On a 2-D coordinate system, draw a line from (n,0) to (0,1-n), for all values of n ranging from 0 to 1. You end up with a solid shape with two straight edges and one curved edge. What is the equation describing the curved edge? (The solution should be of the form y = f(x), for x ranging from 0 to 1.)Here's the solution, but please try to figure it out yourself first. It's a fun problem.
Mail me your solution if you found yet another technique!