New Year's Eve linkage

Interview with Annie Rauwerda (\(\mathbb{M}\), via), known for publishing odd stuff from Wikipedia on her social media accounts.

Pierce College professor Kim Rich tracks down fake student bots that enroll in community college courses in order to commit financial aid fraud (\(\mathbb{M}\)).

Fewer 456075 triangles tile the square (\(\mathbb{M}\), via). It’s possible to tile squares edgetoedge with fewer acute triangles but if you allow nonedgetoedge tilings you can use only a single shape (but different sizes) of acute triangle, this one. The minimum number of triangles has been gradually reduced since 1990 when this was discovered; now it’s down to 32.

I posted a link to Ben Green’s superpolynomial lower bounds for offdiagonal van der Waerden numbers last February, based on a blog post by Gil Kalai; now Quanta Magazine has a writeup (\(\mathbb{M}\)).

Regular number (\(\mathbb{M}\)), the numbers that divide powers of 60, now a Good Article on Wikipedia. These actually have different names in the different contexts they come from:

Regular numbers in the study of Babylonian mathematics

5smooth numbers in modern mathematics

Harmonic whole numbers in music theory and architecture

Hamming numbers in computer science


Lisp in Conway’s Game of Life (\(\mathbb{M}\), via). The implementation involves compiling a C implementation of lisp onto a custom CPU in Life, modified from one used four years ago to implement Tetris in Life. It would be capable of running other C programs in the same way.

Ocean rain, Mendocino, Christmas afternoon (\(\mathbb{M}\)):

Square pyramidal number (\(\mathbb{M}\)), another new Wikipedia Good Article. Some things I learned in working on this article:

They were part of a family of figurate numbers studied by Japanese mathematicians of the wasan period.

As well as counting points or balls in a square pyramid shape, they count the number of acute triangles in an odd regular polygon.

They give the denominators of an infinite alternating summation for \(\pi3\).


Transfinite algorithm analysis: with real edge weights on a finite graph with \(m\) edges, the Ford–Fulkerson algorithm can take time \(\omega^{\Theta(m)}\) (\(\mathbb{M}\)). 2015 preprint by Backman and Huynh, later published in Computability.

Approximation to a fundamental domain for the CannonThurston map for the figure eight knot complement. Henry Segerman posts an image from joint work by Saul Schleimer, of an intricately filled fractallooking shape. One commenter suggests it looks like Escher’s work; my own comparison is to an image of the Crab nebula.

On an angle with magical properties (\(\mathbb{M}\)), Horgan and Murphy in the Notices. The angle is the larger of the two acute angles in the right triangle formed by a side, short diagonal, and long diagonal of a cube, roughly 54.74°. It appears frequently in cylindrical structures reinforced by helical fibers, as the pitch angle maximizing volume per fiber length. Examples occur in worms, octopi arms, elephant trunks, water hoses, and blood vessels.

Born three months before her brother? (\(\mathbb{M}\)) I was amused by this example of how errors or discrepancies (in this case, in the birthdate of a pianist) can propagate through historical sources (including Wikipedia) and how the circularity of that propagation can hamper efforts to determine which of two inconsistent claims is the incorrect one.

Webb and origami (\(\mathbb{M}\)). This site features an origami papercraft model of the 18hex honeycomb mirror of the James Webb Space Telescope, currently on a path to its L2 orbit. But I’m more interested in how the spaceship unfolds itself as it travels, from a more compact configuration that would fit into a rocket into its final form.