a [slightly advanced] mathematical puzzle

[mehtank]

and now i'll continue by giving my thoughts so far.

i have no idea how to even begin solving that.

so how about taking it down a dimension? now, you have 4 edges of unit length, intersecting at right angles, what's the maximum area you can have, and what's the shape that gives it?

well, its obviously symmetrical, so we can look at a quarter of the resulting shape. lets center the shape at the origin, with each corner lying on an axis. then, each edge lies within one quadrant, so we'll only look at the first quadrant.

let the curve representing the edge be described [in polar coordinates] by r = f(theta). we know:
~ the length of the curve is 1
~ the slope of the curve at theta = 0, pi/2 is -1
~ we want to maximize the area under the curve

sounds like calculus of variations or something like that to me. got some fun integrals in there. a cookie to whoever can solve this problem. and if you can solve the original one, i'll be deeply in awe.

-ANkuR