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Sierpinsky triangles in stone, on medieval floors in Rome:, Elisa Conversano and Laura Tedeschini Lalli. See also Kim Williams, "The pavements of the Cosmati",

The collection of images of these on Wikimedia commons,, is a little sad — Conversano and Tedeschini Lalli, and Williams, have a lot more.

_The Topkapı Scroll – Geometry and Ornament in Islamic Architecture_, by Harvard professor Gülru Necipoğlu,

One of many beautiful art books free for download from the Getty Virtual Library,

Giant origami animals in Midtown Manhattan:

But now I want to know if they were really each fabricated from a single uncut square sheet of steel. And if so, how did they get the corners so crisp?

I recently saw a link to Chapter 1 of the MathML 3.0 spec,, using as an example the quadratic formula in both layout markup and content markup. Its totally unwieldy non-human-readable expansion obscures the fact that the MathML authors didn't even get the math right: their content markup silently replaces "±", by which the correct formula represents both solutions, with "+", giving only one of the two.

Time to re-link my old anti-MathML rant ?

New blog post: Multilayered tiles,

The integer-coordinate octagon shown below is an example: it cannot tile the plane (no convex octagon can), but placing copies of it at each integer point produces a 7-ply uniform covering of the plane.

New blog post, "Which integer sequences form denominators of Egyptian fractions?",, and new paper, "Egyptian Fractions with Denominators from Sequences Closed Under Doubling", in the _Journal of Integer Sequences_,

0xDE boosted

It was astonishingly complicated to derive this example of Poncelet's porism from Cayley's innocent-looking criteria.

Twelve threads:
Vi Hart's latest video mixes up discussions of the nature of social media, the philosophy of mathematical creativity, an exploration of symmetry, and an investigation of the spot patterns of 8-sided dice (which turn out not to all be the same) and how to visualize them.

Is it just me or is zbMATH somewhat broken today? I'm finding that for many of the older reviews (the ones old enough to require looking at a scan of a printed review rather than having the text of the review on the review page; example: the "show scanned page" link doesn't work. This includes some that were working for me yesterday (example:

I thought for sure I had posted before about Dinara Kasko's 3d-printed geometric food designs, but grep tells me that if I ever did, it wasn't with her name.

Bold New Mathematical Cake Designs by Dinara Kasko:

La repostería matemática de la arquitecta Dinara Kasko:

Kasko's own web site:

Three sets of talk slides from recent talks (unfortunately I don't have links to recordings of the talks):

The graphs of stably matchable pairs, WG 2021:

A stronger lower bound on parametric minimum spanning trees, WADS 2021:

Limitations on realistic hyperbolic graph drawing, GD 2021:

Inside Higher Ed on the future of academic conferences:

A significant fraction of academics surveyed said that they still felt unsafe going to physical conferences, and with the carbon footprint and reduced expenses of virtual but greater interactivity of physical meetings, some mix of both seems likely going forward. However, trying to mix both in one conference (especially for conferences with many parallel small talks or panels) seems difficult and expensive.

Textbook company Pearson sues Chegg for copyright infringement, for selling solutions to textbook homework problems:

On the one hand, for-profit cheater-enablers like Chegg are a cancer on higher education. On the other, the solution to a problem is generally a concept, not a text, and should not be something that can be locked up under copyright.

So I don't know who to root for?

\(\exists\mathbb{R}\) (existence of solutions to polynomial real equations, is a little harder than \(\mathsf{NP}\), but \(\exists\mathbb{Z}\) is undecidable (Matiyasevich). Today I learned from Marcus Schaefer's GD talk ( that right-angle-crossing graph drawing ( is \(\exists\mathbb{R}\)-complete but requiring integer coordinates makes it \(\exists\mathbb{Q}\)-complete. That means we don't know whether it's decidable!

Why would someone plagiarize the bibliography of their journal paper, by copying someone else's bibliography on a totally unrelated topic, in an inconsistent format to the references in the main text of the paper (no doubt copied from somewhere else)? Thomas Clausen looks more deeply than necessary at the garbage pile that is predatory publishing, triggered by an odd citation alert:

Death of the Jekyll static site generator proclaimed, because of some open source politics I don't understand. Meanwhile for those of us using it as a static site generator and github-pages blog springboard it largely just works as it always has without much need for development. Indeed, a big reason for the lack of momentum for going from Jekyll 3 to 4 is that it was an unnecessary incompatible update that would have broken too much stuff., via

The annual Graph Drawing symposium really loves hybrid formats. This year's ( will be held this Wednesday through Friday as a hybrid of a small in-person meeting in Tübingen and online for those like me still not traveling. And, as in past years, the proceedings is a hybrid of a Springer LNCS volume (not yet out) and an arXiv copy, newly up at

If anything the arXiv version is better: more timely, with appendices and color both allowed.

Citation bias ( how the tendency to cite certain types of results over others (e.g. positive more than negative) and academic games of telephone can herd the research community towards a distorted view of what the scientific record has actually established

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