Peter Kagey @peterkagey.com · 28/09/2026There’s a Sierpinski triangle hiding in there (there’s always a Sierpinski triangle hiding in there) 000
Peter Kagey @peterkagey.com · 26/09/2026Triangular array read by rows: T(n,k) is the number of partial permutations of {1,2,...,n} that have exactly k cycles, 0<=k<=n. 000
Reposted by Peter KageyHarvey Mudd College @hmc.edu · 19/09/2026#HMC #mathematics professor @dyong.bsky.social has been appointed executive director of #MathforAmerica LA. Under Yong’s directorship, the org plans to expand its programs to more schools and build infrastructure for data-gathering and research to inform #PublicEducationPolicy. uqr.to/yong-mfala. 011
Peter Kagey @peterkagey.com · 07/09/2026Number T(n,k) of entries in the k-th blocks of all set partitions of [n] when blocks are ordered by decreasing lengths (and increasing smallest elements); triangle T(n,k), n>=1, 1<=k<=n, read by rows. 010
Peter Kagey @peterkagey.com · 06/09/2026Unique sequence with a(1)=0, a(2)=1, representing an array T(i,j) read by antidiagonals in which every row is this sequence itself. 000
Peter Kagey @peterkagey.com · 20/07/2026It’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. 150
Peter Kagey @peterkagey.com · 17/07/2026Check 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) ⚽️ ⚽️ ⚽️nytimes.comA 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. 042
Peter Kagey @peterkagey.com · 13/07/2026T(n,k) [is] the number of walks from (0,0) to (n,k) using steps (1,1), (1,0), (1,-1) and (0,-1). 040
Peter Kagey @peterkagey.com · 30/06/2026Have you seen the Swirled Series? (isohedral.ca/swirled-seri...) "Early in November, Daniel Piker (aka @KangarooPhysics) suggested that a group of people could get together online, and each create a short segment of animation, arranged so that all the start and end frames are identical..." 221
Peter Kagey @peterkagey.com · 18/06/2026I found out about this here. Check it out for more kite content!publicdomainreview.orgThe Art of Kite Flying (1430–1929)69 images of kite flying from across 5 centuries and some 10 countries. 000
Peter Kagey @peterkagey.com · 18/06/2026Check out Alexander Graham Bell’s Tetrahedral Kites from Public Domain Review! (More photos if you follow the link!) publicdomainreview.org/collection/a... 183
Peter Kagey @peterkagey.com · 13/06/2026Hey! That’s me! Table read by rows: the n-th row gives the lexicographically earliest sequence of length n such that the convex hull of (1, a(1)), ..., (n, a(n)) is an n-gon with minimum height. 000
Peter Kagey @peterkagey.com · 10/06/2026@timchartier.bsky.social—and math can make you better at basketball?popsci.comBasketball can make you better at mathCombining math concepts with sports can help boost your fractions game. 022
Peter Kagey @peterkagey.com · 07/06/2026@rmfrt.com—this made me think of you!designboom.comcrafting the future, thread by threadwhat if the spaces and objects of tomorrow are not mass produced, but meticulously crafted? in crafting the future, we explore what it means to be a maker today. 010
Peter Kagey @peterkagey.com · 06/06/2026See even more renderings on Jiabao Li's website! www.jiabaoli.org/math-playgro... 0132
Peter Kagey @peterkagey.com · 06/06/2026Check 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... 1226
Peter Kagey @peterkagey.com · 05/06/2026Check out this gyroelongated triangular bicupola (J₄₄)!designboom.comabandoned shed in rural japan transforms into monumental sculpture evoking megaliths 1316
Peter Kagey @peterkagey.com · 19/05/2026“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.”noemamag.comThe Little-Known Nuclear Deal That Could Help Our Climate Crisis | NOEMAA project to turn nuclear warheads into safe electricity was astonishingly successful in the post-Cold War era. Could it happen again? 010
Peter Kagey @peterkagey.com · 17/05/2026Check 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... 030
Peter Kagey @peterkagey.com · 17/05/2026This next term, I have more ideas about how to encourage students to work and learn together—not because I want to be out of the loop (I don't!) but because I think the relationship-building aspect of education is extremely important and seems to be weakening in the age of LLMs. 120
Peter Kagey @peterkagey.com · 17/05/2026each other as much as possible. I use points-based grading on my homework assignments (example linked), but students can get points for things like "Answer a classmate's question on Discord or give a hint about a problem on this week's assignment.* (Two points per answer/hint, up to 4.)"classes.peterkagey.comHW 5A place for assignments and other information about Peter Kagey's classes. 110
Peter Kagey @peterkagey.com · 17/05/2026Thanks for writing all of this—I enjoyed reading and thinking about it! In terms of "students are often asking me for questions that are best answered promptly" I'm trying to push as much as possible for students to be collaborating (in person and/or online) to answer these sorts of questions for 110
Peter Kagey @peterkagey.com · 15/05/2026Number 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. 010
Peter Kagey @peterkagey.com · 12/05/2026For 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!peterkagey.comRSS FeedsA list of many of the RSS feeds that I use. 050
Peter Kagey @peterkagey.com · 11/05/2026You might get a kick out of this!peterkagey.comTriangle center patternsA hypnotic 4K video and accompanying code exploring a discrete-state random dynamical system: iterating and interpolating triangle centers (from Kimberling's ETC) to create colorful geometric patterns... 010
Peter Kagey @peterkagey.com · 10/05/2026I made an animation of a camera traveling through a Boerdijk–Coxeter helix (en.wikipedia.org/wiki/Boerdij...) 081
Peter Kagey @peterkagey.com · 17/04/2026Triangle of numbers of partitions of n with total number of odd parts equal to k from {0,...,n}. 050
Peter Kagey @peterkagey.com · 13/04/2026Triangle T(n,d) read by rows: Number of ascent sequences of length n with d zeros. 010
Peter Kagey @peterkagey.com · 08/04/2026I'm not sure I can explain it, but this is @motivickyle.bsky.social. 191
Peter Kagey @peterkagey.com · 21/03/2026Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n that have k double rises above the x-axis (n >= 1, k >= 0). 000
Peter Kagey @peterkagey.com · 15/03/2026Number 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. 041
Reposted by Peter KageyPrison Math Project @prisonmathproject.bsky.social · 14/03/2026Did 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! 🥧🎉 063
Peter Kagey @peterkagey.com · 13/03/2026Lately, 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.peterkagey.comStudents' favorite Abstract Algebra problemsA collection of students' favorite problems from my fall 2022 Introduction to Abstract Algebra I class. 0110
Peter Kagey @peterkagey.com · 10/03/2026Given 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."bloomberg.comThe US Is Counting Traffic Deaths WrongBy 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. 010
Peter Kagey @peterkagey.com · 08/03/2026The 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. 162
Peter Kagey @peterkagey.com · 05/03/2026I love this! It inspires me to start playing with these ideas again! 000
Peter Kagey @peterkagey.com · 05/03/2026Check out @fdecomite.bsky.social’s incredible shelf based on Squaring the Square!en.wikipedia.orgSquaring the square - Wikipedia 140
Peter Kagey @peterkagey.com · 27/02/2026I did! Just got a 3D printer a few days ago! I designed them in OpenSCAD and customized them for some 3mm x 1mm magnets that I bought for about 3¢ each (purchased on Amazon, for better or worse.) I'll try to write a blog post about it soon, but reach out in the meantime if you want the files. 010
Peter Kagey @peterkagey.com · 27/02/2026Inspired 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! 2152
Peter Kagey @peterkagey.com · 25/02/2026Triangle read by rows: T(n,k) = number of step shifted (decimated) sequence structures of length n using exactly k different symbols. 050
Peter Kagey @peterkagey.com · 22/02/2026You can read more about the puzzle here.peterkagey.comPentagonal icositetrahedron puzzleA puzzle on the faces of the pentagonal icositetrahedron with 3D models, STL files, photos, and video illustrations 110
Peter Kagey @peterkagey.com · 22/02/2026That's right! This is a puzzle on the faces of the pentagonal icositetrahedron, which has three short edges and two long edges. 010