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How have developments in 20st century maths affected our living and social life?
nb: This question has been asked before, but I need some starters. Thanks, 220.244.76.78 ( talk) 00:36, 9 June 2008 (UTC)
This is an interseting question. I am sure I will miss some important items, but here is a list of some effects that I jump to mind:
How do you know when an equation has infinitely manyn solutions?How do you know when an equation has no solutions? —Preceding unsigned comment added by Lighteyes22003 ( talk • contribs) 14:02, 9 June 2008 (UTC)
FORMULATION OF ENGINEERING OPTIMIZATION PROBLEMS —Preceding unsigned comment added by 59.94.72.225 ( talk) 14:18, 9 June 2008 (UTC)
I'm intrigued by a figure called as an arc square, which reminded me of some 7th grade math questions...
I found an arc square in
http://www.mathematische-basteleien.de/arcfigures.htm
the picture is
http://www.mathematische-basteleien.de/kreis406.gif
the question is: how to calculate the green area shown? It seems a question that requires me to add and subtract a lot of shapes.
1: Suppose I merge the green area and two adjacent shapes as the red one shown below,
http://www.mathematische-basteleien.de/kreis206.gif
then let me suppose that X, X, and the green area (i.e. the same shape) form this red area.
3: Then, suppose I take a shape which equals to the area of the square minus a quarter circle. This shape should consist of Y, Y, and X.
4: Suppose the width of the square is r cm, which is also the radius of any quarter circle inscribed in it.
Is it only possible to calculate the green area when one knows X and Y? I tried multiple times and it seems the three unknowns cannot be deduced by ordinary additions and subtractions of shapes. Is it necessary to partition the square to figure it out?-- 61.92.239.42 ( talk) 15:18, 9 June 2008 (UTC)
e-infinity=0 obviously, but:
e-x=1 -x +x2/2! -x3/3! +x4/4! + etc
e-x= (1-x) + (3x2-x3)/3! + (5x4-x5)/5! etc
e-x= (1-x) + (3-x)x2)/3! + (5-x)x4)/5! etc (equation A)
if x=infinty then all the terms in equation A are negative (and infinite except at the limit).. Where did I go wrong? 87.102.86.73 ( talk) 17:10, 9 June 2008 (UTC)
In general I was trying to find a way to find the value of an infinite polynomial where the nth coefficient is (-1)n x fnn(x) where fnn(x) has similar properties to the above ie decreases evenntually (converges) for finite x. I need to work out such a sum for x=infinty any suggestions? 87.102.86.73 ( talk) 17:14, 9 June 2008 (UTC)
Thanks - that makes sense. I have another problem below - and related...
I have a power series..
the zeroth coefficient a0 is a 'number' (I want to normalise this function ie make it's integral between 0 and infinty = 1) for now a0 can be 1 or whatever is easier..
a1=ka0/2
a2=(ka1+Ma0)/2x3
in general (not a1 above)
an+2(n+2)(n+3) = kan+1+Man
ie an+2 = (kan+1+Man)/(n+2)(n+3)
so the coefficients are known. k and M are constants. I might be interested in solutions for different values of these constants .. but for now I'd just like to get to 'step1' - that is evaluating the integral.
Integrating is no problem - but I can't evaluate the integral at infinity - what to do? I guess I should try to convert this infinite polynomial into something I can integrate..
Question..How to go about this..I'd really like to do this analytically rather than approximate it numerically.. Clues or links please - I don't think I've yet learnt the tools to do this. Clearly I expect the function to converge , and coverge at infinity (radius of convergence at infinty). (It's not that important that I solve it - please don't 'bust a nut' over it if it's 'difficult' - as I don't intend to..) Thanks. 87.102.86.73 ( talk) 18:38, 9 June 2008 (UTC)
As a short answer: am I right in thinking that the antiderivative of this function; evaluated at infinity, (for finite a0, k, M ) will allways be finite?
87.102.86.73 (
talk) 18:58, 9 June 2008 (UTC)
Mathematics desk | ||
---|---|---|
< June 8 | << May | June | Jul >> | June 10 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
How have developments in 20st century maths affected our living and social life?
nb: This question has been asked before, but I need some starters. Thanks, 220.244.76.78 ( talk) 00:36, 9 June 2008 (UTC)
This is an interseting question. I am sure I will miss some important items, but here is a list of some effects that I jump to mind:
How do you know when an equation has infinitely manyn solutions?How do you know when an equation has no solutions? —Preceding unsigned comment added by Lighteyes22003 ( talk • contribs) 14:02, 9 June 2008 (UTC)
FORMULATION OF ENGINEERING OPTIMIZATION PROBLEMS —Preceding unsigned comment added by 59.94.72.225 ( talk) 14:18, 9 June 2008 (UTC)
I'm intrigued by a figure called as an arc square, which reminded me of some 7th grade math questions...
I found an arc square in
http://www.mathematische-basteleien.de/arcfigures.htm
the picture is
http://www.mathematische-basteleien.de/kreis406.gif
the question is: how to calculate the green area shown? It seems a question that requires me to add and subtract a lot of shapes.
1: Suppose I merge the green area and two adjacent shapes as the red one shown below,
http://www.mathematische-basteleien.de/kreis206.gif
then let me suppose that X, X, and the green area (i.e. the same shape) form this red area.
3: Then, suppose I take a shape which equals to the area of the square minus a quarter circle. This shape should consist of Y, Y, and X.
4: Suppose the width of the square is r cm, which is also the radius of any quarter circle inscribed in it.
Is it only possible to calculate the green area when one knows X and Y? I tried multiple times and it seems the three unknowns cannot be deduced by ordinary additions and subtractions of shapes. Is it necessary to partition the square to figure it out?-- 61.92.239.42 ( talk) 15:18, 9 June 2008 (UTC)
e-infinity=0 obviously, but:
e-x=1 -x +x2/2! -x3/3! +x4/4! + etc
e-x= (1-x) + (3x2-x3)/3! + (5x4-x5)/5! etc
e-x= (1-x) + (3-x)x2)/3! + (5-x)x4)/5! etc (equation A)
if x=infinty then all the terms in equation A are negative (and infinite except at the limit).. Where did I go wrong? 87.102.86.73 ( talk) 17:10, 9 June 2008 (UTC)
In general I was trying to find a way to find the value of an infinite polynomial where the nth coefficient is (-1)n x fnn(x) where fnn(x) has similar properties to the above ie decreases evenntually (converges) for finite x. I need to work out such a sum for x=infinty any suggestions? 87.102.86.73 ( talk) 17:14, 9 June 2008 (UTC)
Thanks - that makes sense. I have another problem below - and related...
I have a power series..
the zeroth coefficient a0 is a 'number' (I want to normalise this function ie make it's integral between 0 and infinty = 1) for now a0 can be 1 or whatever is easier..
a1=ka0/2
a2=(ka1+Ma0)/2x3
in general (not a1 above)
an+2(n+2)(n+3) = kan+1+Man
ie an+2 = (kan+1+Man)/(n+2)(n+3)
so the coefficients are known. k and M are constants. I might be interested in solutions for different values of these constants .. but for now I'd just like to get to 'step1' - that is evaluating the integral.
Integrating is no problem - but I can't evaluate the integral at infinity - what to do? I guess I should try to convert this infinite polynomial into something I can integrate..
Question..How to go about this..I'd really like to do this analytically rather than approximate it numerically.. Clues or links please - I don't think I've yet learnt the tools to do this. Clearly I expect the function to converge , and coverge at infinity (radius of convergence at infinty). (It's not that important that I solve it - please don't 'bust a nut' over it if it's 'difficult' - as I don't intend to..) Thanks. 87.102.86.73 ( talk) 18:38, 9 June 2008 (UTC)
As a short answer: am I right in thinking that the antiderivative of this function; evaluated at infinity, (for finite a0, k, M ) will allways be finite?
87.102.86.73 (
talk) 18:58, 9 June 2008 (UTC)