From: Jeff Senn (firstname.lastname@example.org)
Date: Sat Jan 09 2010 - 16:01:01 CST
[Ignoring the fact that this has gotten so off-topic from this list to be absurd:]
I don't think you need to vary the density for such a die to be "fair" -- it is clearly
fair for the 5 sides-- and clearly the odds of landing on either end (vs one of the 5)
can be varied (I *believe* in a continuous function) from nearly 0 to nearly 1.0 by
adjusting the "width". So you simply must choose the correct width... math (and
resultant width) left as the cliched exercise for the reader...
On Jan 9, 2010, at 4:16 PM, William J Poser wrote:
> A seven-sided die is impossible if it is required to be fully symmetric
> like a six-sided die. There is no seven-sided regular polyhedron.
> The five convex regular polyhedra (aka the Platonic solids) have
> 4, 6, 8, 12, and 20 sides respectively. See the MathWorld article:
> The seven-sided dice that a Google search turns up are not fully symmetric.
> They have five square faces orthogonal to a pair of pentagonal faces.
> I don't know whether asymmetry necessarily means that the dice are
> not fair. I can imagine that one could make them fair by varying the
> density of the material as a function of location within the die
> in a suitable manner, but I haven't thought/calculated enough to see
> if that would really work, and I don't know enough about the materials
> and manufacturing processes to know how easily such a thing could be
> implemented even if mathematically possible.
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