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: http://www.staff.science.uu.nl/~loffl001/publications/slides/trash_compaction.pdf

Quasiperiodic bobbin lace patterns: https://arxiv.org/abs/1910.07935, Veronika Irvine, Therese Biedl, and Craig S. Kaplan, via https://twitter.com/bit_player/status/1185356703065354240 — aperiodic tilings in fiber arts.

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

https://arxiv.org/abs/1909.06947

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.

Escher-like spiral tilings, by Craig Kaplan: http://isohedral.ca/escher-like-spiral-tilings/

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

In this blog from our archives, @mscroggs talks about @henryseg's book on how 3D printing can help with our understanding of geometry! http://chalkdustmagazine.com/blog/visual-mathematics-3d-printing/

Mathematician working mostly in three-dimensional geometry and topology, and mathematical artist working mostly in 3D printing and virtual reality.

Joined Apr 2017