There really IS a polyhedral d1
Jul. 6th, 2007 02:32 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackIn retrospect, it's obvious. That is the best d1 (one-sided die).
ETA: We went to a little difficulty defining a d1, but it was unspokenly assumed you couldn't build one without cheating a little, eg. ingeniously using a sphere... But this works.
It satisfies all the requirements for a dice. It's solid, uniform, all the faces and edges are straight. It's equally fair rolled on any surface provided with random initial orientations. And if you paint a "1" on the only stable side, it always stops on it!
That's better than we managed for d7! :)
ETA: We went to a little difficulty defining a d1, but it was unspokenly assumed you couldn't build one without cheating a little, eg. ingeniously using a sphere... But this works.
It satisfies all the requirements for a dice. It's solid, uniform, all the faces and edges are straight. It's equally fair rolled on any surface provided with random initial orientations. And if you paint a "1" on the only stable side, it always stops on it!
That's better than we managed for d7! :)
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Date: 2007-07-06 02:58 pm (UTC)OK, how about http://blog.sciencenews.org/mathtrek/2007/04/cant_knock_it_down.html ? If they're right, they've a requirement that their shape has at most one stable and one unstable balance point (which it must have, at least). Which seems a good formalisation of the "prisms are cheating" criterion. And have found a shape, but say its unknown if there can be a polyhedron that does it.