Prove that 'pi' is irrational.

The perimeter of an octagon is represented by all of the eight sides of an octagon added together. let 1/2 a side of the octagon = x. we are going to set the radious(i am forgetting my geometry) or apothom i think equal to 1. We now draw a triangle using the apothom one side and then drawn a line to the intersect fo two sides. The inner angle of this triangle will be set equal to A. therefor the tan(a)=x/1. angle a equals 1/2(360/n) where n is the number of sides. tan(180/n)=x 2(pi)r=perimiter of circle 2*x*n=perimeter of octagon 2*tan(180/n)*n=2(pi)*r r=1 in out octagon divide by 2 tan(180/n)*n=pi where the number of sides is equal to infinity ie the larger n is the closer to pi you will get.

Posted by drew on 2003-11-23 13:09:10