Or I could have written: << And here's a fun fact related to Archimedes' insight about the sphere and the cylinder: If X, Y, Z are independent Gaussians of mean 0 and variance 1, |X|/(X^2+Y^2+Z^2) is uniform on [0,1].

...

Another fun result Oded told me is that if X and Y are uniform on [0,1], so is min(X,Y)/max(X,Y) (nice, not-too-hard puzzle: give a pictorial proof).

From this, it's easy to deduce that if X and Y are uniform on [0,a], for any a, then min(X,Y)/max(X,Y) is uniform on [0,1].

Oded says he came up with this as a way you can generate uniform random real numbers in [0,1] if you're writing code in a language with a built-in routine that generates random integers in some range of the form [0,a] but you forget what a is. Jim Propp