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Topic: Five Sided Dice
Replies: 7   Last Post: Sep 1, 2007 12:04 PM

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Ben Rudiak-Gould

Posts: 210
Registered: 2/2/05
Re: Five Sided Dice
Posted: Aug 31, 2007 4:23 PM
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hagman wrote:
> On 31 Aug., 20:21, Ben Rudiak-Gould <br276delet...@cam.ac.uk> wrote:
>> [...] the faces cover equal solid angles with respect
>> to the center of gravity. For a center of gravity in the obvious place, I
>> get that the six triangle edges should be longer than the other three edges
>> by a ratio of sqrt[(15 + 9 sqrt(5)) / 10] ~ 1.87.

>
> I'd rather use physics and say that a thoroughly thrown die will go
> through a lot of bounces and end up in a stable position of potential
> energy W with probability proportional to exp(-kT/W).
> Since W is proportional to height, the center of gravity should be the
> center of a sphere touching all (stable) faces.


Interesting. This (obviously) gives a ratio of sqrt(3) ~ 1.73. I'm not
convinced that this is a good model of the final low-energy settling-down
part of the toss, but then I don't find my model very convincing either. Now
I feel like doing an experiment. (But I'm not going to.)

What I don't get is why anyone would design or use a shape like this in the
first place rather than one that's manifestly symmetrical.

-- Ben



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