(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that you want to undo a square-headed screw of side [tex]a[/tex] using a key that has a regular hexagon hole of side [tex]b[/tex]. What relations must hold between these two number in order for you to succed?

2. Relevant equations

Basic geometry and trigonometry.

3. The attempt at a solution

The obvious solution is that the square must be the largest one that can be inscribed in a given hexagon, e.g. see here (2nd. picture): http://www.yucs.org/~gnivasch/cube/index.html [Broken].

I have a problem visualizating the situation for a slightly smaller square - can it also be undone with the same key? Of course, now there wouldn't be four point of contact between the key and the screw, so my question is, could you undo a screw with three points of contact? If yes, what's the lower limit on a size of a screw?

Thanks!

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# Homework Help: Using a hexagonal key on a square-headed screw

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