Sign in

Peter Kagey

@peterkagey.com
288 followers 203 following 304 posts

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.

PostsRepliesMedia
Peter Kagey @peterkagey.com · 28/09/2026
There’s a Sierpinski triangle hiding in there (there’s always a Sierpinski triangle hiding in there)
000
Peter Kagey @peterkagey.com · 26/09/2026
Triangular 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 Kagey
Harvey 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 · 11/09/2026
You should add it! 😉
011
Peter Kagey @peterkagey.com · 07/09/2026
Number 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 · 06/09/2026
Unique 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 · 20/07/2026
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.
150
Peter Kagey @peterkagey.com · 19/07/2026
Prescient.
100
Peter Kagey @peterkagey.com · 17/07/2026
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) ⚽️ ⚽️ ⚽️
nytimes.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.
042
Peter Kagey @peterkagey.com · 13/07/2026
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).
040
Peter Kagey @peterkagey.com · 30/06/2026
Have 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 · 18/06/2026
I found out about this here. Check it out for more kite content!
publicdomainreview.org
The Art of Kite Flying (1430–1929)
69 images of kite flying from across 5 centuries and some 10 countries.
000
Peter Kagey @peterkagey.com · 18/06/2026
Check out Alexander Graham Bell’s Tetrahedral Kites from Public Domain Review! (More photos if you follow the link!) publicdomainreview.org/collection/a...
Four people standing in a field with a kite that looks like a torusA sierpinski tetrahedron (?) kiteA tetrahedral lattice kiteAn airplane-looking kite made out of a tetrahedral-octahedral configuration
183
Peter Kagey @peterkagey.com · 13/06/2026
Hey! 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.com
Basketball can make you better at math
Combining 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.com
crafting the future, thread by thread
what 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 · 06/06/2026
See even more renderings on Jiabao Li's website! www.jiabaoli.org/math-playgro...
A rendering of a mathematical slideA rendering of a mathematical climbing structure with children playing on it.A rendering of a mathematical merry-go-round.

"Inside the merry-go-round is a zoetrope. The inside wall contains a sequence of models and the outside has narrow slits. As the carousel spins, people sitting on it see the still models animate."Rendering of a Lissajous Swing Set.

"Swings hang from two pivot points so each rider creates a Lissajous curve in the air. A small sandbag under the seat releases sand as the swing moves. The motion leaves patterns in the sand that look like flowers or knots. Each person creates a unique pattern because the curve depends on the person’s weight, the swinging rhythm and speed."
0132
Peter Kagey @peterkagey.com · 06/06/2026
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...
A rendering of a mathematical playground
1226
Peter Kagey @peterkagey.com · 05/06/2026
Check out this gyroelongated triangular bicupola (J₄₄)!
designboom.com
abandoned shed in rural japan transforms into monumental sculpture evoking megaliths
1316
Peter Kagey @peterkagey.com · 22/05/2026
This is indeed gorgeous and worth a read!
051
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.com
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?
010
Peter Kagey @peterkagey.com · 17/05/2026
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...
Giza Pyramids behind a wireframe sculpture of hands during Forever is Now exhibition by Mona Hassan Abo-Abda.
030
Peter Kagey @peterkagey.com · 17/05/2026
This 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 · 17/05/2026
each 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.com
HW 5
A place for assignments and other information about Peter Kagey's classes.
110
Peter Kagey @peterkagey.com · 17/05/2026
Thanks 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 · 15/05/2026
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.
010
Peter Kagey @peterkagey.com · 12/05/2026
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!
peterkagey.com
RSS Feeds
A list of many of the RSS feeds that I use.
050
Peter Kagey @peterkagey.com · 11/05/2026
You might get a kick out of this!
peterkagey.com
Triangle center patterns
A 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 · 10/05/2026
I made an animation of a camera traveling through a Boerdijk–Coxeter helix (en.wikipedia.org/wiki/Boerdij...)
081
Peter Kagey @peterkagey.com · 04/05/2026
Light if coprime, dark if they share a factor.
000
Peter Kagey @peterkagey.com · 17/04/2026
Triangle of numbers of partitions of n with total number of odd parts equal to k from {0,...,n}.
050
Peter Kagey @peterkagey.com · 13/04/2026
Triangle T(n,d) read by rows: Number of ascent sequences of length n with d zeros.
010
Peter Kagey @peterkagey.com · 08/04/2026
I'm not sure I can explain it, but this is @motivickyle.bsky.social.
Profile picture for @motivickyle.bsky.socialTop few rows of parity triangle which vaguely look like a face
191
Peter Kagey @peterkagey.com · 21/03/2026
Triangle 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 · 21/03/2026
Hey! That’s the one in the profile picture!
120
Peter Kagey @peterkagey.com · 15/03/2026
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.
041
Reposted by Peter Kagey
Prison Math Project @prisonmathproject.bsky.social · 14/03/2026
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! 🥧🎉
"Did you know..." section of wikipedia homepage
063
Peter Kagey @peterkagey.com · 13/03/2026
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.
peterkagey.com
Students' favorite Abstract Algebra problems
A collection of students' favorite problems from my fall 2022 Introduction to Abstract Algebra I class.
0110
Peter Kagey @peterkagey.com · 10/03/2026
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."
bloomberg.com
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.
010
Peter Kagey @peterkagey.com · 08/03/2026
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.
162
Peter Kagey @peterkagey.com · 05/03/2026
I love this! It inspires me to start playing with these ideas again!
000
Peter Kagey @peterkagey.com · 05/03/2026
Check out @fdecomite.bsky.social’s incredible shelf based on Squaring the Square!
en.wikipedia.org
Squaring the square - Wikipedia
140
Peter Kagey @peterkagey.com · 27/02/2026
I 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 · 27/02/2026
And a third stellation of a rhombic dodecahedron!
021
Peter Kagey @peterkagey.com · 27/02/2026
And his stellation!
140
Peter Kagey @peterkagey.com · 27/02/2026
Check out Robin's version of a rhombic dodecahedron!
100
Peter Kagey @peterkagey.com · 27/02/2026
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!
2152
Peter Kagey @peterkagey.com · 25/02/2026
Triangle 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 · 22/02/2026
You can read more about the puzzle here.
peterkagey.com
Pentagonal icositetrahedron puzzle
A puzzle on the faces of the pentagonal icositetrahedron with 3D models, STL files, photos, and video illustrations
110
Peter Kagey @peterkagey.com · 22/02/2026
That's right! This is a puzzle on the faces of the pentagonal icositetrahedron, which has three short edges and two long edges.
010