# Pi

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#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!

I have wondered how they found out that:

e = sum of zero to infinity of 1/n!

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#42

(Original post by

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!

**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!

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#43

**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!

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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#44

(Original post by

What's your favourite use of pi in mathematics?

I particularly like the formula for the volume of a sphere!

**Mince Pi**)What's your favourite use of pi in mathematics?

I particularly like the formula for the volume of a sphere!

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#45

(Original post by

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!

**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!

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#46

(Original post by

Fair play... but why does e^x = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! +... ?

**mikesgt2**)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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#47

**Mince Pi**)

What's your favourite use of pi in mathematics?

I particularly like the formula for the volume of a sphere!

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#49

(Original post by

ah the taylor expansion :P

lol oh well i believe u

**keithy**)ah the taylor expansion :P

lol oh well i believe u

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

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#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

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#51

(Original post by

: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

**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

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#52

**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

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#53

(Original post by

taylor expansion wasnt in alevel maths, for me at least

**edders**)taylor expansion wasnt in alevel maths, for me at least

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#55

(Original post by

no problems, what level of maths r u at n e way???

**keithy**)no problems, what level of maths r u at n e way???

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#56

(Original post by

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.

**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.

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#57

(Original post by

oh ok its just a bit of p2 maths

**elpaw**)oh ok its just a bit of p2 maths

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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#58

(Original post by

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.

**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.

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#59

(Original post by

i^i = e^(i ln i)

ln i = i(2n-1)pi

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

the n causes different solutions.

**elpaw**)i^i = e^(i ln i)

ln i = i(2n-1)pi

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

the n causes different solutions.

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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#60

(Original post by

Has to be e^

**Phil_C**)Has to be e^

*i*(pi)=-1 The best equation around and proves there is a GodIts 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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