robinhouston
@robinhouston.mathstodon.xyz.ap.brid.gy
Watching for the card that is so high and wild I’ll never need to deal another
🌉 bridged from ⁂ https://mathstodon.xyz/@robinhouston, follow @ap.brid.gy to interact
🌉 bridged from ⁂ https://mathstodon.xyz/@robinhouston, follow @ap.brid.gy to interact
Continuing their long tradition of being the most geometrically adventurous chocolate manufacturer, Toblerone have a range of enneahedral chocolates.
November 12, 2025 at 2:34 PM
Continuing their long tradition of being the most geometrically adventurous chocolate manufacturer, Toblerone have a range of enneahedral chocolates.
@christianp It's debatable whether they count as mathematical, but William Playfair published books with coloured charts in the 1800s. https://en.wikipedia.org/wiki/William_Playfair
November 11, 2025 at 11:14 PM
@christianp It's debatable whether they count as mathematical, but William Playfair published books with coloured charts in the 1800s. https://en.wikipedia.org/wiki/William_Playfair
The third stellation (with a convenient handle)
November 9, 2025 at 5:42 PM
The third stellation (with a convenient handle)
The second stellation of the rhombic dodecahedron. I didn't count how many units it uses. There must be some way to work it out.
November 9, 2025 at 12:13 PM
The second stellation of the rhombic dodecahedron. I didn't count how many units it uses. There must be some way to work it out.
In fact the middle puzzle in the picture of Grant's puzzles is one of Stewart Coffin's designs, his Twelve-Piece Separation.
See pages 118–119 of Coffin's compendium _AP-ART_, which is online at https://www.puzzlemuseum.com/puzzles/coffin-ap-art/ap-art-2018.pdf
See pages 118–119 of Coffin's compendium _AP-ART_, which is online at https://www.puzzlemuseum.com/puzzles/coffin-ap-art/ap-art-2018.pdf
November 9, 2025 at 11:03 AM
In fact the middle puzzle in the picture of Grant's puzzles is one of Stewart Coffin's designs, his Twelve-Piece Separation.
See pages 118–119 of Coffin's compendium _AP-ART_, which is online at https://www.puzzlemuseum.com/puzzles/coffin-ap-art/ap-art-2018.pdf
See pages 118–119 of Coffin's compendium _AP-ART_, which is online at https://www.puzzlemuseum.com/puzzles/coffin-ap-art/ap-art-2018.pdf
There's a new episode of the Mathematical Objects podcast where the hosts (@stecks and @peterrowlett) interview Grant Sanderson (3blue1brown) about his love of wooden puzzles – specifically the three pictured below.
November 9, 2025 at 9:21 AM
There's a new episode of the Mathematical Objects podcast where the hosts (@stecks and @peterrowlett) interview Grant Sanderson (3blue1brown) about his love of wooden puzzles – specifically the three pictured below.
A surprising tessellation
November 8, 2025 at 5:15 PM
A surprising tessellation
A rhombic dodecahedron assembled from 192 units
November 7, 2025 at 2:19 PM
A rhombic dodecahedron assembled from 192 units
There’s a very funny story in Section 44.2 about what happened when they tried to use it to solve a Smullyan-style logic puzzle (you know the sort of thing – one guard always tells the truth, the other always lies, etc.)
November 6, 2025 at 6:21 PM
There’s a very funny story in Section 44.2 about what happened when they tried to use it to solve a Smullyan-style logic puzzle (you know the sort of thing – one guard always tells the truth, the other always lies, etc.)
The sofa is represented as a point cloud. It looks almost reasonable as a shape for an actual sofa!
November 6, 2025 at 5:56 PM
The sofa is represented as a point cloud. It looks almost reasonable as a shape for an actual sofa!
And a (conjecturally) improved lower bound on the 3D moving sofa problem! Not the famous 2D version, which has been fully solved quite recently, but the problem of finding the largest sofa you can manouvre through a tunnel like this:
November 6, 2025 at 5:53 PM
And a (conjecturally) improved lower bound on the 3D moving sofa problem! Not the famous 2D version, which has been fully solved quite recently, but the problem of finding the largest sofa you can manouvre through a tunnel like this:
There’s also a new record for packing 11 cubes into a cube, but it’s not as funny.
November 6, 2025 at 5:43 PM
There’s also a new record for packing 11 cubes into a cube, but it’s not as funny.
Fans of efficiently packing lots of congruent shapes into a bigger instance of the same shape are going to enjoy this one.
![FIGURE 22. Constructions of the packing problems found by AlphaEvolve. Left: Packing 11 unit hexagons into a regular hexagon of side length 3.931. Right: Packing 12 unit hexagons into a regular hexagon of side length 3.942. Image reproduced from [223].](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:nhakixcsmdow4avnqxtfy6c6/bafkreid3pg4eqsbega2qhl73abqk6blnn3ypzjmzhgrdvn4ciissg4vmxu@jpeg)
November 6, 2025 at 5:39 PM
Fans of efficiently packing lots of congruent shapes into a bigger instance of the same shape are going to enjoy this one.
Need to pack a lot of identical regular tetrahedra together efficiently? This may help!
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
![Figure S5. Details of the highest density (ф = 0.8503) packing of hard tetrahedra observed in this study. This density was obtained by compressing a 2x2x2 cell of the (3,4,37,4) approximant with 656 tetrahedra. (a) For ease of viewing, the 2x2x2 cell has been periodically continued into a 2x2x8 cell. (b) In the translucent image, the twelve- fold logs can be identified. The logs arrange into triangle (c) and square (d) tiles with 9.5 and 22 tetrahedra, respectively. The ratio of the packing densities of the tiles is Triangle / square = 19 / 11V3. (e) Thin rhombi are frequently observed in connection with zipper motion, a dynamical mechanism to rearrange squares and triangles [26]. A rhomb is a structural defect. It consists of 11 tetrahedra and has half the volume of a square. As can be seen in the image, tetrahedra in the middle form a spiral of two interpenetrating logs (light red).](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:nhakixcsmdow4avnqxtfy6c6/bafkreigy4bdtldppaqyjuaq7bgp65xfdafqp2qebraokbmylgojfy2rvka@jpeg)
November 6, 2025 at 11:56 AM
Need to pack a lot of identical regular tetrahedra together efficiently? This may help!
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
Like a tray of freshly-baked cookies!
November 5, 2025 at 8:45 AM
Like a tray of freshly-baked cookies!
New design improves the fitment.
November 2, 2025 at 4:17 PM
New design improves the fitment.
I've just got this book. I hadn't realised that the whole thing is hand lettered!
November 2, 2025 at 9:40 AM
I've just got this book. I hadn't realised that the whole thing is hand lettered!
There's a famous classification of fun into three types: https://essentialwilderness.com/type-1-2-and-3-fun/
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
October 27, 2025 at 9:17 AM
There's a famous classification of fun into three types: https://essentialwilderness.com/type-1-2-and-3-fun/
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
I think this is the first time I've seen ChatGPT credited in the acknowledgements of a paper.
https://arxiv.org/abs/2509.22333
https://arxiv.org/abs/2509.22333
October 24, 2025 at 12:42 PM
I think this is the first time I've seen ChatGPT credited in the acknowledgements of a paper.
https://arxiv.org/abs/2509.22333
https://arxiv.org/abs/2509.22333
I fear CAD could become a dangerous addiction.
October 21, 2025 at 12:31 PM
I fear CAD could become a dangerous addiction.
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?
Was the 1960s an especially auspicious time for excellent titles?
October 20, 2025 at 4:06 PM
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?
Was the 1960s an especially auspicious time for excellent titles?