Gerard Westendorp

I "find" this a bit strange.
The letter combination "fi" is somehow displayed in a funny way
in my feed (been like that for a long time)
https://media.mathstodon.xyz/media_attachments/files/115/974/939/646/650/845/original/2c94343968c74f78.png

2026-01-24 23:03:44 UTC

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@nprofile…zl3j Wow, that is a cool new hinged polyhedron concept! I haven't fully processed this idea yet, but it seems to open up some new possibilities!

2026-01-10 11:35:28 UTC

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@nprofile…5ccq
I once made this web site on "space-time triangles", triangles in (1+1) dimensional space
https://westy31.nl/SpaceTimeTriangles/Space_Time_Triangles.html
This sheds light on the twin paradox.
But also, concepts like sum of internal angles = 180 degrees continue to work.
https://media.mathstodon.xyz/media_attachments/files/115/870/579/261/879/203/original/b4409918d1b0192b.png

2026-01-10 11:22:58 UTC

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@nprofile…u6vt @nprofile…hmdu @nprofile…4hp5
There is the Rayleigh dissipation function:
https://en.wikipedia.org/wiki/Rayleigh_dissipation_function
But when you switch from Lagrangian to Hamiltonian view point with dissipation, you get a Hamiltonian that is not time independent.
OK, that is also possible, but the advantage of using Lagrangian and Hamiltonian methods becomes less obvious in that case.

2026-01-10 11:08:40 UTC

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@nprofile…5ccq
Yes, but in the reference frame of the running person, it is the person in the chair that appears to move slower into the future. The twin paradox.
To resolve the twin paradox, you need to consider which observer turns round so that the 2 can compare their clocks at the same place.

2026-01-08 11:19:29 UTC

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@nprofile…u6vt @nprofile…hmdu @nprofile…4hp5
Well, friction is related to generating entropy, so you could add some extra degrees of freedom that represent entropy. You could then pretend that you do not know exactly the state of these extra degrees of freedom, you just know the average energy. You could study how the energy is initially primarily in some "macroscopic" degrees of freedom, but then over time transfers that to the microscopic degrees of freedom.

2026-01-07 16:15:24 UTC

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@nprofile…4hp5 @nprofile…hmdu
It gets a bit trickier with friction though. A particle falling through a viscous fluid reaches a constant momentum when the force of gravity equals the friction.

2026-01-06 16:52:39 UTC

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@nprofile…ck2y
Pretty good approximation.
https://media.mathstodon.xyz/media_attachments/files/115/849/186/708/830/928/original/111dab41e08e7340.jpg

2025-12-27 22:53:04 UTC

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@nprofile…8eua
I have to admit I don't hear the difference between the Turkish, Persian and Arabic quarter tones, which in certain tuning traditions are subtly different. But that may be a matter of practice.
2 years ago I started singing, it is significantly increasing my awareness for these things, so maybe I will learn it still.
You might like the channel of Peter Pringle, he brings to life ancient instruments and songs, like this song in ancient Sumerian:
https://www.youtube.com/watch?v=QUcTsFe1PVs

2025-12-27 12:20:12 UTC

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@nprofile…8eua @nprofile…5gem
In "Eastern" music (Arabic, Persian, Turkish) they also have quarter tones:
https://en.wikipedia.org/wiki/Quarter_tone
It sounds a bit like these notes are deliberately out of tune. A musician on Youtube explains this is done to create a certain mood called a "Maqam"
https://www.youtube.com/watch?v=ZLbQcs3W0Bs
I am certainly not an expert on this, but it is cool when a real expert is passionate about it.

2025-12-23 17:55:05 UTC

Pick's theorem "knows" Pythagoras' s theorem. According to Pick's theorem, the area of a polygon with vertices on a square grid is given by the number of grid points:
Area =
[interior points] +[border points]/2 -1
https://media.mathstodon.xyz/media_attachments/files/115/770/149/195/207/616/original/fd4dcf3e3ec44754.jpg

2025-12-23 16:30:27 UTC

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@nprofile…pwph
Hmm, that calls for an illustration.
Took a bit more time than I planned...
https://media.mathstodon.xyz/media_attachments/files/115/769/823/809/045/569/original/af5ed6a9c21fdff8.jpg

2025-12-20 22:25:25 UTC

Got some laser-cut Klein Quartics. Mainly Christmas presents.
https://media.mathstodon.xyz/media_attachments/files/115/754/233/497/343/375/original/535352f98e1abf83.jpg

2025-12-17 13:21:05 UTC

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@nprofile…yg3j
I thought the 5 ring puzzels was a dodecahedron, having 5-symmetry, and 20 vertices. But I was surprised: It is a polyhedron wit 6 squares, 12 triangles and 4 pentagons. It has 20 vertices. It seems to be a near-miss Johnson solid, probably the pentagons are slightly non-planar.
https://media.mathstodon.xyz/media_attachments/files/115/735/088/232/983/694/original/95def8d0830e8ffb.jpg

2025-12-17 10:34:45 UTC

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@nprofile…yg3j
I found the "Golden trick", which suddenly makes puzzle becomes easy!
Finding such an insight is what makes the puzzle interesting, and the existence of the insight makes the puzzle a good puzzle.
https://media.mathstodon.xyz/media_attachments/files/115/734/437/097/043/311/original/6d075f13b162eec3.gif

2025-12-15 09:45:25 UTC

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@nprofile…pwph Similar in Dutch: Eergisteren, Overmorgen.

2025-12-15 00:03:44 UTC

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@nprofile…yg3j Aha, nice.
I did 3 octahedron (3 rings) with algebra. Now I will try the docecahedron (5 rings) hopefully without algebra, using the patterns found from the octahedral case)

2025-12-10 14:11:21 UTC

Lately, I have been making some graphs of N-simplices, they have all vertices on a circle. I was wondering what graphs of the Platonic polyhedra would look like, if you put all vertices on a circle. Well, below an answer.
Actually, there are more than 1 ways to do it. The dodecahedron and icosahedron do not have the same "connectivity" (the number of points on the circle they skip to per edge) for each vertex. I tried to find a way to solve this. It turns out the icosahedron and dodecahedron have a Hamiltonian path (didn't know that!), which would correspond to each vertex being at least connected to its 2 neighbors on the circle.
But these Hamiltonian paths also do not lead to a "symmetric" graph. Maybe it is not possible...
https://media.mathstodon.xyz/media_attachments/files/115/695/615/512/592/098/original/8b66afaef2284631.mp4

2025-12-03 22:28:47 UTC

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@nprofile…up6l Indeed, I also only just read that Bosman was apparently the inventor of the Pythagoras tree.

2025-12-03 10:36:44 UTC

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@nprofile…82pn
Hmm, don't know about the dots.
Maybe you could personalize them by putting faces on them.
https://media.mathstodon.xyz/media_attachments/files/115/655/187/482/457/102/original/9cf52f2c5e00a271.gif

2025-12-02 21:46:42 UTC

One of the things I saw on " Ars et Mathesis" day, Masterdam nov 25, were these 3D printed " coral" lamps by Maarten Lemmens. You can print them in "vase mode", a single spiraled line.
https://media.mathstodon.xyz/media_attachments/files/115/652/150/622/145/032/original/284b19d06b329001.jpg

2025-12-02 21:00:46 UTC

Another inspiration I got from Bosman's book is "ellips construction from 2 points". You take 2 points, and construct concentric circles around each, with integer diameters. The you can connect the intersections to form ellipses. You can also form hyperbola if you interconnect the other vertices in each mesh. By using straight lines instead of circles for 1 of the points, you can construct parabola's.
Unlike me, Bosman did not have a computer to make the pictures, it was pre-1960, so all this was with pen and pencil. He called these drawings " beschouwing van 2 punten", roughly translats as view/consideration of 2 points.
https://media.mathstodon.xyz/media_attachments/files/115/651/950/611/863/347/original/1b903b3846eafa93.gif

2025-12-02 20:46:09 UTC

One inspiration I got from Bosman's book is "generalized Yin Yang". You can subdivide the circle into part parts that have both equal area and equal circumference. The lines defining the subdivisions are all circle segments with integer relative diameters.
The Yin Yang is a powerful symbol. The rainbow is also often used these days to symbolize diversity. I was quite pleased with the possibility of combining these 2 concepts.
https://media.mathstodon.xyz/media_attachments/files/115/651/892/551/767/990/original/bdfa0b90ce096c83.gif

2025-12-02 20:35:49 UTC

I got myself a nice laser engraved 24-simplex for my round table. By chance, I also just bought a book with a very similar image on the front cover. The book is about the work of Albert Ernst Bosman (1891-1961). Het was a friend of Escher, lived just across the street from him. Like Escher, he made lots of mathematically interesting drawings. But unlike Escher, he did not sell them. Instead, many of his drawings were slowly decaying in his old home. Until his grandson Fernand Bosman decided to get the drawings restored and published. The result is a very interesting book. I will do some posts inspired by the book.
I got the book on "Ars et Mathesis" day in Amsterdam last month. It turns out I knew Fernand Bosman from Delft university, we had a couple of adventures together...
https://media.mathstodon.xyz/media_attachments/files/115/651/824/592/530/605/original/a0c89da3fc916cbc.jpg

2025-11-14 15:22:13 UTC

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@nprofile…qenv I am thinking, where does the angular momentum go to, when tidal locking occurs?
Hmm, after a while, I realized this must of course be on Wikipedia...
The distance between the body increases.
According to Wikipedia, Pluto and Charon are actually in " Mutial tidal lock"

2025-11-07 00:24:02 UTC

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@nprofile…8eua
I also like the play "Copenhagen", about Heisenberg an Bohr meeting during the war. I saw it once in a theatre. There is a Youtube clip featuring the author of the play:
https://youtu.be/PPI6Hl6V8Sk

2025-11-06 00:19:31 UTC

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@nprofile…8eua The book "The making of the atomic bomb" has quite an extensive account on the correspondence between Meitner, Hahn, Frisch. Meitner had already fed to Sweden, but continued to correspond with Hahn about his experiments with bombarding Uranium with neutrons, asking for her opinion. Frisch and Meitner were hesitant, but then Frisch talked to Bohr, who immediately bought the idea that the bombarding neutron triggered the fission.

2025-11-01 14:36:38 UTC

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@nprofile…pklh Hmm, I wonder how this looks like for the limiting case of the sphere.

2025-10-20 21:56:27 UTC

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@nprofile…ma9f Interesting. I actually cancelled my subscription because of it. I was already less enthusiastic after Krugman left.
I suspect it is not political. They just think "ordinary people" on the street are not interesting.

2025-10-02 18:20:42 UTC

Frans de Waal, chimpansee expert, who wrote a lot of interesting stuff about our them, almost never went into a cage with a chimpansee except famously as described in his book "Mama's last hug", with a dying female chimp. He said they could be dangerous.
Interestingly, Jane Goodall seemed to have a lot less trouble with that.
(This is not meant as a criticism of either)

2025-06-20 12:09:54 UTC

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@nprofile…yu7x Of course, the answer could be "We don't know". But still interesting to think about.

2025-06-20 12:05:48 UTC

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@nprofile…yu7x I am not necessarily trying to prove anyone wrong, just thinking if a cosmology without energy conservation could correspond to physical reality. In the example you gave, you show is possible mathematically, but could our universe be like that, ie not have conserved energy?

2025-06-20 10:30:36 UTC

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@nprofile…yu7x Hmm, I guess if you describe them with an Action that is explicitly time dependent, then you can't use Noether's theorem involving time-shift symmetry. But I feel that nature is not like that. If space-time expands, it should be because of some local field, so that the action is not explicitly time dependent.

2025-06-20 10:13:51 UTC

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@nprofile…yu7x Cool!
Is there some way of including an energy term of space-time itself, such that the total energy of the universe remains constant?

2025-06-16 18:28:14 UTC

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@nprofile…fa4k
Hmm, if a super-AI would need a lot of power, that could motivate it to get rid of humans, who use up a lot of power. On the other hand, it might not be in a hurry, assuming it could keep itself "alive" for a couple of million years.

2025-06-01 11:41:40 UTC

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I like the way the slicer sliced this print. (22 hours to print)
https://media.mathstodon.xyz/media_attachments/files/114/607/914/937/765/887/original/27b5a7feee3bc3de.jpg
https://media.mathstodon.xyz/media_attachments/files/114/607/914/938/633/846/original/26c90d015498ec5c.jpg

2025-06-01 09:09:42 UTC

A Cube tree.
A 3D version of the Pythagoras tree.
https://media.mathstodon.xyz/media_attachments/files/114/607/315/294/911/661/original/401b9ff8f9e1605e.mp4

2025-05-24 22:39:09 UTC

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@nprofile…q8c7
Aha, think I got something. You can tile the plane with both the original quad, and the sub quads.
https://media.mathstodon.xyz/media_attachments/files/114/565/203/631/864/562/original/34035f286e019aa1.jpg

2025-05-24 09:48:13 UTC

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@nprofile…umph @nprofile…cfz8 @nprofile…5rpe
I tried warping higher genus uniform polyhedra into mult-holded doughnuts. I only succeeded for the Octahemioctahedron, which has genus 1.
But an easier project would be to warp the hyperbolic fundamental polygon into the polyhedron. "Easy" in principle, but quite a bit of work.

2025-05-17 10:08:41 UTC

“Lord of the Rings”, “Star Wars”, and “Harry Potter” are 3 fantasy worlds that seem to me to have striking similarities. I put an “equivalence table” in the picture.
But I have notice that the fan-bases of these 3 words are often quite disjoint. I wonder how widespread this phenomenon is. So I thought I’d try a poll. (It is my first poll.)
Unfortunately, I can’t seem to put a picture and a poll in one post. *So I put it in a reply* Also, the poll has a max number of 2 options, I would have like to have used 8.
https://media.mathstodon.xyz/media_attachments/files/114/522/616/163/243/998/original/e13e4c8d66fb6c0b.jpg

2025-05-12 00:18:02 UTC

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@nprofile…fa4k Some of the articles talk about "increased electrical conductivity". If there is conductivity, then there is energy consumption. In the video you see rotation, but also translation.

2025-05-11 13:58:52 UTC

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@nprofile…fa4k I once forced a mid day nap on a child that I was baby sitting 2X per week. The first time, he cried for at least an hour (made me doubt my idea...) The second time, he cried for 5 minutes. The third time, he asked if he could go for a nap.

2025-05-08 09:02:46 UTC

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@nprofile…fa4k I can imagine that if you take the Fourier transform of the pattern, (for a dot you have to use something like a gaussian), then you can get some insight.
The case that is "uniform" in space, is less unform in Fourier space. It will have a wavelength peak near the average distance between dots.

2025-05-04 21:36:53 UTC

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@nprofile…5rpe Reminds me a bit of @nprofile…fa4k recent post on atomic nuclei that spin themselves to death.

2025-05-04 21:33:14 UTC

My new 3D printer is good. I wanted to print a kind of Seifert surface, (a surface bounded by a knot) but in the first try, the surface was so thin it printed just the knot.
https://media.mathstodon.xyz/media_attachments/files/114/451/686/120/830/293/original/a6d02bb17935dc4c.jpg

2025-05-01 13:28:16 UTC

I rolling 3 D printed Hopf link. Actually, a ruled surface generated from a Hopf link.
This is related to to a so-called Oloid, a shape that when rolled, has the property that all points touch the ground exactly once per roll, and the center of mass sys constant during rolling. Such an Oloid would be the union a 2 of these Hopf links.
https://en.wikipedia.org/wiki/Hopf_link
https://en.wikipedia.org/wiki/Oloid
https://media.mathstodon.xyz/media_attachments/files/114/432/779/700/173/421/original/8d98798acb0a9a93.mp4

2025-04-24 05:36:01 UTC

One small leap for Woman,
one giant free fall for Womankind
https://media.mathstodon.xyz/media_attachments/files/114/391/314/740/218/308/original/c51ad41fbd22a400.jpg

2025-04-18 17:09:07 UTC

I got myself a new maxwell equation circuit equivalent shirt, embroidered version.
https://westy31.nl/Electric.html#Maxwell
I am planning to do some new work on this subject.
https://media.mathstodon.xyz/media_attachments/files/114/360/066/885/690/581/original/4d82cd94991fd2f8.jpg

2025-04-08 07:59:11 UTC

The set of 30 possible dice. Together with the 24 ways of orienting each die, they form the 30X24=720 elements of S6, the group of permutations of 6 objects. I posted a couple of other pictures relating to this lately.
There is a nice weblog by Peter Cameron on this:https://cameroncounts.wordpress.com/2010/05/11/the-symmetric-group-3/
He writes that he used to have a set of 30 dice like this, but lost them.
The arrangement of the dice has some special properties:
In each row and column, each opposite pair occurs once and only once. This means that the rows and columns are “synthematic totals”, as Peter Cameron explains.
The dice on opposite sides of the diagonal are mirror images.
https://media.mathstodon.xyz/media_attachments/files/114/301/196/073/626/284/original/d71cb623c111d790.gif

2025-04-07 10:10:43 UTC

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@nprofile…fa4k @nprofile…yu7x
While trying to better understand the relationship between the Cremona Richmond configuration and the Tutte Coxeter graph, I noticed that in the Tutte Coxeter graph, there is an obvious trajectory that passes through all duads twice: going round the large circle. But in the Cremona Richmond configuration, this doesn’t work. So I made a 3D version of it, in which you can follow the same trajectory in Cremona Richmond as in Tutte Coxeter.
As you can check, it works.
I was hoping to get something with a higher “Aha factor”. But I’ll post it anyway. The Tutte Coxeter graph image is by @nprofile…yu7x

2025-04-03 15:35:38 UTC

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@nprofile…paff
Sounds cool!
https://media.mathstodon.xyz/media_attachments/files/114/274/763/546/807/562/original/ee6513439957966a.png

2025-04-03 10:58:15 UTC

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@nprofile…fa4k @nprofile…yu7x
Now for the relationship with the Tutte Coxeter graph. I've printed the "synthemes" (triplets of duads) on triangles, with the mirror image on the back. So I can "Triomino" a labeling of the Tutte Coxeter graph. I've convinced myself that laying down 2 adjacent synthemes conpletely fixes the labeling. Makes sense, there are 720 ways of doing that, and 720 inner automorphisms of the graph.
https://media.mathstodon.xyz/media_attachments/files/114/273/632/953/793/240/original/e898c8dadb604a19.jpg

2025-04-02 09:11:18 UTC

I want to understand group theory a bit better, so I’ll be making a couple of pictures. One statement that sparks curiosity is “The only symmetric group (all permutations of N elements) that has an outer automorphism is S6.” @nprofile…fa4k and @nprofile…yu7x have already made some cool picture about this at:
https://blogs.ams.org/visualinsight/2015/08/15/tutte-coxeter-graph/
Here is an animated version of the Cremona Richmon configuration. Each point is a permutation of a pair of numbers between 1 and 6. Each of the 15 points is in a unique combination of 3 of the 15 lines. Each of the 15 lines has a unique combination of 3 points. Also, dual to the 6 numbers, there are 6 “synthematic totals”, sets of 5 disjoint lines. The 5 thick lines represent one such total, it can be rotated to produce 4 more. The 6th one is the set of all green lines.
More to come...
https://media.mathstodon.xyz/media_attachments/files/114/267/569/199/275/167/original/369136dd301226c6.mp4

2025-04-01 13:27:23 UTC

This sowing thread winding carton is interesting. We CAN divide the circle in 48 positions, 24 "teeth" with 2 sides. the "winding rule" is (-1,17,-1,19,-1,17). These 6 moves advance the thread by 2 positions, or 1 tooth. The position is periodic after 48 lines, but the entire line pattern is only periodic after 3*48 = 144 lines.
https://media.mathstodon.xyz/media_attachments/files/114/262/887/144/082/832/original/639906397e6a895c.png

2025-03-26 08:44:45 UTC

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@nprofile…puk6 Looks a bit like he surface of the sun. Maybe the rules of your model have some relation to magneto hydrodynamics.

2025-03-09 23:52:18 UTC

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@nprofile…qe76 @nprofile…8fmq
Got one too!
https://media.mathstodon.xyz/media_attachments/files/114/135/158/803/839/524/original/f377197fa4593bfd.jpg

2025-02-24 19:00:33 UTC

Interesting correlation between region and voting result in the German election.
https://media.mathstodon.xyz/media_attachments/files/114/060/391/693/235/486/original/e05152fc307bcfec.png

2025-02-23 10:30:11 UTC

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@nprofile…khyw @nprofile…32va
Als je het helemaal doortrekt, 3000 puzzels van 1 stukje zijn direct af.

2025-02-22 18:23:45 UTC

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@nprofile…fqqu
I actually played rugby for about 1 or 2 years long ago, but I was not very good...

2025-02-22 17:27:45 UTC

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@nprofile…yajh @nprofile…fqqu @nprofile…q8c7
I tried to make pictures of the generalization of the modular group resulting from replacing integers by Gaussian integers.
Made a website on it:
https://westy31.nl/ComplexFarey/ComplexFarey.html
https://media.mathstodon.xyz/media_attachments/files/114/048/704/463/172/297/original/36a236946f6c99a0.png

2025-02-22 17:10:39 UTC

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@nprofile…yajh @nprofile…fqqu @nprofile…q8c7
I remember reading that the failure of unique factorization into primes for Gaussian integers led to some failed proofs of Fermat's Last Theorem by reasonably famous mathematicians.

2025-02-09 22:47:48 UTC

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@nprofile…fa4k @nprofile…p3dv
I like also the Mathpages article on Noether's theorem:
https://www.mathpages.com/home/kmath523/kmath523.htm
After reading it, I thought *now* I get it!

2025-01-26 01:47:10 UTC

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@nprofile…3yjd
Check out this Youtube talk for a cool explanation:
https://www.youtube.com/watch?v=5q_sfXY-va8

2025-01-26 01:22:49 UTC

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@nprofile…3yjd You probably know this, but he also proved that the surface of the sphere equals the surface of the enclosing cylinder (not including the top and bottom, ie \( 4 \pi r^2 \)

2025-01-26 01:13:16 UTC

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@nprofile…6nz9 Thanks,
I should learn more about projective geometry.

2025-01-25 18:53:09 UTC

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One reason I was interested again in these polyhedra, was that i want o make a few more animations like this one. Showing how a self-intersecting uniform polyhedron can have a genus larger than zero.
(This was an old Goolge plus post https://westy31.nl/SalvagedGooglePlus/SalvagedGooglePlus_Part1.html)
https://media.mathstodon.xyz/media_attachments/files/113/890/478/853/212/126/original/1343d144a330c14e.mp4

2025-01-25 18:42:24 UTC

This Uniform polyhedron, the Tetrahemihexahedron, is a bit strange. It has Euler characteristic 1, so it kind of has genus (-1/2). It is the only uniform polyhedron with an odd Euler characteristic. Also the only one with an odd number of sides (7). Well OK, apart from the odd prisms. It is non-orientable, like a Klein bottle.
You could see the 4 squares as forming 3 pyramid shape dents. If you consider the polyhedron *composed* of those pyramid dents instead of squares, then the shape is just an ordinary orientable surface with Euler characteristic 2, like the cube. In fact, I folded them like that for easy assembly, the printed side is always on the visible side of the surface.. But when you follow a square as it intersects an other square, you see that it flips orientation.
https://media.mathstodon.xyz/media_attachments/files/113/890/379/199/495/845/original/a0b2f7b74b3ddf27.jpg

2025-01-19 12:28:10 UTC

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@nprofile…fa4k Another thought: Viruses are like computer viruses: The do not copy themselves to other computers, they *get* copied. Computers do things, they need free energy. But viruses are just passive code.

2025-01-19 12:08:39 UTC

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@nprofile…fa4k Well, I think you can have a jar with fluid, containing viruses, that is in thermal equilibrium. I remember a talk I listened to once, in which they described how they changed the pH of the fluid, the viruses discarded their protein capsule (probably this has some technical name). They changed the pH back, and the protein capsules reformed. So they switch between 2 equilibria.
But when viruses interact with other life, there is no longer (global) equilibrium, although if you imagine a box around the virus, you could argue that this box is in equilibrium during the time that no matter or energy is passing through the box boundary.
You could say "a virus injects itself in a cell", but actually it is the cell that is doing the work.

2025-01-19 00:43:30 UTC

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@nprofile…fa4k Viruses are actually in thermal equilibrium, the don't "do" anything.
Some people go to Tbilisi, Georgia to get bacterial infections treated by special viruses:
https://en.wikipedia.org/wiki/Phage_therapy

2025-01-11 13:32:34 UTC

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@nprofile…p7w0 I'm tempted to make one with Rubic cubes, that are transforming while moving.
But that would be quite a bit of work...

2025-01-11 13:30:55 UTC

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@nprofile…p7w0 Nice!
I was confused at how the number of cubes per edge seems to change from 8 to 7. But of course, it is always 7, except I double count the corners when they are all aligned.

2024-12-31 12:07:03 UTC

I made this animation with the online tool by @nprofile…m6g0, (https://hcschuetz.github.io/polyhedron-star/dist/) following up on the thread by @nprofile…fa4k
This one is a near-miss Johnson solid, the hexagons are folded through the middle by about 10 degrees.
It turns out this figure is actually a compound of 2 triangular prisms, 6 square pyramids, and 3 tetrahedra. So I was able to look up the exact bend angles. ("autobend" feature was still having some trouble, but that could be because i did something wrong)
https://media.mathstodon.xyz/media_attachments/files/113/747/321/305/807/766/original/763fc07111e0740b.mp4

2024-12-29 23:06:12 UTC

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@nprofile…m6g0
It is quite possible I made a mistake!
I sent the input file to:
https://github.com/hcschuetz/polyhedron-star/discussions/1

2024-12-29 16:15:23 UTC

@nprofile…m6g0 :
I had a go at trying you program. Managed to do the hexagonal prism. The "autobend" feature had some difficulty here, but all angles are easy to calculate manually in this case.
https://media.mathstodon.xyz/media_attachments/files/113/736/975/242/467/227/original/90651f563a6809bf.png
https://media.mathstodon.xyz/media_attachments/files/113/737/001/619/223/024/original/382c656f262fb663.png

2024-12-28 12:37:18 UTC

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@nprofile…yg3m @nprofile…qmju
An easy example: Suppose in the year 3000, nobody has friends, except Santa Claus. So everybody except Santa has 1 friend, and he has millions. So the average number of friends of your friends is hugely larger than than your own number of friends.

2024-12-23 14:50:03 UTC

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@nprofile…m6g0 @nprofile…fa4k
Ah, nice!
I was thinking about making something like that, but no time to do it...
I'll take a good look at it!
https://media.mathstodon.xyz/media_attachments/files/113/702/679/005/664/485/original/76266effbec26a49.jpg

2024-12-03 07:52:40 UTC

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@nprofile…zccc @nprofile…fa4k
I suspect you can prove generalizations of Pick's theorem by induction: You "glue" together disjoint shapes that already satisfy Pick. You could create an abstract concept of "move", as any operation that preserves all the numbers in the Pick formula. The "minus 1" term should be generalized to "minus number of disjoint objects".
Maybe even generalize to higher dimensions, defining volumes etc.

2024-12-03 00:19:24 UTC

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@nprofile…fa4k Right! I guess you know Pick's theorem? There is probably a version of that on a triangular grid too.

2024-12-02 23:58:04 UTC

I am still playing around a bit with the "Thurston Polyhedra" following the recent discussion started by @nprofile…fa4k, I made a tetrahedron on a square grid. I was surprised that the tetrahedron was tiled exactly by 14 squares. Thinking about it further, I realized that a tetrahedron made from congruent triangles admits sets of parallel geodesic loops of the same length. On the sphere, this is impossible: Latitude lines are not geodesics, and longitude lines intersect at the poles.
https://media.mathstodon.xyz/media_attachments/files/113/585/902/212/831/458/original/23fadca83fb826d6.jpg

2024-11-25 08:35:59 UTC

I realised cycling to my work, after I wrote the post, that the electron would appear to freeze on the event horizon because of time dilation.
So the change from black hole to white hole would appear to take infinitely long to a distant observer.

2024-11-25 08:31:19 UTC

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@nprofile…fa4k @nprofile…e5g0 @nprofile…yu7x @nprofile…cnse @nprofile…j7pr
But wait: The electron would would appear to "freeze" on the event horizon, because of time dilation.

2024-11-25 06:55:58 UTC

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@nprofile…fa4k @nprofile…e5g0 @nprofile…yu7x @nprofile…cnse @nprofile…j7pr
Hmm, I don't understand the diagram yet, but I am puzzled by the fact that time reversal symmetry appears to be broken: You can fall into a black hole, but the time reverse of that would be forbidden.
In practice, time reversing a rocket would violate thermodynamics, but an individual particle like a single electron does not have entropy. So if it can go into a black hole, why can't it go out in the time reverse of how it went in?

2024-11-20 01:06:54 UTC

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Impressive fold work by Henk van der Vorst
https://media.mathstodon.xyz/media_attachments/files/113/512/597/921/190/869/original/8013aa20a765b78b.jpg

2024-11-20 01:01:19 UTC

Last Saturday I was at the Mathematics & Art day "Ars et mathesis" in Eindhoven. I’ll post about a couple of nice things I saw/learned.
The first is about the so-called “Plastic ratio”. It is a bit like the Golden ratio, instead of the solution to \(x^2 = x+1 \) it satisfies \(x^3 = x+1 \); it is about 1.43. Instead of the Fibonacci numbers you have the Padovan numbers, whose recurrence relation is \( n_i = n_{i-2} + n_{i-3} \) .
I figured out how to do a spiral of squares whose sized as the Padovan numbers, similar to the Fibonacci-Golden Ratio spiral.
The Plastic ratio is used in Architecture.
Wikipedia: https://en.wikipedia.org/wiki/Plastic_ratio
https://media.mathstodon.xyz/media_attachments/files/113/512/493/249/109/581/original/ea3fa893c9e8b01e.jpg

2024-11-07 23:22:37 UTC

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@npub1pyk…cthf In Dutch 'snurk' means 'snore'.

2024-11-07 23:02:12 UTC

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@npub1tmp…ydrh She was often on Dutch TV during covid, staying calm in spite of all kinds of death threats. Seems

2024-11-07 22:37:12 UTC

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@npub1tmp…ydrh
You could try Marion Koopmans:
https://www.erasmusmc.nl/nl-nl/research/researchers/koopmans-marion

2024-11-07 18:53:52 UTC

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@npub1knz…c73p I read recently that optimists know that life sucks, while pessimists painfully rediscover it every day.
That's a joke of course...
We should do our best to do as little damage to our planet as possible.

2024-11-07 18:42:54 UTC

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@npub1knz…c73p By, then we will have created some smart AI robots that don't mind these temperatures.

2024-06-27 06:18:43 UTC

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@npub150e…rrqv Well, what I did was not so fancy. First I did all {a,b,c,d} from 1 to N. But then as N gets large, this gets out out of hand. So I used a slightly better method by assuming a>=b>=c>=d, and also a*b*c*d <Max, where Max is about 15000. Then it takes a could of minutes in VBA.

2024-06-26 22:50:58 UTC

Found a reference and a mistake in my list.
The reference:
https://oeis.org/A027563
The largest number is now 52061=79*659
I post the new list, and a graph.
https://media.mathstodon.xyz/media_attachments/files/112/685/329/420/451/064/original/114ef2db5c308a14.jpg
https://media.mathstodon.xyz/media_attachments/files/112/685/363/226/598/113/original/8504a6d684c8fd87.jpg

2024-06-23 20:41:23 UTC

A uniform tiling that fold-transforms into another uniform tiling,
https://media.mathstodon.xyz/media_attachments/files/112/667/866/826/318/452/original/cdf8a9676cb5a5e4.mp4

2024-04-26 13:16:51 UTC

A rigidly foldable tessellation, based on the "square twist". Square twists are alternately connected to their mirror image.
https://media.mathstodon.xyz/media_attachments/files/112/337/684/704/027/718/original/dd49d029d53b5801.mp4