New blog post: Congratulations, Dr. Matias!
(One of our students who just passed his doctoral defense.)

Dujiangyan Zhongshuge, bookstore in Chengdu with mirrored floors and ceilings creating the feeling of an infinite Escher palace of books:, via

I couldn't resist picking up a copy of _The Architecture of Trees_, a coffee-table book centered on pen-and-ink illustrations of the summer and winter forms of over 200 types of tree, on a recent visit to the Mendocino Coast Botanical Gardens (beautiful this time of year with many flowers in bloom).

Some reviews:

Three correlations and a samosa:

3x3 symmetric matrices with unit diagonals form a three-dimensional linear space, in which the samosa is a curvy 3d convex set representing the positive definite matrices. Taking sections of it allows you to infer the possible correlations between two variables, given each of their correlations with a third. See also and

For a centrally symmetric star-shaped set in the plane, each line through the center cuts its perimeter into two equal-length curves. But these are not the only shapes with this property: 18th-century Jesuit polymath Roger Boscovich ( observed that a heart-like shape formed by three semicircles has the same property. Via Banchoff and Giblin, "On the geometry of piecewise circular curves", Amer. Math. Monthly 1994,

That other microblogging site has a bot specifically devoted to replacing links to pdf versions of arxiv preprints by links to the abstracts of the same preprint:

Is there something like that for mastodon? If not there should be.

Statement from concern from Amer.Stat.Assoc. over the Greek government's persecution of former chief statistician Andreas Georgiou for (according to the ASA) producing accurate and truthful statistical reports on the Greek economy that cast disrepute on the unverifiable claims of earlier governments:

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The Takagi Function and Its Properties
Article by Jeffrey C. Lagarias
In collections: Easily explained, Fun maths facts
The Takagi function is a continuous non-differentiable function on [0,1] introduced by Teiji Takagi in 1903. It has since appeared in a surprising number of different mathematical contexts, including mathematical analysis, probability theory and number theory. This paper surveys the...
Entry: read.somethingorotherwhatever.

Tetrahedra passing through a hole:

This is from eight years ago, but was active again recently. The question is: what's the smallest-area hole in a plane through which you can push a unit tetrahedron? DPKR has a very pretty animated answer, but sadly it's not optimal: there's a triangular hole with smaller area \(1/\sqrt{8}\), known minimal for translational motion ( The problem for more general motion seems to be still open.

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This week I built the Mercator Rotator.

Mercator maps famously make Africa small and Greenland big, but by changing which way around we apply the projection we can make any place we like any size we like. Spin the globe, and see what you can create.

Apparently it is unknown whether one can find a pentagon so that four congruent copies can be placed in the plane with each pair sharing a nonzero length of boundary. It is possible with hexagons: see (new Wikipedia article, not by me).

The art of mathematics in chalk:

Teaser for the forthcoming book Do Not Erase: Mathematicians and Their Chalkboards, featuring several photographic spreads of chalkboard illustrations and formulas and their explanations.

They appear to be mostly set-ups rather than captured from active research, but still pretty and interesting. I linked an earlier post on this in 2019 ( but with fewer photos and no explanations.

Paper engineering from the Bauhaus and reverse-engineering Bauhaus paper designs: and

More curved kirigami than origami, but interesting methods for getting smooth 3d shapes from cut sheets of flat paper

Or, you could recognize that it's the norm of the Eisenstein integers (under a small change of basis from the usual one) and that they have six-fold rotational symmetry:

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University of Minnesota assistant professor Kangjie Lu caught allegedly deliberately sending buggy patches to Linux kernel as some kind of breaching experiment, resulting in the whole university being banned from Linux kernel development:,, via

They claim to have been declared IRB-exempt but this appears to be a mistake by the IRB.

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