Posts by divbyzero@mathstodon.xyz
(DIR) Post #APQzLJ8AeSWH8BwpP6 by divbyzero@mathstodon.xyz
2022-11-09T14:23:14Z
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I figured out a way to fold a regular octagon from a strip of paper (a different method than is in the Hilton/Pedersen book). The key techniques are to fold a strip over itself to get a perpendicular line and to fold the edge down to an earlier fold to bisect an angle. 1/2
(DIR) Post #APQzLL2vWvVt4VVfVY by divbyzero@mathstodon.xyz
2022-11-09T14:23:47Z
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I believe an analogous technique will work for any regular 2^n-gon. Here's the 16-gon (and the square which is a very simplified version). 2/2
(DIR) Post #ATz0CzyR4WCgJLA7uq by divbyzero@mathstodon.xyz
2023-03-21T14:56:35Z
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Super exciting news about Smith, @jsm28, @csk, Goodman-Strauss's discovery of an "einstein"—a single shape that tiles the plane aperiodically! I decided to create a 3D-printable version of it. You can find it here: https://www.thingiverse.com/thing:5923307(I now see that others did this as well—probably not surprising since the geometry of the shape is so simple, relatively speaking.)Here's their preprint: https://arxiv.org/abs/2303.10798
(DIR) Post #ATz0D0trd08nBS1zQe by divbyzero@mathstodon.xyz
2023-03-22T00:44:02Z
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Here are 30 tiles that I printed today and the beginning of an aperiodic tiling. The red ones are mirror images of the others.
(DIR) Post #ATz0D2MyAH15k0ekQy by divbyzero@mathstodon.xyz
2023-03-22T02:42:33Z
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@OscarCunningham The center blue tile has five neighbors. So those six tiles require four colors. But I had a similar thought—about colorability. I was wondering if you color all the “reversed” tiles one color (red in this picture), can you still four-color the tiles?
(DIR) Post #AV1AVBEEwDo1MF9LEW by divbyzero@mathstodon.xyz
2023-04-24T20:11:24Z
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I made another infinity cube. This time I printed 48 squares with Truchet tiles on them, randomly made them faces of eight cubes, and then randomly arranged the cubes to make the infinity cube.It was neat to realize that they could be two-colored!Thanks to @drMathArt for the idea of using a Truchet pattern.
(DIR) Post #AV1AVDAPjPvxMxNJY0 by divbyzero@mathstodon.xyz
2023-04-24T20:11:55Z
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Here's the pattern I used.
(DIR) Post #AZBnWcyhPu209vZ3lw by divbyzero@mathstodon.xyz
2023-08-28T02:15:28Z
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@11011110 About ten years ago I made Gabriel's horn out of paper https://divisbyzero.com/2014/03/25/gabriels-paper-horn/ I was inspired by this blog post that made the pseudosphere out of paper. https://danielwalsh.tumblr.com/post/2173134224/sudo-make-me-a-pseudosphere
(DIR) Post #AtQkHVFgLkkNMG8sIC by divbyzero@mathstodon.xyz
2025-04-24T21:22:27Z
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I designed and 3D printed a couple of models of Riemann sums for multivariable functions—the monkey saddle and the sombrero function. (I also got to try out this cool filament.) The files are on Thingiverse. https://www.thingiverse.com/thing:7019158 https://www.thingiverse.com/thing:7019184
(DIR) Post #AupbgRdC4kbhUDJIOm by divbyzero@mathstodon.xyz
2025-06-02T02:12:26Z
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I got an email from someone asking for my "Essential Trigonometry for Calculus" cheat sheet, which I give to my calculus students. So, I thought I'd put it on GitHub for anyone to download (compiled PDF and source code). https://github.com/divisbyzero/Essential-Trig-for-Calculus
(DIR) Post #Aur8MJEP5UnrHwgIBU by divbyzero@mathstodon.xyz
2025-06-06T14:13:38Z
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@futurebird Thanks!
(DIR) Post #AxDAQXChdNztfC0L3I by divbyzero@mathstodon.xyz
2025-08-13T13:58:00Z
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Yesterday at the MoMath MOVES conference, Erik Demaine discussed QR codes and showed examples of how to incorporate images into them so they are still scannable. I had to give it a try. This QR code should take you to my website. More details: The second image is the QR code I started with (I used this page to create it https://www.nayuki.io/page/qr-code-generator-library). Certain "finder patterns" must be in the code—the nested squares and a row and column of alternating pixels. The rest are black and white pixels encoding the text. But for these, all that matters is whether the center of the pixel is black or white. So, if you shrink the black and white pixels by a factor of three, say, you can use the rest of the area however you want. I used Photoshop to turn my profile photo into a black-and-white pixellated image of the correct size. Then, I placed the QR code on top of it.
(DIR) Post #AxDAQZHNuwvm6ID6cy by divbyzero@mathstodon.xyz
2025-08-15T11:41:48Z
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@edemaine Thanks! I made mine "by hand"—Adobe Illustrator + Photoshop.
(DIR) Post #AxDAQexkmqnDj94VrU by divbyzero@mathstodon.xyz
2025-08-13T16:43:38Z
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Just playing around. Here are a couple more that I think I like better.
(DIR) Post #AxpI7h0b8f2OD6LWpE by divbyzero@mathstodon.xyz
2025-09-02T23:58:44Z
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As I was walking home today, I had this idea: Is it possible to turn a QR code into a Truchet tiling that's still a functioning QR code? Yep.
(DIR) Post #Az1satmfdyIrvIZaU4 by divbyzero@mathstodon.xyz
2025-10-09T03:00:49Z
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New blog post! Through a sequence of images, I verify that the unknotting number of the connected sum of a (2,7) torus knot and its mirror is less than 6: I show that this first image is the connected sum, and after changing those crossings, it produces the unknot! https://divisbyzero.com/2025/10/08/the-unknotting-number-is-not-additive/
(DIR) Post #B0tALOAFEalLkcVozA by divbyzero@mathstodon.xyz
2025-11-30T16:42:35Z
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I learned this folding technique yesterday, so I had to make something with it.