How is the number Pi, derived?

[ruko]

How is the number 3.14159...etc, derived? I know it has been calculated out to very great lengths and I'm wondering how it's done.

 

[hotvette]

Link below provides some interesting history:

http://en.wikipedia.org/wiki/Pi

 

[MWIGuy]

Just find the proportion of radius to circumferance, I believe. I know it is some kind of proportion.

 

[Unit]

My personal favourite:

$$\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdot \cdots\!$$

 

[hotvette]

Modern calculation of pi no doubt use infinite series, first formulated in Newton's time (mid 1600's). Archimedes used circumscribed polygons w/ 96 sides to calculate pi with three digit accuracy.