Excuse Me While I Drill A Hole My Head  by eNtRopY Tags: drill,
excuse, head, hole Apr19-03, 11:36 PM P: n/a Maybe I'm a little
slow, but the true meaning of pi just occured to me.  tan(pi/4)
= 1  arctan(x) = [sum]n=0[oo] (-1)n * [ x2n+1 / (2n + 1) ]  pi =
4 * arctan(1) = 4 * [sum]n=0[oo] (-1)n * [ 1 / (2n + 1) ] = 4 *
( 2/3 + 2/35 + 2/99 + ... ) = 4 * [(1 * 2/3) + (4 * 1/70) + (8 *
1/396) + ...]  Remember the equation for the area of a circle.
A = pi * R2 = (2*R)2 * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) +
...]  Now, draw a circle with diameter D. In that circle, place
a square with area (2/3)*D2. Notice that there is still some
empty space left on the sides square (where the square and the
circle do not both exist). Place four squares with area 1/70*D2
in each of these four empty spaces. Continue to fill up the
unoccupied space of the circle with progressively smaller
squares ad infinitum.  Pi is simply an infinite series sum of
scaling factors needed for filling a circle with squares in
order to perform a