Timeline for Fair but irregular polyhedral dice
Current License: CC BY-SA 3.0
27 events
| when toggle format | what | by | license | comment | |
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| Feb 15 at 11:18 | comment | added | Maxxer | My first intuition is that full symmetry group acting transivly on sides should be sufficient condition. | |
| May 27, 2017 at 13:29 | comment | added | YCor | @JosephO'Rourke Thanks! I actually looked into online Cambridge and Webster dictionary and found nothing at "die", but a reference to "die" at "dice". Then at Oxford dictionary there is (en.oxforddictionaries.com/definition/die) en entry "die" in this sense: "Singular form of dice (...) In modern standard English, the singular die (rather than dice) is uncommon. Dice is used for both the singular and the plural" | |
| May 27, 2017 at 12:08 | comment | added | Joseph O'Rourke | @YCor: "dice" is the plural. Each cuboid is a "die," the singular. Thus we have "the die is cast," meaning the roll of fate has happened and events cannot be changed. | |
| May 27, 2017 at 11:07 | comment | added | YCor | I'm not native English speaker; is there any reason several users write "die" / "fair die" instead of "dice"? Is it a pun? slang? or just a typo? | |
| S May 27, 2017 at 6:04 | history | suggested | Martin Sleziak | CC BY-SA 3.0 |
Replaced picture by imgur link (which should be more stable); removed deprecated (geometry) tag
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| May 27, 2017 at 5:54 | review | Suggested edits | |||
| S May 27, 2017 at 6:04 | |||||
| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://people.csail.mit.edu/ with https://people.csail.mit.edu/
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| Dec 9, 2011 at 21:27 | answer | added | Valerio Capraro | timeline score: 3 | |
| Dec 9, 2011 at 13:23 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Moved image to another server.
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| Dec 9, 2011 at 6:45 | answer | added | Scott Sherman | timeline score: 9 | |
| Jan 1, 2011 at 2:10 | vote | accept | Joseph O'Rourke | ||
| Dec 15, 2010 at 23:05 | comment | added | Joseph O'Rourke | @Michael: Given Bill Th.'s latest comments, the "obviously fair" examples may be of considerable interest! | |
| Dec 15, 2010 at 3:10 | answer | added | Bill Thurston | timeline score: 30 | |
| Dec 8, 2010 at 23:30 | answer | added | Robert Connelly | timeline score: 14 | |
| Nov 20, 2010 at 21:31 | comment | added | Michael Hardy | I've seen polyhedra that are obviously fair without any reference to the intermediate value theorem. But if you want a right circular cylinder that's "fair", the intermediate value theorem would seem to provide a nonconstructive existence proof. A constructive proof might be difficult, I would guess. | |
| Nov 20, 2010 at 20:38 | answer | added | sleepless in beantown | timeline score: 4 | |
| Nov 20, 2010 at 15:23 | comment | added | Joseph O'Rourke | @Guillaume: Excellent point that even 2D seems interesting (and difficult!). | |
| Nov 20, 2010 at 15:13 | answer | added | Joseph O'Rourke | timeline score: 11 | |
| Nov 20, 2010 at 13:03 | answer | added | Matt Fayers | timeline score: 29 | |
| Nov 20, 2010 at 3:25 | answer | added | sleepless in beantown | timeline score: 3 | |
| Nov 20, 2010 at 2:28 | comment | added | J. M. isn't a mathematician | Also if the die bounces after being thrown... | |
| Nov 20, 2010 at 0:51 | comment | added | Tom Goodwillie | Without symmetry the answer would seem to have to depend on physical assumptions about friction and about how hard the die is thrown and how fast it is spinning. | |
| Nov 20, 2010 at 0:30 | comment | added | Guillaume Brunerie | @J.M. I don’t think so, if you take a bipyramidal die with many faces, it will be fair (because it is isohedral), but the dihedral angles will be very close to 180 degrees. | |
| Nov 19, 2010 at 23:30 | comment | added | J. M. isn't a mathematician | I'd speculate that the dihedral angles can't be too "near" (making this rigorous, I'll leave to other people) a straight (180 degrees) angle; it might become easy to cheat with the die by blowing on it (or a subtle nudge, or somesuch) to show a possibly different face. | |
| Nov 19, 2010 at 22:59 | comment | added | Guillaume Brunerie | Even the two dimensional case seems interesting, one can perhaps compute explicitely the probability of each face of a given convex polygon. But I don’t know how to model the shock of the die with the floor. | |
| Nov 19, 2010 at 22:38 | comment | added | Steve Huntsman | Notwithstanding the "Fair dice" paper, if the moments of inertia are unequal it's hard to see how you can get physical randomness of outcomes in a really strong sense: blog.eqnets.com/2009/08/24/dynamical-bias-in-the-dice-roll | |
| Nov 19, 2010 at 22:12 | history | asked | Joseph O'Rourke | CC BY-SA 2.5 |