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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.

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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.
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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.
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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.
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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.
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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).
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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
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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.
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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.
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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
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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
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Peter Kagey @peterkagey.com · 22/05/2026
This is indeed gorgeous and worth a read!
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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?
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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.
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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.
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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.
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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...)
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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}.
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Peter Kagey @peterkagey.com · 13/04/2026
Triangle T(n,d) read by rows: Number of ascent sequences of length n with d zeros.
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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
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Peter Kagey @peterkagey.com · 21/03/2026
Hey! That’s the one in the profile picture!
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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.
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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
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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.
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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.
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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.
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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
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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!
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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.
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Peter Kagey @peterkagey.com · 22/02/2026
I wrote a blog post about my G4G16 gift. If you want a copy of your own, download and print the files!
peterkagey.com
G4G16 Gift Exchange
The gift I made for Gathering 4 Gardner in 2026, together with files so you can make more at home.
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Reposted by Peter Kagey
Andy Huss @wizucorn.bsky.social · 02/02/2025
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!
The photo shows identical soft cell units assembled into a lattice structure. The shape seems to have the same qualities as a truncated octahedron, It won’t dense pack as efficient as the Kelvin or Weaire-Phelan structures because the deformation of the faces increases the surface area of the individual units and makes the ratio of the volume of the object to the edge length less efficient. But it looks pretty and I’m working on filling in the holes now .
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Reposted by Peter Kagey
David Jekel @davidjekel.myatproto.social · 26/01/2026
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)
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Reposted by Peter Kagey
David @dcarew.com · 16/01/2026
Peter has a nice blog post about making his card. Check it out peterkagey.com/blog/2025/12...
peterkagey.com
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.
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Reposted by Peter Kagey
David @dcarew.com · 16/01/2026
I got some nice #ptpx cards in the mail today. Thanks @peterkagey.com @aotearoan!
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Peter Kagey @peterkagey.com · 14/01/2026
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!
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Peter Kagey @peterkagey.com · 27/12/2025
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.
peterkagey.com
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.
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Peter Kagey @peterkagey.com · 11/12/2025
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!
oeis.org
A391478 - OEIS
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Peter Kagey @peterkagey.com · 27/11/2025
I wrote a blog post about human polyhedra, which truly *embodies* mathematics.
peterkagey.com
Human rhombic dodecahedron
Based on a delightful video of people forming a 'human rhombic dodecahedron,' I look for other examples of human polyhedra with some help from an LAPL librarian.
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Peter Kagey @peterkagey.com · 17/11/2025
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!
peterkagey.com
Square Game
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Reposted by Peter Kagey
Benjamin Cornish @mathematicians-pod.bsky.social · 12/11/2025
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!
oeis.org
A389751 - OEIS
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Peter Kagey @peterkagey.com · 13/11/2025
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!
peterkagey.com
Squaring the shelf
Designing a shelf based on the 'squaring the square' problem
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Peter Kagey @peterkagey.com · 11/11/2025
I got a shoutout in the 245th edition of Carnival of Mathematics!
theoremoftheday.org
Theorem of the Day
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Reposted by Peter Kagey
上木 敬士郎 / Keishiro Ueki @keishiroueki.bsky.social · 10/11/2025
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Peter Kagey @peterkagey.com · 05/11/2025
Looks like #plotparty postcards have landed in mailboxes! Read my new blog post about the cards I designed.
peterkagey.com
Plot party postcard exchange
Polyhedral postcard #plot-party!
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Reposted by Peter Kagey
Harvey Mudd College @hmc.edu · 28/10/2025
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.
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Peter Kagey @peterkagey.com · 28/10/2025
Triangle T(m,n) giving of number of steps in the Euclidean algorithm for gcd(m,n) with 0<=m<n.
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Peter Kagey @peterkagey.com · 27/10/2025
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)!
codegolf.stackexchange.com
Gluing tetrahedra together
(This challenge exists to extend sequence A276272 in the On-Line Encyclopedia of Integer Sequences, and perhaps create a new OEIS sequence1.) This is a code-challenge, which will have you write cod...
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Peter Kagey @peterkagey.com · 26/10/2025
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).
peterkagey.com
RSS for the OEIS
An RSS feed based on searches on the On-Line Encyclopedia of Integer Sequences
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Reposted by Peter Kagey
John Rock @johnrockmath.bsky.social · 25/10/2025
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
Cover of the textbook Arbitrarily Close: An Introduction to Real Analysis.
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Peter Kagey @peterkagey.com · 25/10/2025
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...
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Reposted by Peter Kagey
amandagefter @amandagefter.bsky.social · 23/07/2025
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.
nautil.us
Finding Peter Putnam
The forgotten janitor who discovered the logic of the mind
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