# Pi

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18 years ago
#41
Talking about calculating numbers... elpaw may know the answer to this one

I have wondered how they found out that:

e = sum of zero to infinity of 1/n!
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18 years ago
#42
(Original post by mikesgt2)
Talking about calculating numbers... elpaw may know the answer to this one

I have wondered how they found out that:

e = sum of zero to infinity of 1/n!
chance? thats the kind of thing id calculate just out of boredom when bashing around with my calculator...
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18 years ago
#43
(Original post by mikesgt2)
Talking about calculating numbers... elpaw may know the answer to this one

I have wondered how they found out that:

e = sum of zero to infinity of 1/n!
using the taylor expansion of e^x:

e^x = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! +...

= sum 0->n->infinity (x^n)/n!

e is just e^1, so it is sum 0->n->infinity of 1/n!
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18 years ago
#44
(Original post by Mince Pi)
What's your favourite use of pi in mathematics?
I particularly like the formula for the volume of a sphere!
i hste pi and acnt understand it
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18 years ago
#45
(Original post by elpaw)
using the taylor expansion of e^x:

e^x = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! +...

= sum 0->n->infinity (x^n)/n!

e is just e^1, so it is sum 0->n->infinity of 1/n!
Fair play... but why does e^x = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! +... ?
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18 years ago
#46
(Original post by mikesgt2)
Fair play... but why does e^x = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! +... ?
because it is the taylor expansion of the e^x function.
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18 years ago
#47
(Original post by Mince Pi)
What's your favourite use of pi in mathematics?
I particularly like the formula for the volume of a sphere!
you are a geek
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18 years ago
#48
ah the taylor expansion :P

lol oh well i believe u
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18 years ago
#49
(Original post by keithy)
ah the taylor expansion :P

lol oh well i believe u
oh ok its just a bit of p2 maths

f(x) = f(0) + x f'(0) + (x^2)/2! f''(0) + ... + (x^n)/n! f^(n) (0) + ...
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18 years ago
#50
:O i got 94 in P2 and did not recognise it. taylor expansion does ring a bell but i swore it weren't from P2 i am not sure now 0
18 years ago
#51
(Original post by keithy)
:O i got 94 in P2 and did not recognise it. taylor expansion does ring a bell but i swore it weren't from P2 i am not sure now it might be p3 im not sure (or it could even be p4 p5 or p6, its all a blur to me)
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18 years ago
#52
(Original post by keithy)
:O i got 94 in P2 and did not recognise it. taylor expansion does ring a bell but i swore it weren't from P2 i am not sure now taylor expansion wasnt in alevel maths, for me at least
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18 years ago
#53
(Original post by edders)
taylor expansion wasnt in alevel maths, for me at least
Ah. its on p6, ive just checked the syllabus. sorry for confusing everyone.
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18 years ago
#54
no problems, what level of maths r u at n e way???
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18 years ago
#55
(Original post by keithy)
no problems, what level of maths r u at n e way???
I've done alevel further maths. i am at uni doing a physics degree. hence why alevel maths is all a blur to me. you should see some of the maths we are doing here.
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18 years ago
#56
(Original post by elpaw)
I've done alevel further maths. i am at uni doing a physics degree. hence why alevel maths is all a blur to me. you should see some of the maths we are doing here.
Pi is irrational
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18 years ago
#57
(Original post by elpaw)
oh ok its just a bit of p2 maths
Coming from someone studying physics at Oxford... lol

I looked on the internet to see why it is true... but I do not think you can prove it just by writing out:

f(x) = f(0) + x f'(0) + (x^2)/2! f''(0) + ... + (x^n)/n! f^(n) (0) + ...

Hardly obvious is it!

If anyone is interested look on http://www.nrich.maths.org.uk/askedN...ited/1282.html.
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18 years ago
#58
(Original post by mikesgt2)
Coming from someone studying physics at Oxford... lol

I looked on the internet to see why it is true... but I do not think you can prove it just by writing out:

f(x) = f(0) + x f'(0) + (x^2)/2! f''(0) + ... + (x^n)/n! f^(n) (0) + ...

Hardly obvious is it!

If anyone is interested look on http://www.nrich.maths.org.uk/askedN...ited/1282.html.
yes, i know its not true just written out like that, but it's been proven true in our tutorials. just right out f(x) = a + b (x) + c(x^2) + ...., differentiate it, and work out what a, b, c, etc are.
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18 years ago
#59
(Original post by elpaw)
i^i = e^(i ln i)

ln i = i(2n-1)pi

i^i = e^(- (2n-1)pi)

the n causes different solutions.
Sorry to drag this thread up but isn't this wrong?

We know that e^( i(2n-1)pi ) = -1
=> ln(-1) = i(2n-1)pi

But, ln(i) = ln(-1)/2 = i(2n-1)pi / 2

So, i^i = e^(i ln i) = e^( (1-2n)pi / 2 )
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18 years ago
#60
(Original post by Phil_C)
Has to be e^i(pi)=-1 The best equation around and proves there is a God
Errrrrrrrrrrrrrrhm

Its supposed to be:

e^(i * pi) + 1 = 0

This way yoy get all the fundamental constants of mathematics (e , i , pi, 1 and 0 ) in a single equation. If you use -1 you dont get the 0 so that is not at all equally pretty...
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