Estimating Pi ~ How Fun! (1 Viewer)

[hyparzero]

I found for the following condition:
Q = [ bSin(360/b) ] / 2

that Q approaches the value of Pi as b -> ∞

Probably everyone already knows it, but cool nonetheless.

 

[hyparzero]

this is clearly a ext2 topic, so enlighten me of why it was moved

 

[SeDaTeD]

That would only work if you are using degrees, which you shouldn't. You can replace 360 with 2pi, but then you'd be using the value you are trying to estimate.

Actually... for any constant k

[ bSin(k/b) ] / 2 = (k/2)[Sin(k/b)]/(k/b) = (k/2)[Sin(a)]/a, where a = k/b
as b -> inf, a -> 0, so the above just goes to k/2 (using the fact that sinx/x ->1 as x-> 0). So you function was just one particular case of k.

 

[hyparzero]

That would only work if you are using degrees, which you shouldn't. You can replace 360 with 2pi, but then you'd be using the value you are trying to estimate.

Actually... for any constant k

[ bSin(k/b) ] / 2 = (k/2)[Sin(k/b)]/(k/b) = (k/2)[Sin(a)]/a, where a = k/b
as b -> inf, a -> 0, so the above just goes to k/2 (using the fact that sinx/x ->1 as x-> 0). So you function was just one particular case of k.

boo, you've just ruined the fun for everyone else

oh, and since you mentioned it, for the following

1 / [((6541681608)/(640320)^3/2)∑{n= 0 -> ∞}(13591409/77877162 + n)[((6n)!(-1)ⁿ)/(3n!)(n!)³640320³ⁿ]]

will also give an approximation of Pi

goodluck

 

[Flugzeug]

Why estimate when it is done for you.

http://3.141592653589793238462643383279502884197169399375105820974944592.com/index1.html

This is a real site too.
http://3.141592653589793238462643383279502884197169399375105820974944592.com/index1.html

 

[pLuvia]

Because you are using your mathematical ability?

 

[acmilan]

boo, you've just ruined the fun for everyone else

oh, and since you mentioned it, for the following

1 / [((6541681608)/(640320)^3/2)∑{n= 0 -> ∞}(13591409/77877162 + n)[((6n)!(-1)ⁿ)/(3n!)(n!)³640320³ⁿ]]

will also give an approximation of Pi

goodluck

Theres a large amount of series that give you the exact value of pi which look a lot simpler than that

 

[hyparzero]

Theres a large amount of series that give you the exact value of pi which look a lot simpler than that

how do you get an 'exact' value of pi? isnt pi transcendental

 

[SeDaTeD]

sum from n=1 to infinity of 1/n^2 gives pi^2/6 comes to mind.
A limit of a series (well of partial sums to be precise) can still be equal to a transcendental number.

 

[shimmerz_777]

i figured out that the cubed root of 31 is closer than 22/7, but its still irrational

 

[haque]

u can simply use the power seiries for tan inverse x and substitute values for x to get approximations for pi-i mean that would be simpler than for example 1/1^2 +1/2^2 and so on for pi squared on six wouldn't it?(well it'd be easier for me because i don't know fourier analysis!)

 

[Affinity]

this is clearly a ext2 topic, so enlighten me of why it was moved

Actually no.. it's 2unit.. somewhere one's taught the equality lim x-> 0 of sin(x)/x = 1

and so it follows that lim x-> infinity of sin(1/x) / (1/x) = 1 etc. etc.


hmm in practice you can't use this to estimate pi.... reminds me of a project I undertook when I was a kid.. calculate pi! what I tried to do involved taking tangents of angles (which I had to look up in the tables) come to think about it now.. it defeats the purpose since the tables themselves were constructed with knowledge of what pi is.

 

[Affinity]

u can simply use the power seiries for tan inverse x and substitute values for x to get approximations for pi-i mean that would be simpler than for example 1/1^2 +1/2^2 and so on for pi squared on six wouldn't it?(well it'd be easier for me because i don't know fourier analysis!)

Since when did someone used techniques in fourier analysis?

the series for inverse tan isn't that good for the purpose.. the series alternates and the convergence is slow.

 

[Forbidden.]

22/7