[ExI] tumbling pyramids again

spike spike66 at att.net
Thu Feb 16 06:25:47 UTC 2017


 

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?

 

spike

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