Re: Seven-sided die (was Re: This just in)

From: Jeff Senn (senn@maya.com)
Date: Sat Jan 09 2010 - 16:01:01 CST

  • Next message: Marcin 'Qrczak' Kowalczyk: "Re: Seven-sided die (was Re: This just in)"

    [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...

    -Jas

    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:
    > http://mathworld.wolfram.com/RegularPolyhedron.html
    >
    > 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.
    >
    > Bill
    >
    >
    >



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