Today at lunch, I've learned about the Trash Compaction problem: Can you push objects on a grid into the compact shape of a rectangle if you're only allowed to push all objects from one side simultaneously. Akitaya, Aloupis, Löffler, and Rounds showed that the problem is NP-complete.

The fun variant of this problem talks about pushing around coconuts with a giant coconut pusher... Here are some neat slides:

Quasiperiodic bobbin lace patterns:, Veronika Irvine, Therese Biedl, and Craig S. Kaplan, via — aperiodic tilings in fiber arts.

The attached image is a photo of lace (not an illustration), braided into an Ammann–Beenker tiling pattern.

‪A variant of gripping gears adds “pass-through” holes so that a solid object can pass through the connection between the gears. Joint work with Will Segerman and Sabetta Matsumoto. Full video:

In which we show that the knots K13n592 and K15n41127 (pictured) both have stick number 10. These are the first non-torus knots with more than 9 crossings for which the exact stick number is known.

Gripping gears: two gears mesh with and rotate around each other, with no axles and no frame. Joint work with Will Segerman and Sabetta Matsumoto. Full video at

Escher-like spiral tilings, by Craig Kaplan:

(Sadly with no angels, devils, fish, or geese, but maybe some talented artist will take up that challenge.)


Extensor cube in motion! Made by @christianp at the Talking Maths in Public conference today.

:chalkdust_scorpion: In this blog from our archives, @mscroggs talks about @henryseg's book on how 3D printing can help with our understanding of geometry!

Added an option to view the edges of the tetrahedra in our Cannon-Thurston map explorer. This should make it easier to (eventually) explain a bit how the images are generated.

My video on non-euclidean ray-marching virtual reality (joint work with Roice Nelson and Michael Woodard) was one of four winners of the NSF's "We Are Mathematics" competition!

GPUs are amazing. I generated these images at a full resolution of 12,288 x 24,576, each one taking a couple of minutes. My old python code would have taken most of a month to generate each of these!

There's still work to do, but our Cannon-Thurston map explorer web app is already lots of fun to play around with. You can rotate the view with WASD and move with the arrow keys. The controls tab has lots of other options: different triangulations, colouring choices, etc. With Saul Schleimer and David Bachman.

Just remembered that I ordered @henryseg's book yonks ago and hadn't checked my pigeon hole since. Getting stuck in now!

Here’s a video on simulating a non-euclidean space in virtual reality with ray marching. This project is joint work with Michael Woodard and Roice Nelson.

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