[ExI] tumbling pyramids again

[BillK]

On 17 February 2017 at 00:34, spike  wrote:
> Eh... BillK, the question isn't about creating a device with five equal
> probability outcomes.  That is easy: that triangular prism device, or a
> simple spinner.  The question is to figure out with equations and theories
> what the dimensions of such a device would be.  I have three possible
> answers: h = 1.41, h = 1.58 and h = 1.675 but I disagree with the reasoning
> behind that last one.
>

Having slept on the problem (and ordered my subconscious to find the
solution) I awoke to a new world! :)

I still think that any die where the sides were not equal in shape and
area would be very unlikely to have equal probability outcomes in all
circumstances.  i.e. symmetry matters.

So pursuing confirmation bias, I found some mathematicians discussing
this pyramid problem.

<https://math.stackexchange.com/questions/1333962/fair-5-sided-die>

Quote:
Lacking symmetry this question cannot be answered purely
mathematically. We need some physics: When the die is tossed against
the table surface, it bounces and rotates irregularly until it comes
to halt in one of finitely many states of equilibrium. The probability
distribution governing this final state can be viewed as following
Boltzmann statistics.
---------

(I think this means the answer is really complicated).  :)

BillK

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