Linkage

A happy 75th birthday to Dick Lipton and 1000th post on his blog with Ken Regan, Gödel’s Lost Letter and \(\mathsf{P}=\mathsf{NP}\) (\(\mathbb{M}\)).

A quick roundup of three recent Wikipedia Good Articles (\(\mathbb{M}\)):

Factorial – you know, \(n!\).

Jessen’s icosahedron – polyhedron with allright dihedrals despite not having axisparallel sides; the shape of the “Skwish” tensegrity.

Erdős–Straus conjecture – the question of whether \(\tfrac4n=\tfrac1x+\tfrac1y+\tfrac1z\) has positive integer solutions for all \(n\gt 1\).


Infinite Hex is a draw, Joel David Hamkins and Davide Leonessi (\(\mathbb{M}\), via). The paper uses a winning condition for the infinite game that seems pretty technical: you need a bidirectional infinite path of your pieces, whose two ends eventually stay inside all translations of two opposite quadrants (NESW or NWSE depending on the player). They give a simple mirroring strategy for drawing, and explain why other winning conditions aren’t as nice.

The Art of Computer Programming, Volume 4, PreFascicle 12A: Components and Traversal (\(\mathbb{M}\)). It’s labeled as “ridiculously preliminary”, but includes interesting material on weak components of directed graphs. Strong components are the finest partially ordered vertex sets under reachability; analogously, weak components are the finest total order. Every vertex can reach all vertices in later sets, and none in earlier ones.

Some Applications Of Mechanics To Mathematics by V. A. Uspenskii (\(\mathbb{M}\)). Usually it goes the other way around. One of the Mir free book series, translated from Russian into English.

JIGGRAPH (\(\mathbb{M}\)). A game of holding hands or, if you prefer something more abstract, fitting vertices with known local geometries together into a graph.

History of Mathematics Project (\(\mathbb{M}\), via, via2), an online exhibit for MOMATH. I’m not convinced of the soundness of a project whose timeline of prime numbers starts with Eratosthenes instead of Euclid, skips from Greeks to enlightenment Europe completely bypassing Ibn alHaytham (using an ordinal time scale to hide the gap), and doesn’t mention the prime number theorem, but still this looks interesting or at least entertaining.

Asymptotics of the number of \(n\)queens placements, Michael Simkin (\(\mathbb{M}\), via, via2). “The chief innovation is the introduction of limit objects for \(n\)queens configurations, which we call queenons.”

More women in a STEM field leads people to label it as a “soft science” (\(\mathbb{M}\)). Alysson Light provides a generalaudience explanation of her research with Tessa BensonGreenwald and Amanda Diekman in J. Experimental Social Psych..

Today’s observation on overlooked history of mathematics (\(\mathbb{M}\)): The binary tiling of the hyperbolic plane, generally attributed to a 1974 paper by Károly Böröczky, was already used by M. C. Escher in a 1957 print, Regular Division of the Plane VI.

If the pigeonhole principle is the idea that more than \(n\) items distributed into containers lead to a container with more than one item (\(\mathbb{M}\)), what is the name for the principle that fewer than \(n\) items distributed into containers lead to an empty container?

Do androids dream of mathematics (\(\mathbb{M}\))? A popularaudience essay by algebraic combinatorist Jonathan Kujawa on data vs insight in mathematics, and the use of computers in sifting through piles of data on mathematical objects and their invariants in order to focus on potential relations between them.

I upgraded from MacOS 11 to 12.2 recently (\(\mathbb{M}\)). Today was our first day of inperson classes. I could not get my laptop working with the lecture hall display. Fortunately I was broadcasting the lecture over Zoom and everyone in the classroom had a laptop so we did it that way. But this video looks like it describes the problem, and a fix (in System Preferences : Battery : Battery, uncheck “Automatic graphics switching”) — I’m hopeful this will work and I can lecture from the big screen next time.