Fair die
Quote:GAMERS rejoice: researchers have discovered that it is possible to transform any shape - from dragons to kittens - into a fair die.
"We started from the idea of: 'If you look at an object, can you tell its resting probabilities?'" says Keenan Crane at Carnegie Mellon University in Pittsburgh, Pennsylvania. In other words, if you roll a particular shape, what is the probability it lands in a particular orientation?
To answer this question, Crane and his colleagues developed a geometric model to compute the resting poses of any object. Rather than physically simulate the object, the model maps the corners, edges and faces of that object onto a
CARNEGIE MELLON UNIVERSITY
sphere, allowing the researchers to describe how it would fall under gravity before coming to rest.
For example, if a corner is the first part of the object to touch the ground, it will then fall onto an edge determined by the position of its centre of mass, and from there onto a face.
Using their model, the researchers 3D-printed seven unusual designs.
These included armadillos and kittens, both designed to land in one of three orientations with equal probability, and more exotic concepts, like a single die with
The oddly shaped dice produced and tested by the research team included armadillos and kittens
probabilities equivalent to rolling two standard six-sided dice.
To test each design, the team dropped them from the same height onto a hard wooden floor between 100 and 1000 times, with different people throwing the dice to limit bias, and counted how often they landed in each orientation.
The probabilities produced by these real-world tests came within 3 or 4 per cent of those predicted by their model (ACM Transactions on Graphics, in press).
Crane says the work isn't an
"ideal solution" to the problem, but he was surprised by how momentum seemed to play only a small role in the outcome of rolling the dice.
It's not clear if they also did this, but it would be interesting to design and produce a single die with the same outcome probabilities of the sum of a pair of dice. So it would be an 11-sided die, the probability of the 7 side would be 1/6, the probabilities of the 2 and 12 sides 1/36, and so on.
Quote: DieterSomehow, I don't think a standard kitten is going to pass a micrometer spin test satisfactorily.
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If it can pass the spin test without vomiting, perhaps it could be the first kitten in space…
ETA: Would this also make the kitten a soldier?
Quote: camaplQuote: DieterSomehow, I don't think a standard kitten is going to pass a micrometer spin test satisfactorily.
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If it can pass the spin test without vomiting, perhaps it could be the first kitten in space…
ETA: Would this also make the kitten a soldier?
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Just guessing, but I think that takes us outside the constraints of standard kitten and brings us back into regular kitten...
