[ExI] tumbling pyramids again

[BillK]

On 16 February 2017 at 06:25, spike  wrote:

>
>
> A question I posed a long time ago, but I have new insights.
>
>
>
> Imagine a cube a cm on a side, tossed like a gaming die.  By symmetry, any
> face has the same probability of coming up (or down): one in six.
> Likewise, a tetrahedron could be tossed and each face would have a one in
> four chance of landing face down.  The same symmetry argument could be made
> for any of the five platonic solids.
>
>
>
> Cool but what if we wanted to create an unsymmetrical solid, such as a
> square based pyramid one cm on a side for the square, and we wanted to make
> it such that the probability of landing face down on any of the five
> surfaces was the same.  How tall do we need to make it?
>
>
> I get a CG height of h/4.
>
>
>
> So if we want to make a fair pyramid shaped five sided die, what is h?
>
>
>

The internet spoils everything.  :)
You can buy 5-side dice already, but in order to roll they must have
bevelled edges.

<
http://www.gamesciencedice.com/Gamescience-Amethyst-d5--Five-sided-die--Plain_p_138.html
>




BillK
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