Inspired by @robinhouston.mathstodon.xyz.ap.brid.gy's G4G16 gift of tetragonal disphenoidal blocks, I've made some magnetized versions, which are satisfyingly click-y!

Triangle read by rows: T(n,k) = number of step shifted (decimated) sequence structures of length n using exactly k different symbols.

I wrote a blog post about my G4G16 gift. If you want a copy of your own, download and print the files!

Enlarging 3D printed models. I am imagining the structure of our physical universe just above the Planck scale, where quantum forces overcome the force of gravity. If you are exploring the fundamental structure of three dimensional form, this is the place to be!

Petition: Christopher Havens is an inmate in the Washington state prison system who has been collaborating on mathematics with people both inside and outside prison. He was recommended for clemency by the parole board. However, governor Bob Ferguson has not granted it yet. (link below)

Peter has a nice blog post about making his card. Check it out peterkagey.com/blog/2025/12...

I got some nice #ptpx cards in the mail today. Thanks @peterkagey.com @aotearoan!

Three podcasts that I loved that have since stopped releasing new episodes, but which I wish more people knew about. – Hakai Magazine Audio Edition – Ox Tales (by the Oxford Symposium on Food and Cookery) – 70 Over 70 (by Pineapple Street Studios) Please recommend defunct podcasts to me too!

I wrote about the postcard I designed for the 2025 plotter postcard exchange #ptpx on my blog, based on a potato-based game that M.C. Escher used to play with his kids.

Don Knuth just published OEIS sequence: "A391478: T(m,n) is the number of Hamiltonian cycles on an m×n torus where each step goes north (N), east (E), or northeast (NE), with 2 ≤ n ≤ m." It references three sequences, two of which are sequences I published in 2019!

I wrote a blog post about human polyhedra, which truly *embodies* mathematics.

In October 2014, a few months out of college, I made my first web app so users could submit examples of constructions of upper bounds for a graph theory problem. This last week, I've updated it to make it more mobile-friendly and colorful! Try it out and see if you can improve any of the bounds!

I am absolutely buzzing following the publication of my very first OEIS sequence. oeis.org/A389751 Numbers k such that k^3 can be represented as the sum of k consecutive nonprimes. Eg a(3) = 9^3 = 76+77+78+80+81+82+84+85+86 Only the first 16 numbers found so far, so please come and add more!

Check out my new blog post on a prototype shelf that I designed and made out of cardboard based on the "squaring the square" problem, which asks if you can partition a square into smaller squares all of different sizes. (You can!) Come for the photos, stay for the 3D model!

I got a shoutout in the 245th edition of Carnival of Mathematics!

Looks like #plotparty postcards have landed in mailboxes! Read my new blog post about the cards I designed.

HMC CS prof Lucas Bang is helping students gain access to learning & networking opportunities in the computer programming languages field. Bang received a three-year NSF grant to fund as many as 10 students per year to attend international workshops in programming languages. uqr.to/bang-nsf.

Triangle T(m,n) giving of number of steps in the Euclidean algorithm for gcd(m,n) with 0<=m<n.

Five years ago today, I asked a question on Stack Exchange about the number of "n-polytets," which are ways of gluing n tetrahedra together. Recently user Deadcode (David Ellsworth) answered the question and used some novel ideas to extend OEIS sequence oeis.org/A276272 from a(6)–a(17)!

I wrote a blog post about how I made an RSS feed that allows you to get updated when new sequences matching your search are added to the On-Line Encyclopedia of Integer Sequences (OEIS).

Arbitrarily Close: An Introduction to Real Analysis has been published by 619 Wreath! Free PDF, Desmos, and GeoGebra available on my faculty webpage (at least for the time being): www.cpp.edu/faculty/jaro... Hardcover and paperback copies are available from 619 Wreath: www.619wreath.com/acl.html

I made a RSS feed that to see when new sequences are posted to the On-Line Encyclopedia of Integer Sequences (OEIS). For example, if you want to see all of my new sequences or all those with keyword "nice", subscribe to api.peterkagey.com/oeis_feed.xm... api.peterkagey.com/oeis_feed.xm...

I recently wrote a story about Peter Putnam, a forgotten physicist-turned-janitor with a groundbreaking theory of the mind, for @nautil.us. I was able to piece together Putnam's incredible story thanks to a few people who kept the ember of his work glowing for decades after his tragic death.

Every Cobb salad is a macabre salad to me (because of the bacon).

T(n,k) is the number number of partitions of n into distinct odd parts, where every part is ≤ k.

Tomorrow's the last day to get the "early bird" registration price for the Gathering 4 Gardner conference. This time, it will be in San Francisco! Featured speakers include computer scientist Donald Knuth, Mythbuster's Adam Savage, and Pixar's Danielle Feinberg. www.gathering4gardner.org/g4g16-info/

Cool! Bert Dobbelaere and I counted that there are 10924738869 ways of putting 19 of these together! (oeis.org/A385024)

Celebrated the centennial of the MAA SoCal-Nevada Section this afternoon by building the MAA icosahedron logo in real life! Designed by Glen Whitney, who oversaw the construction. @joinmaa.bsky.social

If you work for ICE, you should quit.

Triangle read by rows giving Whitney numbers [of the second kind] T(n,k) of Fibonacci lattices. en.wikipedia.org/wiki/Matroid...

There's a nice article by Siobhan Roberts about the Bridges 2025 conference in Eindhoven in the NY Times. I can now say that I am in The NY Times! (A photo credit for the shot of Chaim Goodman-Strauss and Edmund Harriss,... but still!) www.nytimes.com/2025/10/10/s...

Amazing: due to github.com/python/cpyth..., once you've updated to Python 3.14, you can use the command πthon to run your code

I was curious how many New Yorkers lived Upstate, so I looked on Wikipedia. The ratio of (population of NYC metro area)/(population of NY state) is (19940274)/(19867248)=1.00368, with a population of just -73026 people in Upstate New York.

The #illustratingMath Seminar Online returns on Friday, October 10th, 9 am Pacific / 12 pm Eastern / 6 pm Europe. @3blue1brown.com will be "Exploring Zeta Function Visualizations." Gabriel and Jim will provide some "Show and Ask" input. See you online on Friday!

I just re-designed my website away from Wordpress so that I could more easily embed 3D objects, Javascript, and more. Check out my first blog post that takes advantage of these new features, based on a Bluesky post that I made back in May.

Two puzzles I'm building: 🔴 12 pieces slide into a cube with coordinated motions in 2D abstract space. 🔵 30 pieces form a dodecahedron with 4D motions. Inspired by John Kostick's designs. john-kostick.github.io/vzome-sharin...

The k-th entry of the n-th row here is (n^4 % k) % 2 with 0 colored dark blue and 1 colored light blue.

Today in the NYT

CMU students and math artist Glen Whitney created “Knight’s Move,” an 8-foot sculpture on Wean Hall’s patio. Representing 288 knight moves on a 3D chessboard, it’s a bold mix of math and art. Check it out this fall! www.cmu.edu/mcs/news-eve...

Just heard of vZome for the first time. www.vzome.com/app/ #mathapp seems great.

My first OEIS entry: https://oeis.org/A387361

The conjecture that every convex polyhedron is Rupert is settled in the negative! The convex body in the image cannot pass straight through a hole inside itself. arxiv.org/abs/2508.18475 #Mathematics #Geometry #MathSky

Minimum number of integer-sided squares needed to tile an m X n rectangle.

A Mathematica demo I made of wandering around a parameter space of the convex hull of various scalings the vertices of a icosahedron, dodecahedron, and icosidodecahedron. Given the right parameters, we can recover all Platonic and Catalan solids with full icosahedral symmetry.

I can tell you first-hand that this is a terrific department to work in! (Not least because @dyong.bsky.social is a world-class colleague!)

Made some Escher-inspired magnetic refrigerator magnets by using my AxiDraw V3 pen plotter to draw some tiles on a magnetic vent cover.

Painted my flower pot with Truchet tiles. (1 of 7429) (oeis.org/A368306)

The second talk is by @peterkagey.com, who is speaking about "Enumerating Truchet tiles on the faces of polyhedra." This is a collaborative project within the @prisonmathproject.bsky.social, together with William Keehn. Starting from M.C. Escher, the two explore some rich combinatorics problems.