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

From: verdy_p (
Date: Sun Jan 10 2010 - 14:32:15 CST

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

    > Message du 09/01/10 23:37
    > De : "Marcin 'Qrczak' Kowalczyk"
    > A : "William J Poser"
    > Copie à :
    > Objet : Re: Seven-sided die (was Re: This just in)
    > In practice it is quite possible to have a symmetric dice with 7 sides. Make
    > a pyramid with 7 triangular sides, letting its base be something that the
    > dice won't stay on, like half of sphere.

    Hmmm.. due to the spacial distribution of weight, the center of gravity will be WITHIN the half-sphere, so it is
    likely that the dice will finish exactly laying on the middle point of the rounded "face".

    And the other faces would also have different surfaces (unless they are circular by cutting 7 "pole" areas in the
    sphere, and placing these in a more balanced way, but you will do everything you want, you will always have 3
    circular faces on one half of the sphere, and 4 circular faces on the other half.

    Then, to rebalance the center of grativity, you will need to make the center of the 5 circular faces cur more than
    half the sphere, by placing them nearer from the plane separating them.

    But even in this case, the result will not be balanced, because the dice will not always roll on the spheric surface
    but will roll along the periphery of the faces (where the center of gravity will "jump" down and up) with different
    probabilities between the two sphere halves.

    This dice would not produce equally balanced chances for all the 7 faces, and you'll observe easily that 3 faces
    have a higher probability of result than the 4 others (that will tend to be on the table).

    On the opposite, it is perfectly possible to create a more qually balanced dice with 12 faces (place them in two
    sets of 6 circular faces on the sphere, each set being disposed in a hexagon.)

    There will still be some very light probability that the dice will stop laying on the spheric surface around faces
    (but due to movement instabilities and the fact that the center of grabity will jump up and down, it will be
    impossible after some time to jump up again due to insufficient cinetic energy: such probability also exists with
    most cubic dice with spheric angles, but it is exceptional to see the dice finishing its course on one of the
    rounded corners)

    Then you could imagine 14 faces (by placing two additional faces in the center of each hexagon, but here again the
    dice will become unbalanced: these two faces will have higher probability (because the center of gravity will be
    lower when the dice stops laying on one of the two faces, than when it stops on any of the 12 other faces).

    Only the dice that are made with regular polyedres are correctly balanced, and there's a finite number of them. You
    can't have more than 12 faces (triangular), possibly with spheric courners. For more, the dice is not enough, you
    have to use a rotating wheel, or like in Lottos, a set of numbered balls extracted from within a bigger rotating

    This archive was generated by hypermail 2.1.5 : Sun Jan 10 2010 - 14:34:55 CST