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Nov 29, 2022 at 6:20 history edited YCor
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Nov 29, 2022 at 4:50 history edited felipeh CC BY-SA 4.0
Edited to include constraint about angles.
Nov 29, 2022 at 4:46 comment added Noam D. Elkies @SamHopkins In R^3 the unit vectors have 2 degrees of freedom, and specifying the angle removes only one of them so there's still a cone of possible directions.
Nov 29, 2022 at 4:40 comment added Sam Hopkins I think it’s sometimes okay to change the question if you left something off. But regarding your proposed change: I’m confused how you could know all the angles but not know the entire trajectory.
Nov 29, 2022 at 4:30 comment added felipeh Ok, good point. I missed a detail when I (incorrectly) translated another problem into this question about lasers and mirrors. The very important detail that I missed is I would like the angle of reflection off of each mirror to be the same. I think the correct thing to do on MO is to leave this question as is and perhaps ask my corrected question separately, after more carefully checking that it is not trivial.
Nov 29, 2022 at 4:25 comment added Sam Hopkins Even more explicitly: compare a (regular) pentagon and pentagram.
Nov 29, 2022 at 4:17 comment added Sam Hopkins Isn’t this already possible in 2D with “spirograph” type configurations (the $x_i$ being vertices of a regular polygon).
Nov 29, 2022 at 4:08 history asked felipeh CC BY-SA 4.0