Linkage with a fold-and-cut hat

Fractals from hinged hexagon and triangle tilings (\(\mathbb{M}\)), Helena Verrill, from Bridges 2024. See also Verrill’s interactive site for generating these patterns.

Nature on Ken Ono’s work modeling and tuning the performance of Olympic swimmers (\(\mathbb{M}\), via; not very heavy on details).

Regular and semi-regular tessellations of origami flashers (\(\mathbb{M}\)). A flasher is a pattern that folds into a prismatic shape with a spiral wrapping around the sides of the prism. In this work from 8OSME, Nachat Jatusripitak and Manan Arya show that tessellated fold patterns can fold to tessellations by triangular, square, and hexagonal flashers.

Somehow I missed this when Antoine Chambert-Loir noted it last June (\(\mathbb{M}\)), but zbMATH is the inaugural winner of the Jean-Pierre Demailly Prize for Open Science in Mathematics, sponsored by the French societies for mathematics, applied mathematics, and statisti]cs (SMF, SMAI, and SFdS).

David Wood encourages combinatorists to send their papers to broad-focus mathematics journals, and when reviewing such submissions, to affirm that they are of broad interest to mathematics, to counter the widespread bias against combinatorics in such journals. See also Wood’s list of combinatorists in editorial positions in these journals, and of major journals that have no representation of combinatorics on their editorial boards.

Dan Drake collects pilgrimage sites for the mathematical tourist. That is, places where something important in the history of mathematics happened, not merely places where mathematical content can be found now.

Catherine Pfaff shows off some notes from her mathematics research, writing “When one isn’t sure of what’s actually true, sometimes it helps to just compute it all, or at least it feels good to do so.”

Peter Rowlett in New Scientist on connections between mathematics and poetry (\(\mathbb{M}\), archived).

Better Living Through Algorithms, by Naomi Kritzer in ClarkesWorld, just won the Hugo for short SF story (\(\mathbb{M}\), via), which put just enough pressure on me to actually read it (a little ironically given the story content; mild spoiler) and I’m happy I did.

Evolution of the notation for the empty set, with a cute story about André Weil impressing his daughter as the inventor of the \(\emptyset\) notation.

A binary number system from 1617: Napier’s location numerals (\(\mathbb{M}\)). Chris Staecker explains why these numbers never caught on: like a binary version of Roman numerals, they were simultaneously far ahead of and far behind their time. See also Staecker’s previous video on Napier’s binary multiplication board using this system.

Fold-and-cut hat and spectre tiles (\(\mathbb{M}\)). Dave Richeson used the straight skeleton method to construct the downloadable folding patterns for these, which led me to wonder how the kite tiling construction of the hat, the diamond-kite circle packing, and the circle-packing based fold-and-cut construction might play together.

My guess (not having worked it out in detail) is that there is some simple origami molecule that can fold all the kites of the plane tiling by kites into a half-plane, with their boundaries all on the same line segment; that you can then pop the kites of the hat onto the opposite side of the line segment, and that cutting nearly along the line segment (on the side away from the hat’s kites) will cut out a hat with a little bit of boundary fringe. But one might not find that boundary fringe part satisfactory.

Welcome to the Fold (\(\mathbb{M}\)). American Mathematical Society feature column by Sara Chari and Adriana Salerno on the mathematical properties of point systems constructed by paper folding.