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MathematicalPhysicist
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do those constants have any relation to each other?
does something like pi-e or pi/e has any significance?
does something like pi-e or pi/e has any significance?
r=[oo]
[pi] = 4 * [sum] ((-1)^r) = 4 - 4 + 4 - 4 + 4
r=1 (------) - - - - ... etc.
( 2r-1 ) 3 5 7 9
And
r=[oo]
e = [sum] ( 1 ) = 1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1
r=1 (------) -- -- -- -- -- ... etc. - - -- ... etc.
((r-1)!) 0! 1! 2! 3! 4! 2 6 24
A few years back I took Complex Analysis from Dr. King, then Chairman of the Lehigh U Math Department. He spent a fair amount of time with this relationship. He preferred to write itOriginally posted by mathman
e(pi)i=-1
i forgot about this equation.Originally posted by mathman
e(pi)i=-1
the condition for the summations in both cases is the same, ie r=infinity r=1.Originally posted by lavalamp
If it's any help these are the power series for [pi] and e:
Code:r=[oo] [pi] = 4 * [sum] ((-1)^r) = 4 - 4 + 4 - 4 + 4 r=1 (------) - - - - ... etc. ( 2r-1 ) 3 5 7 9 And r=[oo] e = [sum] ( 1 ) = 1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 r=1 (------) -- -- -- -- -- ... etc. - - -- ... etc. ((r-1)!) 0! 1! 2! 3! 4! 2 6 24
[pi] can also be obtained like this:
x * Sin (180/x) where x is a very large number and 180/x is in degrees.
I've attached a script to calculate pi and e using the above power series', however I have not been able to calculate pi using the Sin method as JavaScript assumes that the angle is measured in radians and it does not have a built in Math.pi method to allow me to convert the angle from radians into degrees.
Be careful if you are calculating pi to 1,000,000 iterations, I have an Athlon 1800+ and it caused my PC to hang for a couple of seconds, although I was listening to music at the time.
If you want to view the source, generally in Windows browsers, you can go View > Source.
And I put that, what do you think this is:Originally posted by loop quantum gravity
the condition for the summations in both cases is the same, ie r=infinity r=1.
r=[oo]
e = [sum]
r=1
+---+--+
| | |
| | |
| | |
+---+--+
is there any reason why this condition applies in both of them?Originally posted by lavalamp
And I put that, what do you think this is:
It's just that if I were to make a script that would run forever you'd never get an answer so what would the point of it be?Code:r=[oo] e = [sum] r=1
Anyway I've re-posted the script if anyone's interested, it includes the (1 + (1/k))^k way to calculate e.
By the way, does anyone know the formula for finding the decimal places of [pi]? I have heard of a formula that when you put in a number (say n, for the nth decimal place), you get an answer. I assume there is one for e as well, so does anyone have that?
another way to write this (which i hope no one has yet written it) is:Originally posted by mathman
e(pi)i=-1
Originally posted by loop quantum gravity
another way to write this (which i hope no one has yet written it) is:
e^(i*pi)=-1
e^[(i*pi)/2]=-1^0.5
e^[(i*pi)/2]=i
Originally posted by loop quantum gravity
i forgot about this equation.
any significance to it?
Originally posted by lavalamp
If you would like I can post how it is possible to arrive at that solution (by that solution, I mean this - e^(i[pi])+1=0).
It uses the power series of e^x, but replaces x with i[pi], and you wind up with the power series for cos and sin, then when substituting in [pi], you get the equation mentioned above.
Originally posted by synergy
phi+phi^2 which is phi^3
Originally posted by jcsd
sin x = (eix - e-ix)/2i
cos x = (eix + e-ix)/2