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## Main Question or Discussion Point

Hello

I am trying to make a uniform distribution of points on a sphere. I can find the answer

[tex]\theta=\pi R_1[/tex]

[tex]\phi = arccos(1-2R_2)[/tex]

where R1 and R2 are uniformly distributed random numbers between 0 and 1.

To me, it feels like

[tex]\theta=\pi R_1 sin(R1)[/tex]

[tex]\phi = 2\pi R_2[/tex]

should also give the correct distribution. Is that the case, and if not how can I understand why not this but the above solution is true? How can I calculate my way to the first answer?

thanks!

Tomas

I am trying to make a uniform distribution of points on a sphere. I can find the answer

[tex]\theta=\pi R_1[/tex]

[tex]\phi = arccos(1-2R_2)[/tex]

where R1 and R2 are uniformly distributed random numbers between 0 and 1.

To me, it feels like

[tex]\theta=\pi R_1 sin(R1)[/tex]

[tex]\phi = 2\pi R_2[/tex]

should also give the correct distribution. Is that the case, and if not how can I understand why not this but the above solution is true? How can I calculate my way to the first answer?

thanks!

Tomas