Linkage

Textbook company Pearson sues Chegg for copyright infringement, for selling solutions to textbook homework problems (\(\mathbb{M}\)). 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?
Inside Higher Ed on the future of academic conferences (\(\mathbb{M}\)). 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.
Color map advice for scientific visualization (\(\mathbb{M}\), via).
Three sets of talk slides from recent talks (\(\mathbb{M}\)):
Unfortunately I don’t have links to recordings of the talks.
I thought for sure I had posted before about Dinara Kasko’s 3d-printed geometric food designs (\(\mathbb{M}\), see also, home page), but grep tells me that if I ever did, it wasn’t with her name.
The zbMATH mathematics review database was broken for a day (\(\mathbb{M}\)), unable to show the old scans of printed reviews, but fortunately it got better.
Twelve threads (\(\mathbb{M}\)). 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.
Visualization of Poncelet’s porism, calculated with difficulty by mathcination from Cayley’s criteria. It would have been easier to calculate a regular hendecagram and then perturb it by a projective transformation, but that wasn’t the point.
I recently saw a link to Chapter 1 of the MathML 3.0 spec (\(\mathbb{M}\)), 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 the plus-minus sign, by which the correct formula represents both solutions, with an addition operation, giving only one of the two. Time to re-link my old anti-MathML rant?
Giant origami animals in Midtown Manhattan (\(\mathbb{M}\)). 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?
The Topkapı Scroll – Geometry and Ornament in Islamic Architecture, by Harvard professor Gülru Necipoğlu (\(\mathbb{M}\)). One of many beautiful art books free for download from the Getty Virtual Library.
Sierpiński triangles in stone, on medieval floors in Rome (\(\mathbb{M}\)), 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.
Every invertible function computable both ways in polynomial time has polynomial-size reversible logic circuits, using extra “dummy” values that are zero on both input and output (\(\mathbb{M}\)): See Jacopini, Mentrasti, & Sontacchi, “Reversible turing machines and polynomial time reversibly computable functions”, SIAM J. Disc. Math. 1990.

Theorem: No circuit of reversible gates of arity less than \(n\), without dummy values, can compute \(n\)-bit 2’s-complement negation.

Proof: Each gate performs an even permutation on the \(2^n\) inputs, but negation is an odd permutation. \(\Box\)