If I wanted to surround myself with mirrors how would I need to arrange them so that if I stood in the middle of them I couldn't see myself in any reflection?
For simplicity let's just say we only do the sides, not the ceiling and the floor.
How many panels would I need and in what configuration?
It seems to me that only a star formation could work, where all the mirrors are angled slightly outwards from me, but I'm not sure that at some point I would be reflected.
Is this even possible? Any ideas?
UPDATE:
Based on all the responses below I believe the problem is that I cannot have any angle facing me that is at 180 degrees or less.
For example, this is at about a 30 degree angle and doesn't work (thanks @mmesser314):
And this one is exactly 180 degrees and obviously will not work:
But from 181 degrees onward light is reflected away, like this:
So if we could figure out a configuration where I cannot see any angle that is less than 180 degrees I should never be able to see my reflection. This is what I came up with. Can anyone tell me if this (or some variation of it) seems valid?
Best Answer
This would work, but you might think it is cheating.
If there can be no gaps, I would guess it is not possible. Your star idea won't work. Light that leaves you will bounce up the V and back out. The ray shown misses you. But if you look at a fan of rays, some will go to the left of you and some to the right. There is always one that will hit you.
If you use a smooth curve instead of planar mirrors, you cannot avoid seeing at least a point. This shows a ray that goes to the left and another that goes to the right. Some ray in between will hit you.
You might try to avoid it by putting mirror in the way to block that ray. But that piece has the same problem.
You might try to make a mirror where all the rays are deflected to the left. But that is a spiral, not a closed curve.