A math problem

Here's a fun little math problem I came up with a while back. I recently posed it to some other people and was interested to find that they solved it in completely different ways from me.

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!

Last updated 26 October 1998
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