Timeline for Controlling angles between vectors using sum of subvector angles?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jul 17, 2018 at 19:02 | history | suggested | Ju Sun | CC BY-SA 4.0 |
generalization of the result
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| Jul 17, 2018 at 18:54 | review | Suggested edits | |||
| S Jul 17, 2018 at 19:02 | |||||
| Jul 17, 2018 at 15:02 | comment | added | Fedor Petrov | @AmirSagiv essentially the same proof works: the square of the sine does not exceed the sum of squares of the sines by Lagrange identity. | |
| Jul 17, 2018 at 6:19 | comment | added | Amir Sagiv | @JuSun, If you know how to generalize it, I suggest you add this as an answer to your own question. This way everyone can benefit from it! | |
| Jul 16, 2018 at 22:16 | vote | accept | Ju Sun | ||
| Jul 16, 2018 at 22:16 | comment | added | Ju Sun | @FedorPetrov Also I realize the argument can be generalized to $\mathbb R^n$ using Lagrange's identity. This also avoids the difficulty of directly generalizing the cross product. | |
| Jul 16, 2018 at 21:55 | comment | added | Ju Sun | @FedorPetrov Many thanks, Fedor! That solves the $\mathbb R^3$ case. | |
| Jul 16, 2018 at 21:37 | comment | added | Fedor Petrov | I need the sum to be less than $\pi/2$, without contradiction this is not always so | |
| Jul 16, 2018 at 21:36 | comment | added | Luc Guyot | Very nice! You would make your proof even shorter by avoiding "contradiction" in the reasonning. | |
| Jul 16, 2018 at 20:48 | history | answered | Fedor Petrov | CC BY-SA 4.0 |