Nostr notes by robinhouston

I feel this is getting a disproportionate amount of attention on ...

2026-10-08T13:01:15Z

In reply to nevent1q…kjwc
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I feel this is getting a disproportionate amount of attention on here, relative to the 369 papers that haven't been withdrawn

They’ve just withdrawn three of the papers: * Algebraicity of ...

2026-10-08T07:48:59Z

They’ve just withdrawn three of the papers:

* Algebraicity of Weil classes on split abelian eightfolds
* Algebraicity of Kuga–Satake Correspondences for K3 Surfaces
* The rational Hodge conjecture for products of K3 surfaces

https://github.com/openai/math/blob/main/history.md

Looks like something big dropped overnight: ...

2026-10-07T07:23:22Z

Looks like something big dropped overnight: https://github.com/openai/math/tree/main/preprints

This is going to take some digestion…

2π - 5 cos⁻¹(1/3), or a bit more than 7° in normal human ...

2026-10-03T22:06:29Z

In reply to nevent1q…9uv2
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2π - 5 cos⁻¹(1/3), or a bit more than 7° in normal human terms.

Absolutely amazing progress on short superpermutations from Jay ...

2026-10-01T09:06:35Z

Absolutely amazing progress on short superpermutations from Jay Pantone and his AI collaborators: https://github.com/jaypantone/superperm-upper-43-80

This breaks the existing records for all n > 7.

Here is a superpermutation on 8 symbols of length 46,181 – a lot shorter than any that was previously known: https://github.com/jaypantone/superperm-upper-43-80/blob/main/words/8/superpermutation-8-46181.txt

Five regular octahedra don't quite make a ring. ...

2026-09-30T17:48:12Z

Five regular octahedra don't quite make a ring.

For my birthday, my brother-in-law gave me a 4992-digit hex ...

2026-09-28T09:15:44Z

For my birthday, my brother-in-law gave me a 4992-digit hex number that, when used as a seed for Python’s random number generator, makes it so that printing a sequence of “random” ASCII characters actually prints a birthday greeting.

I find it rather amazing that this is possible!

This is the program he sent with the seed:

with open("seed.txt", encoding="ascii") as handle:
seed = int(handle.read().strip(), 0)
r = random.Random(seed)
pending = ""
while True:
character = chr(r.randrange(128))
if pending + character == "\x1e\x1f":
break
print(pending, end="")
pending = character
print()

And so has Chaim Goodman-Strauss: ...

2026-09-22T20:33:06Z

In reply to nevent1q…7v2q
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And so has Chaim Goodman-Strauss: https://arxiv.org/abs/2609.24779

Good news: Felix Flicker has written a nice short readable paper ...

2026-09-22T14:07:03Z

In reply to nevent1q…nyh4
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Good news: Felix Flicker has written a nice short readable paper about it. https://arxiv.org/abs/2609.23783

Yes, I see. You're worried about nasty people who wield ...

2026-09-18T18:01:47Z

In reply to nevent1q…5mnv
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Yes, I see. You're worried about nasty people who wield power, rather than fringe lunatics. Sorry for the tangent.

I'm afraid my rather cynical view on that is that I don't really believe them to be fundamentally nastier than any of the other groups who wield power in the world – and it might even be the other way around.

I don't really have anything useful to say about that. ...

2026-09-18T17:32:02Z

In reply to nevent1q…ct3a
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I don't really have anything useful to say about that. I'm very much a distant observer rather than an insider.

Oh goodness, there's much worse than that if you're ...

2026-09-18T16:45:23Z

In reply to nevent1q…dsv8
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Oh goodness, there's much worse than that if you're interested in bad behaviour by rationalist-adjacent groups. Look up the Zizians, for example!

(FWIW I don't think the ideas are great either! But I ...

2026-09-18T16:17:59Z

In reply to nevent1q…rm4n
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(FWIW I don't think the ideas are great either! But I don't think the odd lifestyles of the Berkeley rationalists constitute evidence either way…)

The facts are mostly right, but the implication that we should ...

2026-09-18T16:10:42Z

In reply to nevent1q…hfss
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The facts are mostly right, but the implication that we should reject ideas because they were proposed by unconventional people is surely a textbook example of the ad hominem fallacy

I don't believe that the human whose name is on the paper ...

2026-09-18T14:40:29Z

In reply to nevent1q…zvvx
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I don't believe that the human whose name is on the paper played any real role in this discovery.

Are we going to be excited about the discovery of an elegant 3d ...

2026-09-18T12:25:33Z

Are we going to be excited about the discovery of an elegant 3d aperiodic monotile, or sad that it was published as 60 pages of badly-written AI slop?

Why not both!

https://arxiv.org/abs/2609.19214

I did not notice, when I wrote that reply, that the post I was ...

2026-09-12T18:22:46Z

In reply to nevent1q…w6gu
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I did not notice, when I wrote that reply, that the post I was replying to was made six months ago! I would not have written it, had I noticed.

There is a regular tetrahedron whose vertices all have integer ...

2026-09-12T18:02:56Z

In reply to nevent1q…d0aq
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There is a regular tetrahedron whose vertices all have integer coordinates, e.g.

(-1, -1, -1)
(+1, +1, -1)
(-1, +1, +1)
(+1, -1, +1)

That last part is really unfortunate. I hate to say it, but ...

2026-09-10T10:34:10Z

In reply to nevent1q…8lk7
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That last part is really unfortunate. I hate to say it, but recently there have been more interesting conversations happening on Twitter than here. I feel that here it's mildly taboo to discuss AI/maths in anything other than a dismissive way.

Wow, autoformalization is a lot further along than I realised. I ...

2026-09-04T21:56:42Z

In reply to nevent1q…g96k
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Wow, autoformalization is a lot further along than I realised. I can't help thinking this is very good news for mathematics.

I think the unstated context here is that one of the AI labs has ...

2026-08-31T13:37:41Z

In reply to nevent1q…zyn5
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I think the unstated context here is that one of the AI labs has an unannounced proof of this conjecture. At least that's the rumour.

I thought Hugo Duminil-Copin's post yesterday was interesting ...

2026-08-31T13:00:18Z

In reply to nevent1q…cv9j
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I thought Hugo Duminil-Copin's post yesterday was interesting too. https://proofsandprompts.com/2026/08/30/care-for-a-little-more-ai/

Levent Alpöge posted it to Twitter.

2026-08-24T08:10:05Z

In reply to nevent1q…esp4
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Levent Alpöge posted it to Twitter.

And here is a claimed complex structure on S^6: ...

2026-08-23T21:50:53Z

And here is a claimed complex structure on S^6: https://alpo.ge/s6.pdf

This is a notorious problem that has attracted many claimed solutions that did not stand up to scrutiny, so some caution is warranted, but IMHO there are also grounds for optimism.

(Context: https://mathoverflow.net/questions/1973/is-there-a-complex-structure-on-the-6-sphere)

There have been a lot of new discoveries about superpermutations ...

2026-08-20T09:53:19Z

There have been a lot of new discoveries about superpermutations of late, but my absolute favourite is Andrei Teodorescu’s discovery of a length-5905 superpermutation on 7 symbols.

This is one shorter than the best that was previously known – and honestly one shorter than I would have guessed was possible.

https://groups.google.com/g/superpermutators/c/D5sKkV2jBuc/m/MYVQA8UsAQAJ

Ok sure, but they're also the only people who actually know ...

2026-08-11T09:48:00Z

In reply to nevent1q…xjs6
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Ok sure, but they're also the only people who actually know the details of what happened.

No, it's not his presentation. That blog is written by Zvi ...

2026-08-11T09:35:00Z

In reply to nevent1q…7rku
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No, it's not his presentation. That blog is written by Zvi Mowshowitz, and the presentation is by Eric Wallace and Michael Dalton.

I believe the primary source for most of that information is this ...

2026-08-11T09:18:05Z

In reply to nevent1q…t4e2
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I believe the primary source for most of that information is this talk, which is very interesting: https://youtu.be/87DyyMV0kCY

An interesting effect: photographing this projected screen with ...

2026-08-06T21:34:36Z

An interesting effect: photographing this projected screen with my phone camera causes a rainbow effect on the photograph, which isn't visible to the naked eye.

Is this a common phenomenon? I don't remember seeing it before.

I very much agree with that! But radical change in large ...

2026-07-07T09:41:58Z

In reply to nevent1q…fnwk
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I very much agree with that! But radical change in large institutions is hard and takes time, so stopgap measures may, regrettably, be useful in the interim.

In any case we definitely need teachers and administrators to be ...

2026-07-07T09:27:50Z

In reply to nevent1q…kd9t
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In any case we definitely need teachers and administrators to be much more cautious about drawing conclusions from these tools than in some cases they have been, so this article is pushing in the right direction.

Mike Perkins's argument in the article does not strike me as ...

2026-07-07T09:24:45Z

In reply to nevent1q…k0de
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Mike Perkins's argument in the article does not strike me as logically sound

Do you agree? I don't see why it couldn't be used as ...

2026-07-07T09:23:08Z

In reply to nevent1q…94t9
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Do you agree? I don't see why it couldn't be used as evidence alongside other evidence. I don't think capitulation is our only option. But I'm sure reasonable people may disagree…

AFAICT of the purported AI detectors, only Pangram has a ...

2026-07-07T09:14:05Z

In reply to nevent1q…tyk8
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AFAICT of the purported AI detectors, only Pangram has a sufficiently low rate of false positives to be potentially useful.

I have wondered whether it's the only place in the world you ...

2026-05-29T17:26:38Z

In reply to nevent1q…fmxg
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I have wondered whether it's the only place in the world you can take a steam train to a nuclear power station.

It looks as though he’s also going to present this work next ...

2026-05-14T17:46:34Z

In reply to nevent1q…dgtd
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It looks as though he’s also going to present this work next week at the 13th International Conference on Fun with Algorithms, which has a bunch of cool-sounding topics.

https://fun2026.limos.fr/accepted/

How many sheets of A10 paper can you fit into one sheet of A0? ...

2026-05-14T17:43:21Z

How many sheets of A10 paper can you fit into one sheet of A0?

This video has the answer! (And the answer is probably not the first thing you thought of.)

https://youtu.be/zDKBCIMkDbw

I thought Peter Selinger was on here, but I can't find him. ...

2026-04-24T06:13:14Z

I thought Peter Selinger was on here, but I can't find him. Has he left us?

Just looking at this interesting new paper https://arxiv.org/abs/2604.20964 which does cite Mathstodon posts by Pieter Mostert (npub1l3c…nw2k).

(Christian Lawson-Perfect (npub197g…q2n4) first citation of Mathstodon in a paper, or have there been others?)

Yes, trig functions are defined using exponentials and i. This ...

2026-04-15T22:07:20Z

In reply to nevent1q…sm58
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Yes, trig functions are defined using exponentials and i. This table from the supplementary information document shows how each function is defined in terms of functions earlier in the table.

There are definitely some subtleties related to the choice of branch, which is discussed at various points in the paper and the supplementary document, though I won’t pretend I have tried to understand it completely. See the discussion on p. 11 of the paper, for example.

There’s a fun paper showing that you can define all elementary ...

2026-04-15T21:30:26Z

There’s a fun paper showing that you can define all elementary functions using just two primitive operations: the constant 1, and the binary function eml(x, y) := e^x - log(y).

https://arxiv.org/abs/2603.21852

That’s a neat little result, which makes for some fun games.

What’s the simplest expression you can find that evaluates to your favourite constant?

The best I have found for 2 is:

eml(1, eml(eml(eml(1, eml(eml(1, eml(1, eml(1, 1))), 1)), eml(1, 1)), 1))

Yes, if one didn't already know that spherical excess is just ...

2026-04-08T09:42:36Z

In reply to nevent1q…69q4
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Yes, if one didn't already know that spherical excess is just a funny word for the area (on a unit sphere) it would be very confusing.

I can't immediately find a better link that describes the theorem; perhaps this from John D. Cook’s blog is a little more expansive: https://www.johndcook.com/blog/2025/11/08/heron-on-a-sphere/

Did you know that there's a spherical analogue of Heron's ...

2026-04-08T09:27:23Z

Did you know that there's a spherical analogue of Heron's formula? (TIL)

https://mathworld.wolfram.com/LHuiliersTheorem.html

I deleted mine some years ago, because its only function seemed ...

2026-03-26T14:08:12Z

In reply to nevent1q…hh9l
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I deleted mine some years ago, because its only function seemed to be to make it easier for unpleasant people to contact me for cynical reasons. But I appreciate it's a professional necessity for some people, and that I am fortunate not to need it.

I am sorry for your loss.

2026-03-26T13:55:33Z

In reply to nevent1q…d877
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I am sorry for your loss.

I wouldn't blame him if he couldn't: it looks incredibly ...

2026-03-26T08:41:55Z

In reply to nevent1q…t3kd
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I wouldn't blame him if he couldn't: it looks incredibly hard!

Wow, Penrose’s tetrahedron puzzle was a lot more complicated ...

2026-03-25T23:01:06Z

In reply to nevent1q…flng
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Wow, Penrose’s tetrahedron puzzle was a lot more complicated than I had imagined it to be.

https://www.youtube.com/watch?v=CD-21ytpCJU

Does this really work? I wish I had known when I were younger. ...

2026-03-21T21:32:20Z

Does this really work? I wish I had known when I were younger.

TIL. In April 1974, in the middle of the night, a small group of ...

2026-03-11T13:37:14Z

TIL. In April 1974, in the middle of the night, a small group of conspirators secretly installed a large tensegrity icosahedron made from discarded telephone poles on the campus of Twente University in the Netherlands.

It’s still there. People call it Het Ding (“the thing”).

https://www.utwente.nl/en/alumni/inspiring-alumni/ut-canon/stories/het-ding/

You can fill space with this shape, its mirror image, and some ...

2026-03-11T12:49:09Z

In reply to nevent1q…46kl
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You can fill space with this shape, its mirror image, and some small cubes.

Here’s another way to do it. This one would make a fine ...

2026-03-03T23:18:30Z

In reply to nevent1q…fqkp
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Here’s another way to do it. This one would make a fine paperweight!

https://skfb.ly/pH6VB

It would be fun to make a hinged model, so you can flip between all the different possible variations physically.

An unusual polyhedron whose dihedral angles are all right angles. ...

2026-03-02T22:51:46Z

An unusual polyhedron whose dihedral angles are all right angles. https://sketchfab.com/3d-models/orthogonalized-tetrahedron-c26dd2789da3406bbb00e5df769ade6d

In that case I'm even more inclined to think you'll like ...

2026-02-26T19:23:08Z

In reply to nevent1q…0h6m
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In that case I'm even more inclined to think you'll like it.

I have, and I expect that you would. It is well written, clever ...

2026-02-26T18:27:05Z

In reply to nevent1q…n79t
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I have, and I expect that you would. It is well written, clever and interesting.

It's quite frightening in parts. My wife had nightmares about it.

“In this paper we present work on enumerating all the ...

2026-02-26T11:57:39Z

“In this paper we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2,423,206 dodecahedra and 16,096,166 icosahedra.”

https://arxiv.org/abs/2602.20425

I have a counter-clockwise clock in my kitchen, which I was given ...

2026-02-25T01:41:24Z

In reply to nevent1q…7yrd
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I have a counter-clockwise clock in my kitchen, which I was given a few years ago. It's very rare for anyone to notice that there's anything unusual about it.

Thanks. I do like videos. I've just finished watching the ...

2026-01-04T13:18:47Z

In reply to nevent1q…aps6
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Thanks. I do like videos. I've just finished watching the first one, which was great.

I'm ok with a “bring your own motivation” text in this ...

2026-01-04T11:45:12Z

In reply to nevent1q…5nrj
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I'm ok with a “bring your own motivation” text in this case, because I already know why I want to understand this theory, and I just need someone who already understands it to lay it out carefully and correctly. But I will check out your lectures too!

It’s a subject I know less about than I feel I ought to, which ...

2026-01-04T01:27:08Z

In reply to nevent1q…pg70
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It’s a subject I know less about than I feel I ought to, which means I always feel vaguely guilty when it comes up. I am hoping a careful study of the book will correct that.

Imagine reading this if you didn't know what a reflection ...

2026-01-04T00:31:25Z

Imagine reading this if you didn't know what a reflection was.

(This is not a criticism, just a thought that amused me.)

If multiplication is commutative for the numbers in your ...

2026-01-01T22:15:33Z

In reply to nevent1q…chjl
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If multiplication is commutative for the numbers in your matrices, then you can do it in 21 multiplications according to https://arxiv.org/abs/1904.07683

A 58-Addition, Rank-23 Scheme for General 3x3 Matrix ...

2026-01-01T17:57:45Z

A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication https://arxiv.org/abs/2512.21980

I love this sort of explicit work. The algorithm fits in a screenshot:

A lovely new video from @npub10zc…tds5: ...

2025-12-30T15:53:49Z

A lovely new video from Henry Segerman (npub10zc…tds5): https://youtu.be/NEJZlGuWGV8

Stunning photography, as well as a fascinating mechanism.

That's only accessible to members of the University of ...

2025-12-22T17:50:50Z

In reply to nevent1q…nkeu
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That's only accessible to members of the University of Edinburgh; at least I _think_ that's what the error message is trying to tell me.

At last I have achieved my ambition of making all the stellations ...

2025-12-22T12:54:27Z

At last I have achieved my ambition of making all the stellations of the rhombic dodecahedron from my blocks

Incidentally, that's how we know that such a spaceship can ...

2025-12-04T10:36:13Z

In reply to nevent1q…7dvt
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Incidentally, that's how we know that such a spaceship can only move horizontally (i.e. along the line it occupies). Because the linear configuration is symmetrical in the vertical direction, it cannot possibly move vertically.

Funnily enough it was eating tapioca pudding, and wondering where ...

2025-12-03T15:11:59Z

In reply to nevent1q…ntul
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Funnily enough it was eating tapioca pudding, and wondering where such a peculiar word might have originated, that led me to this.

A language I had never heard of till just now turns out to be the ...

2025-12-03T13:29:18Z

A language I had never heard of till just now turns out to be the origin of the words tapir, toucan, coati, capybara, piranha, jaguar and tapioca.

https://en.wikipedia.org/wiki/Tupi_language

I would not have guessed this was possible! Vladan Majerech has ...

2025-12-03T03:54:22Z

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

I had a cool experience on Saturday night at MathsJam. Mike ...

2025-11-24T10:30:18Z

I had a cool experience on Saturday night at MathsJam. Mike Borcherds had brought a pile of 3D-printed puzzles for people to play with; and I recognised one of the puzzles in the pile as one I had designed!

(It was this one: https://sketchfab.com/3d-models/third-of-a-cube-assemblable-5c3e1b3550cf490b8c34c7aafc85e887, which we've talked about on here before.)

I'm missing some context for this conversation, but I was at ...

2025-11-24T04:46:19Z

In reply to nevent1q…48us
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I'm missing some context for this conversation, but I was at the talk you're discussing. The speaker said, IIRC, that the rationale for making credit cards that size has never been made public, but it's a reasonable guess that it's not a coincidence that you can fit exactly 4 × 4 on a sheet of foolscap.

is the author’s name joe

2025-11-23T20:38:00Z

In reply to nevent1q…v0zm
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is the author’s name joe

I'm tempted to update the location in my profile to ...

2025-10-07T13:04:22Z

I'm tempted to update the location in my profile to ‘somewhere in Idaho and uncontactable’, but I fear someone would take it literally.

Why on earth does this video already have so many low-effort ...

2025-10-03T07:05:16Z

In reply to nevent1q…gp20
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Why on earth does this video already have so many low-effort negative comments? How are those people coming across it?

Usually videos like this are only seen by people who are interested in the topic. Is the mighty YouTube algorithm advertising it to random people? Is it linked from some other popular website?

I enjoyed this talk from Kevin Buzzard, _Where is Mathematics ...

2025-10-03T06:52:02Z

I enjoyed this talk from Kevin Buzzard, _Where is Mathematics Going?_

https://www.youtube.com/watch?v=K5w7VS2sxD0

See section 3 of https://arxiv.org/pdf/2307.14769

2025-09-26T18:16:11Z

In reply to nevent1q…0qmd
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See section 3 of https://arxiv.org/pdf/2307.14769

One of his great-grandsons is Geoffrey Hinton, the ‘Godfather ...

2025-09-25T09:46:50Z

In reply to nevent1q…8rlv
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One of his great-grandsons is Geoffrey Hinton, the ‘Godfather of AI’.

I didn't know about Charles Howard Hinton. Interesting chap! ...

2025-09-24T18:25:19Z

I didn't know about Charles Howard Hinton. Interesting chap! I just discovered him via researching the etymology and origin of the word tesseract. (Turns out it was coined by Hinton, combining Greek words meaning ‘four’ and ‘ray’.)

He married George Boole's daughter Mary Ellen Boole, with whom he had four children. Unusually, he also married another woman concurrently, as a result of which he spent time in prison for bigamy.

https://en.wikipedia.org/wiki/Charles_Howard_Hinton

I'm indifferent to the specific behaviour you describe, but I ...

2025-09-16T08:46:49Z

In reply to nevent1q…fu55
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I'm indifferent to the specific behaviour you describe, but I sometimes have text in one app that I want to search for in a different app, and I like being able to do that very easily just by hitting ⌘E / ⌘⇥ / ⌘G.

I like it. It sounds like something an action movie hero might ...

2025-09-04T09:08:15Z

In reply to nevent1q…lnxt
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I like it. It sounds like something an action movie hero might say just before saving the world.

That's the most American thing I've ever heard.

2025-09-02T03:17:00Z

In reply to nevent1q…55cl
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That's the most American thing I've ever heard.

The paper does talk explicitly about why they crafted a new ...

2025-08-28T13:15:53Z

In reply to nevent1q…sapd
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The paper does talk explicitly about why they crafted a new polyhedron for the proof, even though they still believe the rhombicosidodecahedron to be non-Rupert.

A very interesting geometric model that Jeannine Mosely presented ...

2025-08-16T10:06:53Z

A very interesting geometric model that Jeannine Mosely presented at MOVES. Sadly I can't find anything about it online.

It's a hinged chain, alternating between 12 pentahedra and 12 tetrahedra, that can be folded into either a regular dodecahedron or a rhombic dodecahedron.

Interesting: they all decode ok on my iOS phone. I wonder ...

2025-08-16T09:30:47Z

In reply to nevent1q…npd0
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Interesting: they all decode ok on my iOS phone. I wonder what's different.

I think he said that he predicted 8 years ago that it would be ...

2025-08-11T20:49:10Z

In reply to nevent1q…2yz7
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I think he said that he predicted 8 years ago that it would be resolved within 5 years using control theory, which I assume is a reference to https://arxiv.org/abs/1703.01352

No, it's still open! He did say a little sadly that it has ...

2025-08-11T20:47:32Z

In reply to nevent1q…a6rz
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No, it's still open! He did say a little sadly that it has proved harder to resolve than he hoped it would be.

Thomas Hales at MOVES is showing @npub12cu…d38p’s animation ...

2025-08-11T20:39:59Z

Thomas Hales at MOVES is showing Greg Egan (npub12cu…d38p)’s animation of Reinhardt's smoothed octagon from John Carlos Baez (npub1nf4…nqe4)’s blog.

Here is the promised animation. ...

2025-07-29T06:14:38Z

In reply to nevent1q…sgg0
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Here is the promised animation.

I’m hoping that it’s actually possible to physically assemble ...

2025-07-29T06:09:54Z

I’m hoping that it’s actually possible to physically assemble three of *these* into a cube. https://skfb.ly/pzCW9

I don’t currently have the means to physically test this, but it looks plausible in the animation I made, which I’ll attempt to share in a followup post.

I think it’s at least mildly surprising that three of these can ...

2025-07-28T04:08:51Z

I think it’s at least mildly surprising that three of these can be combined into a cube. https://skfb.ly/pzByn

Oskar van Deventer has a new video where he demonstrates his ...

2025-07-19T09:39:36Z

Oskar van Deventer has a new video where he demonstrates his ‘Bolts Cube’ puzzle: an evolution of the Bolts Loop that we have been talking about, but this time based on an 8-bar linkage.

https://youtu.be/M4xVaBqg-8U

There’s a nice mathematical question here from Oskar van ...

2025-07-14T21:12:38Z

There’s a nice mathematical question here from Oskar van Deventer: what is the correct shape for the spiral grooves in this puzzle he designed?

(He was forced to use an approximation in the puzzle as made.)

https://www.youtube.com/watch?v=EHqqXBqckjs

I find it very hard to visualise the motion that’s taking place here! I’d never even heard of Astrolabacus before.

Having a 3d printer in the house is forcing me to reckon with the ...

2025-07-08T21:28:12Z

Having a 3d printer in the house is forcing me to reckon with the question ‘How many dodecahedra do I need, really?’.

> Are these the only two meeting some nice constraints, or are ...

2025-07-06T15:04:29Z

In reply to nevent1q…caz0
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> Are these the only two meeting some nice constraints, or are there more?

Yes, I believe these are the only two convex dodecahedra whose faces are congruent rhombi. That belief of mine is based on this article of Grümbaum https://faculty.washington.edu/moishe/branko/BG285%20Bilinski%20dodecahedron.pdf

It stands in roughly the same relation to the normal rhombic ...

2025-07-06T08:22:55Z

In reply to nevent1q…uar5
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It stands in roughly the same relation to the normal rhombic dodecahedron as US paper does to international standard paper: it's made from rhombuses whose long diagonal is ϕ times the short diagonal, whereas the normal rhombic dodecahedron is made from rhombuses whose long diagonal is √2 times the short diagonal.

It was (re)discovered in 1960 by a chap called Stanko Bilinski. ...

2025-07-06T08:15:54Z

In reply to nevent1q…a2mx
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It was (re)discovered in 1960 by a chap called Stanko Bilinski. https://en.wikipedia.org/wiki/Bilinski_dodecahedron

Did you all know that there is a SECOND rhombic dodecahedron ...

2025-07-06T08:14:42Z

Did you all know that there is a SECOND rhombic dodecahedron whose faces are all congruent rhombuses, that is less symmetrical than the normal rhombic dodecahedron?

Building a monostable tetrahedron ...

2025-06-25T20:01:46Z

Building a monostable tetrahedron https://arxiv.org/abs/2506.19244

Do you think most laypeople would regard “these shapes as ...

2025-06-15T14:11:29Z

In reply to nevent1q…kp2k
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Do you think most laypeople would regard “these shapes as identical” as true if one were a uniformly scaled copy of the other?

(If not, what do we call that? My schema would suggest ‘simila’, of course.)

There really should be a word for when two geometric objects are ...

2025-06-15T13:54:24Z

There really should be a word for when two geometric objects are related by a direct (positive) isometry – i.e. they're actually the same size and shape, not mirror images of each other.

I sometimes say ‘congruent’, but technically that includes mirror images as well, so isn't what I really meant.

If there really isn't a word for this, can I propose ‘conguent’ – i.e. congruent without the (r)eflections?

This has the added benefit that it will give copy editors the heebie-jeebies.

I made a book of ten thousand times no, and it’s only 13 pages ...

2025-06-15T11:53:57Z

In reply to nevent1q…qvtv
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I made a book of ten thousand times no, and it’s only 13 pages long, which is shorter than I would have guessed. I can’t share PDFs on here, so here are the first two pages. You can imagine the rest.