear that I didn't know how is it 'proved', since I don't know the math of it in the first place and I admit it. second...by God I mean 'actual infinity' like Cantor did,and by 'escapinc Cantor's reasoning' I mean that since he said he 'prooved the existence of an actual infinite which he equated with God'...I believe there must be detractors...what I asked was if the detractors had consistent arguments and theorems like Cantor's to 'disprove' 'actual infinity' or 'god'.
ps. take it easy KSmrq...I'm dumb.-- Cosmic girl 04:32, 28 February 2006 (UTC)
He did equate the actual infinite with God...and I believe transfinite numbers stand for numbers that are composed of an infinite ammount of numbers that are infinite as well...not something that isn't finite nor infinite...but correct me if I'm wrong.-- Cosmic girl 04:42, 28 February 2006 (UTC)
Are you sure? ok, I bet you are right...but my understanding was that the actual infinite was a 'real infinity' and transfinite numbers where infinite numbers but only potentially... :S. -- Cosmic girl 05:02, 28 February 2006 (UTC)
I see...thanx :).-- Cosmic girl 16:57, 28 February 2006 (UTC)
Hello mathematicians, I've been having fun with Euler's equation and have managed to juggle a homework equation up to the point where I'm left with
, where A is a constant. This looks to me like I should be getting y equal to something with arcsin or arccos, and need a push in the right direction. Sorry this is a homework question guys, but pretend it isn't
(Can someone put this into maths syntax if possible, ;) ): Thanks -- 131.251.0.8 10:02, 28 February 2006 (UTC)
2cos(ci+i) = cos(ci), with c constant and i the sqrt(-1). Surely there's no solution to cos(i) is there? cosine only applies to real numbers surely. -- 131.251.0.7 12:23, 28 February 2006 (UTC)
Richard Feynman once asked if there was a "natural" "square root" of the exponential function - that is, a function f defined on the reals such that
It's "obvious" that there are continuous solutions, and less obviously solutions, and I've been told there are real analytic solutions, but is there a "natural" solution?
One can find all continuous solutions by letting a be an arbitrary real strictly between 0 and 1, and f an arbitrary monotone increasing continuous function from [0,a] onto [a,1]. One can then extend f uniquely to a solution of the specified equation.
It's not too difficult to do the same with solutions -- all you need to do is for the initial f to be and the formal derivatives of f(f(x)) must match the derivatives of ex at x=0.
Also "obviously", if there is a "natural" solution g of
then we could take
Any ideas? Arthur Rubin | (talk) 16:00, 28 February 2006 (UTC)
Arthur Rubin | (talk) 02:49, 1 March 2006 (UTC)
Yes, well, silly me. Where I was trying to go with this was to look at sequences of functions, since "naturalness" often manifests itself in terms of some related sequence which has some particularly nice properties. But I'm taking a naive aproach here, clearly there's a raft of literature, which Kusma references. linas 03:07, 1 March 2006 (UTC)