Linkage

Discrete spirograph-like patterns from Gaussian periods and their analogues (\(\mathbb{M}\), via): see figures by Samantha Platt, based on her paper “Visual aspects of gaussian periods and analogues” which has many more. Here the Gaussian periods are certain sums of roots of unity.

On the unreliability of ChatGPT for mathematical proofs and even for finding references for proofs.

3d-hinged polygonal dissection in a cabinet door (\(\mathbb{M}\), via). It’s labeled as “Staatliche Meisterschule für Schreiner Gunzenhausen”, which led me to the school’s facebook page where it appears on May 3, unlabeled but sandwiched between other Meisterprüfungsprojekte, which I assume this is also. Anyone know where to find a better non-siloed link for this?

The shape that should be impossible (\(\mathbb{M}\)). StandUpMaths on Robin Houston’s discovery of a simplified Sydler polyhedron with one 45° angle and the rest all 90°. See also a response from a mechanical nuclear power engineer and a paperfolding net.

Places named after mathematicians starting with the Praça de Gomes Teixeira in Lisbon. My contribution: I live near a Hypatia Court and a Turing Street.

Sparse representations of binary matroids (\(\mathbb{M}\)). Rose McCarty has more questions than answers on the independence patterns that can be represented by sparse matrices.

One of many discussions on Adobe changing their terms to say “we can use any picture you make in Photoshop to train our AI” and why it’s such a bad idea for software one might want to use with confidential information. They’ve since tried to backtrack, I’m not sure very convincingly.

Curved surface folding in the wild (\(\mathbb{M}\)). How certain freshwater-pond microorganisms (about 0.1mm in size) can extend a “neck-like feeding apparatus” about ten times the length of their body using an origami-like curved crease structure.

Beyond the wall: Working with aperiodic tilings using finite-state transducers (\(\mathbb{M}\)). Simon Tatham on how to generate inflation-based tilings based on lazily-generated label sequences saying where you are at each level of inflation. Moving from tile to tile in the resulting tiling involves going up enough levels in the sequence to tell what’s on the other side of each edge. If higher-level labels are random, everything works, but deterministic choices may produce infinite loops. This misbehavior turns out to be connected to tilings with interesting (finite) symmetry patterns.

Computation is all around us, if you look for it (\(\mathbb{M}\)). Lance Fortnow in Quanta.

Professors ask: are we just grading robots? (\(\mathbb{M}\), archived). A timely article in the Chronicle of Higher Education for final exam week here. To avoid this issue, I am trying a grading strategy this quarter based only on in-class exams; I still assign weekly problem sets but don’t collect and grade them. But it would be worse in a writing-based discipline.

Do hares eat lynx? (\(\mathbb{M}\)) As professor and textbook author Nicole Rust tells us in the linked post, the textbook story of population cycle peaks for lynx trailing those of hares is reversed in the actual data. The explanation may involve another level of predation in the system: the fur trappers whose pelt counts were used as the data.

Analysis of the social networks of bees and the flowers they visit (\(\mathbb{M}\)). This seems to me an interesting example for the way it combines geographic factors (how near the flowers are to each other), combinatorial factors (multiple bee and flower species), and some amount of randomness. And the drawing of one of these networks on page 7 shows some interesting structure: a central core of dense and random-looking connectivity with a lot of smaller highly clustered subnetworks. But the fieldwork needed to record these networks sounds incredibly tedious. Maybe that part could be automated.