Linkage

Real-world application of square packing: Packing ten quart bottles in a milk crate slightly larger than a \(3\times 3\) packing.

Significant increases in perceived cheating, and decreased willingness of honest students to turn in cheaters, lead Stanford and Princeton to give up on honor code based unproctored exams (\(\mathbb{M}\), via). Ars Technica blames the cheating on AI, but although it seems likely to me that the ease of cheating with AI is a factor, I’m skeptical that it’s the root cause.

Belgian public transport company De Lijn promote themselves via a QR code that looks like a metro map.

Triple cover of a \(4\times 5\) rectangle by the twelve pentominoes poses challenges for visualization. The original posting by Alexandre Muñiz uses diagonal stripes with three colors per unit square; the comments include an animated version adding black outlines to each tile, and a couple of ball-and-stick diagrams.

On the classification of quadrilaterals and the visualization of the classification using Hasse diagrams.

An explicit lower bound for the unit distance problem (\(\mathbb{M}\)), Will Sawin. Human “digestion” of a computer-discovered breakthrough gets a far better version.

On leading people who don’t want to be led (\(\mathbb{M}\)). Gillian Hayes, UC Irvine’s vice provost for academic personnel (and professor in the School of Information and Computer Sciences) on the significant differences between her job and that of a manager in a corporation.

Kate Holladay Claghorn: first female ASA Fellow, activist statistician (\(\mathbb{M}\)). The American Statistical Association has published a nice profile by Penny Reynolds of Kate Claghorn (1864–1938), an important and influential figure in Progressive Era New York, known for opposing anti-Jewish sentiment, championing better legal systems for minors and non-English speakers, fighting sexual harassment in the workplace, and helping to found the National Association for the Advancement of Colored People. See also Claghorn’s Wikipedia article.

Range avoidance (\(\mathbb{M}\)). For a function with a bigger range than domain, there always exists a missing value, a member of the range not hit by the function, and a random search will find such a value quickly (given an oracle that tells you whether you’re successful). As Lance Fortnow writes, solving the same problem without randomness is central to modern complexity theory. Lance also links a recent Bull. EATCS survey by Oliver Korten, “Range avoidance and the complexity of explicit constructions”.

Tschirnhausen cubic (\(\mathbb{M}\)), now a Good Article on Wikipedia: This is a cubic curve that crosses itself to form a loop. It came to my attention because it’s easy to draw as a spline and can be parameterized (giving its coordinates as rational functions of a real parameter) in such a way that its speed, normal vectors, length, and offset curves also have rational parameterizations. It’s the simplest curve after a line with this property.

But among its real-world applications is a more colorful one: if a person and their dog go out for a walk, the person walks at constant speed on a straight line, and the dog runs at twice the speed to catch up from a point off the line, always running straight towards the person, this curve (or rather half of it, up to the tightest-curving point on the loop) is what the dog will follow.

Zeno Rogue uses Dandelin spheres in a a cylinder to develop an elliptic model of the hyperbolic plane. It’s conformal at the foci of the ellipse (but not elsewhere) and somehow corresponds to how someone with binocular vision would see hyperbolic space.

“Wikipedia’s gender gap has flipped for one group of scientists: A new study finds women biology faculty are now more likely than men to have a biography on the popular website” (\(\mathbb{M}\), via). It’s a milestone, but it doesn’t mean the same is true of other fields nor that we have eliminated the institutional sexist barriers that disproportionately push women out of STEM.

The sadly-neglected Caltech snub cube fountain. Another one to add to the collection of places to visit as a mathematical tourist.

Two new Wikipedia articles on little puzzles in geometric probability (\(\mathbb{M}\)):

• Sylvester’s four point problem: if you pick four points randomly in the plane, what is the probability that they form a convex quadrilateral?

• Broken stick problem: if you break a line segment randomly into three parts, what is the probability that they can form the sides of a triangle?

In both cases the answer depends on how you choose a probability distribution to formalize the problems. And if your answer for the first one is the uniform distribution on the plane, independently for the four points, you’re in good company with Sylvester but mistaken: there is no such distribution.

The Office of Management and Budget tries to cripple US science (\(\mathbb{M}\)) by blocking grant-funded US scientists from publishing, traveling to conferences, and collaborating with others, and by making all grants subject to political whim rather than scientific peer review. As Juande Santander-Vela writes, “If you wanted to cripple science research and were disappointed that Congress continued to fund it, this is the sort of document you would produce.”