Consider a problem here :
There is a wall in your backyard. It is so long that you can’t see its endpoints. You want to build a fence of length L such that the area enclosed between the wall and the fence is maximized. The fence can be of arbitrary shape, but only its two endpoints may touch the wall.
what is the shape of fence ? answer is semi circle . But how does one arrive at such a conclusion without using high level mathematics ?? any simple answers ??
this problem is asked on : http://www.spoj.com/problems/FENCE1/