Peter Kagey
@peterkagey.com
Maker, Educator, Mathematician | Assistant Professor at Cal Poly Pomona “My interests include music, science, justice, animals, shapes, feelings” —Lisa Simpson Creator of @oeistriangles.peterkagey.com.
It’s not obvious to me why this is symmetric, ignoring the right boundary: Regular triangle where T(n,k) is the number of strict trees of weight n with k leaves.
OEIS Parity Triangles@oeistriangles.peterkagey.com · last mo.OEIS sequence A301365 by Gus Wiseman (March 2018). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
Check out Siobhan Roberts’s NYT article about truncated icosahedra and more—featuring a bunch of photos of Jon-Paul Wheatley’s hand-stitched soccer balls. (12p.com) ⚽️ ⚽️ ⚽️
A Mathematical Tribute to the Soccer Ball (Gift Article)
As the World Cup final approaches, take a moment to appreciate the beautiful symmetries of humanity’s favorite truncated icosahedron.
nytimes.com
T(n,k) [is] the number of walks from (0,0) to (n,k) using steps (1,1), (1,0), (1,-1) and (0,-1).
OEIS Parity Triangles@oeistriangles.peterkagey.com · last mo.OEIS sequence A223092 by N. J. A. Sloane (March 2013). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
Check out Alexander Graham Bell’s Tetrahedral Kites from Public Domain Review! (More photos if you follow the link!) publicdomainreview.org/collection/a...
Check out Jiabao Li's project of "transforming abstract math into climbable sculptures," complete with a rendering of a mathematical playground! "What if others could literally play with math—climb on it, move around it, think about it differently?" infinitesums.simonsfoundation.org/math-ambassa...
Check out this gyroelongated triangular bicupola (J₄₄)!
abandoned shed in rural japan transforms into monumental sculpture evoking megaliths
designboom.com
“By its conclusion, a massive quantity of weapons-grade uranium — enough for about 20,000 warheads — had been diluted and fashioned into fuel pellets. The resulting fuel supplied roughly 10% of all electricity generated in the U.S. during those 18 years.”
The Little-Known Nuclear Deal That Could Help Our Climate Crisis | NOEMA
A project to turn nuclear warheads into safe electricity was astonishingly successful in the post-Cold War era. Could it happen again?
noemamag.com
Check this amazing photo which was taken by Mona Hassan Abo-Abda of the Giza Pyramids during Forever is Now exhibition in Cairo, Egypt which won the Wiki Loves Monuments competition in 2023. www.wikilovesmonuments.org/galleries/20...
Number T(n,k) of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and exactly k colors are used; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
OEIS Parity Triangles@oeistriangles.peterkagey.com · 3mo agoOEIS sequence A322670 by Alois P. Heinz (August 2019). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
For the last few months, I've been happy using RSS to keep up with the news publications I care about the most. However, I found it was tedious to initially compile that list of RSS feeds, and I couldn't find good lists online—so I made a guide to help you get started!
RSS Feeds
A list of many of the RSS feeds that I use.
peterkagey.com
I made an animation of a camera traveling through a Boerdijk–Coxeter helix (en.wikipedia.org/wiki/Boerdij...)
Triangle of numbers of partitions of n with total number of odd parts equal to k from {0,...,n}.
OEIS Parity Triangles@oeistriangles.peterkagey.com · 4mo agoOEIS sequence A103919 by Wolfdieter Lang (March 2005). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
Triangle T(n,d) read by rows: Number of ascent sequences of length n with d zeros.
OEIS Parity Triangles@oeistriangles.peterkagey.com · 4mo agoOEIS sequence A175579 by R. J. Mathar (July 2010). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
Number T(n,k) of entries in the k-th cycles of all permutations of [n] when cycles are ordered by decreasing lengths (and increasing smallest elements); triangle T(n,k), n>=1, 1<=k<=n, read by rows.
OEIS Parity Triangles@oeistriangles.peterkagey.com · 5mo agoOEIS sequence A322384 by Alois P. Heinz (December 2018). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
Did you know... PMP made the front page of Wikipedia? Thank you, @wikipedia.org. We're thrilled to be featured in the "Did you know..." section on Pi Day. Happy Pi Day! 🥧🎉
Lately, I've been assigning my upper division math students "Choice Exercises" as a part of their homework assignments, where they get to choose from several options. When I taught Abstract Algebra in fall 2024, I asked students to say which problem was their favorite, which I've recorded here.
Students' favorite Abstract Algebra problems
A collection of students' favorite problems from my fall 2022 Introduction to Abstract Algebra I class.
peterkagey.com
Given reports that Americans buy SUVs in part because the other cars on the road are big, it surprised me that "The likelihood that someone gets into a fatal collision while traveling to and from work [is] higher if they drive a heavy SUV or pickup truck with big blind spots instead of a […] sedan."
The US Is Counting Traffic Deaths Wrong
By emphasizing the number of people killed per mile rather than deaths per capita, traffic safety groups risk normalizing the factors that make American roads so deadly.
bloomberg.com
The number of non-equivalent distinguishing coloring partitions of the path on n vertices (n>=1) with exactly k parts (k>=1). Regular triangle read by rows: the rows are indexed by n, the number of vertices of the path, and the columns are indexed by k, the number of parts.
OEIS Parity Triangles@oeistriangles.peterkagey.com · 6mo agoOEIS sequence A309748 by Mohammad Hadi Shekarriz (August 2019). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
Check out @fdecomite.bsky.social’s incredible shelf based on Squaring the Square!
Squaring the square - Wikipedia
en.wikipedia.org
@fdecomite.bsky.social · 6mo agofinished ! There is also a mini-3D version
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!
robinhouston@robinhouston.mathstodon.xyz.ap.brid.gy · 10mo agoI'm going to invent a new kind of building block toy based on the tetragonal disphenoid tetrahedral honeycomb. I think we've all had enough fun with cubes by now.
Triangle read by rows: T(n,k) = number of step shifted (decimated) sequence structures of length n using exactly k different symbols.
OEIS Parity Triangles@oeistriangles.peterkagey.com · 6mo agoOEIS sequence A288620 by Andrew Howroyd (June 2017). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)
I wrote a blog post about my G4G16 gift. If you want a copy of your own, download and print the files!
G4G16 Gift Exchange
The gift I made for Gathering 4 Gardner in 2026, together with files so you can make more at home.
peterkagey.com
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...
Potato printing plot party postcards
A postcard designed for the 2025 plotter postcard exchange #ptpx based on 'Potato Printing,' a game that M.C. Escher played with his kids.
peterkagey.com
