Random Points on a Sphere (Part 1)

John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances where and were two randomly chosen unit quaternions:

• John D. Cook, How far is xy from yx on average for quaternions?, 5 July 2018.

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Three things to note before we move on:

• Click the pictures to see the source and get more information—I made none of them!

• We’ll be ‘randomly choosing’ lots of points on sphe...