3 ms·
I don't agree with the way he normalizes the radius in the last 2 methods. I think it should be a square root, not a cubic one. This is because the volume difer
by expuexto 8y ago
I don't agree with the way he normalizes the radius in the last 2 methods. I think it should be a square root, not a cubic one.
This is because the volume diferential r^2•sin(phi)•d_phi•d_theta•dr is proportional to the square of r.
This mistake is also made in a source he cites: https://math.stackexchange.com/questions/87230/picking-random-points-in-the-volume-of-sphere-with-uniform-probability/2872878 https://math.stackexchange.com/questions/87230/picking-rando...
and I tried to point it out there as well.
- improbable22 8y agoThat's the correct volume element, but not what you want. The volume inside radius r grows as r^3. It's the inverse of this _cumulative_ density function which maps uniform-in-r numbers to uniform-in-volume ones.
- antidesitter 8y agoDid you empirically check your hypothesis? What's the integral of r^2 dr? Think about whether your claim makes sense when n = 1.
- expuexto 8y agoYou both are right. Thank you for the comments.