Posts by robinhouston@mathstodon.xyz
(DIR) Post #AxPISPVyKAYpvPwTHE by robinhouston@mathstodon.xyz
2025-08-21T21:28:48Z
0 likes, 1 repeats
I have been given what must surely be the largest model yet made of my dodecahedron whose adjacent faces meet at right angles, except on one edge where they meet at 45°.(Yes, I do need to find a better name for it.)
(DIR) Post #AxPIvEQ4eeeBubvUgK by robinhouston@mathstodon.xyz
2025-08-21T21:36:27Z
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@futurebird That’s an excellent question. The answer is not terribly easy to convey in written form, but I made an attempt in https://s3.boskent.com/single-angle-polyhedra/g4g-paper.pdf
(DIR) Post #AxRcA2OFws1IOPllg0 by robinhouston@mathstodon.xyz
2025-08-22T12:25:07Z
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I’ve been reminded of the little booklet about this shape that I wrote for the last G4G. I’ve read it through for the first time since then, and I’m still pretty happy with it. I’ve also corrected a mistake on the last page (which I had to correct by hand in 200 copies originally).https://s3.boskent.com/single-angle-polyhedra/g4g-paper.pdf
(DIR) Post #AxRcA3Fmjqq14QoW6y by robinhouston@mathstodon.xyz
2025-08-22T12:26:46Z
2 likes, 0 repeats
(DIR) Post #Axysyg2snO37LMcPS4 by robinhouston@mathstodon.xyz
2025-09-06T05:35:18Z
1 likes, 0 repeats
“Unlike a typical mesh, which stores per-vertex 3D positions, a mescher stores per-vertex 2D screen-space positions and a per-edge depth difference. Whereas differences in depth across edges must sum up to zero as we travel around a standard mesh, this is not necessarily the case for a mescher. It is a mathematical way of describing the perceptual impossibility.” https://anadodik.github.io/publication/meschers/
(DIR) Post #AxysyodgqQFFzptuvw by robinhouston@mathstodon.xyz
2025-09-06T05:36:49Z
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Full paper: https://dl.acm.org/doi/10.1145/3731422
(DIR) Post #AyEHgLJ3KKD1v8ZNVQ by robinhouston@mathstodon.xyz
2025-09-15T11:20:43Z
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Who would win in a game of chess between a dinosaur and a rhombic dodecahedron?
(DIR) Post #AyEHgNKXnkagCLHb6m by robinhouston@mathstodon.xyz
2025-09-15T11:40:34Z
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@OscarCunningham You can tell that this board was set up by someone who doesn't play chess, even if the dinosaur didn't give it away
(DIR) Post #AyEHgO76tBRGcy0No8 by robinhouston@mathstodon.xyz
2025-09-15T11:44:13Z
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@OscarCunningham It is relatively unusual for the fold in a folding chessboard to be in that orientation, isn't it? Which way was the fold in the board from your childhood memory?
(DIR) Post #AzPH6PWeXswisfiaCO by robinhouston@mathstodon.xyz
2025-10-20T16:05:47Z
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This is up there with “Can One Hear the Shape of a Drum” in the annals of great titles.Was the 1960s an especially auspicious time for excellent titles?
(DIR) Post #AzZHuOBRkhcomKEJ5k by robinhouston@mathstodon.xyz
2025-10-24T21:24:21Z
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I love the feeling of going to bed leaving a search algorithm running. Will it have found anything by the time I wake up tomorrow? So exciting.
(DIR) Post #AzZHuPNXJEtEU6tTZg by robinhouston@mathstodon.xyz
2025-10-25T06:59:37Z
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(It has not found anything.)
(DIR) Post #AzZHuQE0AArD6pRNLs by robinhouston@mathstodon.xyz
2025-10-25T09:50:58Z
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But, having slept on it, I thought of a faster algorithm, which ran to completion in less than two seconds.
(DIR) Post #AzZHuS21RgSmiFqpxQ by robinhouston@mathstodon.xyz
2025-10-25T12:52:45Z
1 likes, 0 repeats
@massimolauria The slow algorithm hadn't completely explored the search space (and in fact had not found the optimal element). The faster algorithm exhausted the whole search space in a couple of seconds.
(DIR) Post #B0p3VkmWWPHCTwZY8W by robinhouston@mathstodon.xyz
2025-12-02T00:41:30Z
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@rzeta0 What a peculiar mistake.
(DIR) Post #B0p3VlY1fnH2rGnUB6 by robinhouston@mathstodon.xyz
2025-12-02T00:43:41Z
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@rzeta0 The next part doesn't make sense either. You can't write 3 as the sum of two squares, but e.g. 53 = 7² + 2².Does your book have a lot of mistakes, or is this page unusual?
(DIR) Post #B0p7E3vR0TjiSXYmwq by robinhouston@mathstodon.xyz
2025-12-02T02:01:32Z
1 likes, 0 repeats
@rzeta0 The truth is that an integer can be written as the difference of two squares iff it is not congruent to 2 modulo 4. Primality is irrelevant.This situation for sums of two squares is a bit more subtle and interesting: https://en.wikipedia.org/wiki/Sum_of_two_squares_theorem
(DIR) Post #B0rcArTkJPl1spTyqm by robinhouston@mathstodon.xyz
2025-12-03T03:54:22Z
3 likes, 4 repeats
I would not have guessed this was possible!Vladan Majerech has found a one-dimensional spaceship in the Game of Life: a pattern just one cell high and 3,707,300,605 cells wide that, after 133,076,755,768 generations (during which it is not confined to the one-dimensional line, of course) recreates the starting pattern but translated two cells to the right.https://conwaylife.com/forums/viewtopic.php?&p=222136#p222136
(DIR) Post #B16R3y1TOmv21lAPo0 by robinhouston@mathstodon.xyz
2025-12-10T09:47:24Z
1 likes, 0 repeats
The mysterious network problem that cost me most of yesterday turns out to have been caused by someone helpfully plugging in a network cable that wasn't meant to be plugged in.This is the second time I've found a tricky network problem to have such a cause.I think there's some sort of cognitive illusion that afflicts people who don't regularly mess with networks, where they would never _unplug_ a random cable without worrying it might cause problems, but somehow it doesn't occur to them that _plugging in_ a random cable could also cause problems.
(DIR) Post #B2Td6aroKXESDsshkW by robinhouston@mathstodon.xyz
2026-01-20T13:00:12Z
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We hear so much about symmetrical polyhedra. What about their asymmetrical cousins?Here are the two simplest – I think – convex polyhedra that have no symmetry at all, even combinatorially. In other words, they have no non-trivial automorphisms as graphs.Both of them have 7 vertices and 7 faces.https://sketchfab.com/3d-models/asymmetric-heptahedron-1-bc580cf801444bbea24e8f7ac42fb88chttps://sketchfab.com/3d-models/asymmetric-heptahedron-2-0b6db5620b4b486186edbca686dd5bff