calculating pi (1 Viewer)

[stag_j]

im just wondering...i know that you can calculate e by finding the sum from 0 to infinity of 1/n!, ie 1/1+1/1+1/2+1/6+1/24....

does anyone know of a similar formula for pi?

 

[ezzy85]

measure circumference of a circle with string, measure diameter of that circle and divide circumference by diameter?

 

[Affinity]

4 * ( 1 - 1/3 + 1/5 - 1/7 + 1/9 ...) is the only one I can think of now, but it's not a very good one since it's only conditionally convergent.

 

[snow bum]

There was some way you could do it empirically, by having a circle in a box with the circle touching each side and finding the probablility of a point being in the circle as opposed to outside the circle but in the box.

 

[Affinity]

by the way,
both formulae were obtained from the taylor/maclaurin series expansion of functions.

f(x) = SUM {n=0 -> inf} [( f_n(a) * (x-a)^n ) / n! ]
where a any number.
the approximation for e used f(x) = e^x and a = 0

the approximation for Pi used f(x) = arctan(x) and a = 0

 

[Lazarus]

"Calculating Pi - Brent-Salamin Algorithm"
http://mathforum.org/library/drmath/view/58283.html

"The Uselessness of Pi and its Irrational Friends"
http://www.go2net.com/useless/useless/pi.html

 

[Archman]

hmm.. i thought e = lim(n-> infinity) (1+1/n)^n

 

[Affinity]

Archman: that's a bad way to find e numerically, converges too slowly..
that's also why the series I posted for Pi was bad.
besides that, It takes much more time on a computer to calculate multiplication -> another reason for not using lim n->inf (1+1/n)^n

 

[Archman]

fair enough