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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 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!
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
(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!
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 Mince Pi)
What's your favourite use of pi in mathematics?
I particularly like the formula for the volume of a sphere!
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 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!
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 mikesgt2)
Fair play... but why does e^x = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ... + (x^n)/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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#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!
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 keithy)
ah the taylor expansion
:P
lol oh well i believe u
ah the taylor expansion
:Plol 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 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
: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
(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
: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 edders)
taylor expansion wasnt in alevel maths, for me at least
taylor expansion wasnt in alevel maths, for me at least
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#55
(Original post by keithy)
no problems, what level of maths r u at n e way???
no problems, what level of maths r u at n e way???
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#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.
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 elpaw)
oh ok its just a bit of p2 maths
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 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.
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 elpaw)
i^i = e^(i ln i)
ln i = i(2n-1)pi
i^i = e^(- (2n-1)pi)
the n causes different solutions.
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 Phil_C)
Has to be e^i(pi)=-1 The best equation around and proves there is a God
Has to be e^i(pi)=-1 The best equation around and proves there is a God
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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