As Allan says, there is always more physics. Somehow I can no longer find the web page about the d5 robot. Someone -- maybe it was Lou Zocchi, or Koplow Games? -- wanted to make fair 5-sided dice, using a prism with equilateral triangular base and whatever height made it all work out (which "must exist by continuity"). They built cut dice of a bunch of different heights at 1mm increments, and had a die-rolling robot with a computer vision system that could tell whether it landed on one of the triangular or rectangular faces. Turned out the correct prism height varied a lot depending on whether the die was being rolled onto a 5mm-thick or 15mm-thick piece of plexiglass. Sigh. I don't want dice that become unfair if I roll them onto a tabletop that is more bouncy or more sticky or more slanted. Or when I roll them underwater, or on the moon, or in a storm. Well, *maybe* I'll be OK with the d48 or d120, which are fair by symmetry except that some of the symmetries involve taking a mirror image. Those are fair until I want to roll them in a tornado, at which point a right-handed vs. left-handed funnel cloud would matter. https://www.mathartfun.com/thedicelab.com/d120.html --Michael On Wed, Jan 30, 2019 at 8:00 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
<< The word my father taught me for the three-dimensional analogue of a rectangle is "parallelopiped" >> I don't think so. See https://en.wikipedia.org/wiki/Parallelepiped
I suggest "oblong" is the word required.
WFL
On 1/30/19, Mike Speciner <ms@alum.mit.edu> wrote:
Actually, it's parallelepiped.
On 30-Jan-19 18:19, Allan Wechsler wrote:
The word my father taught me for the three-dimensional analogue of a rectangle is "parallelopiped". Some author, I can't remember who, writes "2-box" and "3-box" and the like.
On Wed, Jan 30, 2019 at 6:07 PM Dan Asimov <dasimov@earthlink.net> wrote:
Good point!* I will now try to find if something comparable has been done for more general polyhedra.
—Dan
—————————————————————————————————————————————————————————————— * If you've never tried it, get a fat mass-market paperback (i.e., small format, c. 4"x7"), put a rubber band about it to hold it together, and note the disparate efforts needed in order to get it to spin 360º midair about the three axes perpendicular to the faces of this rectangular solid.**
** "Rectangular solid"??? Surely there is a shorter and punchier word for this common concept!
Andy Latto <andy.latto@pobox.com> écrit: ----- Assuming the die has 3 distinct moments, there are two stable ways to have the die spinning as it is tossed. I don't see any reason to expect the probabilities will be the same for these two different ways to throw the die. Or the unstable ways, but those are harder for the thrower to reproduce accurately. -----
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.