Linkage

Two sites on toroidal polyhedra: Bonnie Stewarts Hohlkörper and Alex Doskey’s virtual reality models of Stewart’s polyhedra (\(\mathbb{M}\)). Found while researching a new WP article on Stewart’s book Adventures Among the Toroids. The first link is in German but readable through Google translate and has lots of pretty pictures. The second needs VR software to be usable.

The map folding problem, illustrated by Robert Dickau (\(\mathbb{M}\)). See Dickau’s home page for many more mathematical illustrations, mostly of combinatorial enumeration problems and fractals.

For some reason I wanted the name of a surface of revolution of a circular arc less than \(\pi\) around its chord (\(\mathbb{M}\)). Wikipedia said “lemon” but sourced to MathWorld so I thought maybe MathWorld had made it up. Not so. Better sources say the same. And the surface for the complementary arc is an “apple”. It looks like a North American football but a “football” is a different surface of revolution, of constant positive Gaussian curvature.

Special issue of Discrete & Computational Geometry in memory of Branko Grünbaum (\(\mathbb{M}\)). I think many of the research papers in it are interesting but I want to draw particular attention to the preface by Gil Kalai, Bojan Mohar, and Isabella Novik, which provides a nice brief survey both of Grünbaum’s many contributions to discrete geometry and of the lines of active research they have led to.

2020 Bridges Conference Mathematical Art Gallery (\(\mathbb{M}\)). Many are great but a couple of my favorites are Conan Chadbourne’s grid partition enumeration and Martin Levin’s ten-tetrahedron tensegrity. I didn’t participate but apparently the Bridges conference itself was held virtually a few days ago; see the conference site for more including papers and videos.

Paper plotter (\(\mathbb{M}\), via): tool to make 3d paper cut-and-assemble models of the graphs of bivariate functions.

Kowhaiwhai (\(\mathbb{M}\)). are repeating decorative patterns used in New Zealand on Maori buildings. The National Library of NZ has a number of good examples, including the sketches of patterns by Tamati Ngakoho (top) and of a traditional Arawa pattern (bottom) shown below. There’s also a brief guide to their interpretation online. I can’t find much analysis of their structure, though, beyond pointing to frieze groups for their symmetries. The part that interests me more is their fractal-like swooping structure, reminiscent of (and in some cases directly modeled on) fern fronds.

Why Wikipedia decided to stop calling Fox a reliable source (\(\mathbb{M}\)). Note however that Fox has not actually been deemed unreliable, in general. The discussion had a no-consensus close.

Untangling random polygons (\(\mathbb{M}\)): repeatedly rescaling midpoint polygons always leads to an ellipse.

The mesmerizing geometry of Malaysia’s most complex cakes: Bold colors and designs set kek lapis Sarawak apart (\(\mathbb{M}\), via). As seen on The Great British Bake Off. These cakes have many parallel layers in bright colors, cut and rearranged to form complex designs. Mostly they involve 45 and 90-degree angles but at least one of the examples uses hexagonal symmetry instead.

My Google Scholar profile has mildly broken down (\(\mathbb{M}\)). When I go there, it offers me two new profiles to link as my coauthors: Man-Kwun Chiu and Matí Korman. They are indeed coauthors, from my new CCCG papers. But when I click to accept them as listed coauthors, it tells me I have too many coauthors, refuses to add them, and returns to offering me new profiles to link. I can see no way out of this other than to not accept my coauthors, which would be wrong. Google, fix this limitation!

A use for old CDs: cut them up and glue the pieces together to make visualizations of great circle arrangements on the sphere (\(\mathbb{M}\)). The mathematical question posed by this is: for which numbers of great circles is it possible to make an arrangement in which all the arcs between pairs of neighbors have equal lengths?

The Renaissance Mathematicus (\(\mathbb{M}\)), an interesting blogger on the history of science. See also the crowdfunding drive to replace their old creaky iMac, from which I found this.