Timeline for Scalar product of random unit vectors
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 29, 2020 at 12:57 | vote | accept | Gin Pat | ||
| May 29, 2020 at 7:42 | comment | added | Gin Pat | Thank you! And if I didn't make mistakes it should be possible to rewrite the distribution $f_R$ as $f(\alpha) = C(d) \sin^{d-2}(\alpha) \,1\{0<\alpha<\pi\}$ in order ti obtain the distribution of the angle between vectors $X,X'$ | |
| May 29, 2020 at 2:29 | comment | added | Iosif Pinelis | @GabeK : Good point. | |
| May 29, 2020 at 1:39 | comment | added | Gabe K | One beautiful fact here is that when $d=3$, this is a uniform distribution. Actually, this fact is in some sense due to Archimedes, who showed that the sphere and cylinder have the same surface area. More precisely, the height and polar angle are Darboux coordinates for both spaces. | |
| May 29, 2020 at 0:29 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 2 characters in body
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| May 28, 2020 at 23:39 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |