8 Jul
2014
8 Jul
'14
12:08 p.m.
On Sat, 5 Jul 2014, Cris Moore wrote:
Consider also the following lovely fact: choose a point on the unit sphere uniformly at random. It's z-coordinate is uniformly distributed in the interval [-1,+1]!
To put it differently, you can generate a random point (x,y,z) like this:
choose z uniformly in [-1,+1] choose theta uniformly in [0,2pi] set x = sqrt(1-z^2) cos theta, y = sqrt(1-z^2) sin theta
This is only true for the 3-dimensional sphere, of course!
Oddly, I had a dream last night that hinged on this fact. Now I'm sorry that I can't remember any more details... -- Tom Duff. NONSPILLABLE BATTERY INSIDE.