Peter Kagey

A list of many of the RSS feeds that I use.

A collection of students' favorite problems from my fall 2022 Introduction to Abstract Algebra I class.

The gift I made for Gathering 4 Gardner in 2026, together with files so you can make more at home.

A postcard designed for the 2025 plotter postcard exchange #ptpx based on 'Potato Printing,' a game that M.C.

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.

A shelf design inspired by the 'squaring the square' puzzle, with prototype photos, an interactive 3D model, and downloadable SVG/STL files for laser-cutting or 3D printing.

Pen‑plotted polyhedral postcards from a #plot-party — 15 perspectives of nested icosahedron/dodecahedron/icosidodecahedron, with plot timelapses and the postcards I received.

An RSS feed based on searches on the On-Line Encyclopedia of Integer Sequences

A puzzle on the faces of the pentagonal icositetrahedron with 3D models, STL files, photos, and video illustrations

An open problem about polyomino tilings, that suggests the possibility of a surprisingly fast-growing function

Images and visualizations of points, lines, and circles obtainable with straightedge-and-compass constructions up to five steps — including 5,743 ruler+compass points, 1,704 compass-only points, 1,337 circles, 596 lines, and 480 compass-only circles, star…

Enumerating distinct straightedge-and-compass constructions with n lines and circles (OEIS A383082–A383087), illustrated with images and a video and computed using Haskell.

Photos and code exploring tiles with reflectional and rotational symmetries, plus programmatic n×m grid and torus tilings using Mathematica and Python.

Story of 'Fibonachos' — a 2017 reddit puzzle about taking Fibonacci-numbered nachos, my OEIS submissions (A280521, A280523, A382814), Neil Sloane featuring the sequences, and a conjecture about who ends up with the most nachos.

Animations, images, and Mathematica code for inscribing and superimposing hexagonal arrays inside an equilateral triangle, inspired by triangular numbers and a G4G gift-exchange project.

At G4G15 I created 200 hand-cut, pen-plotted 'parity triangle' cards generated from OEIS sequences—made with a Cricut, AxiDraw, and a Python script; includes photos, videos, and info on how to request one.

Reflections on Yan Zhang’s threads about status, power, and recognition in mathematics — the damage of status hierarchies, the value of teaching and mentoring, and why John Conway’s playful work is undervalued.

Inspired by Dave Richeson’s Truchet tilings, I designed and built my own LEGO version using Stud.io, Bricklink parts, and a few hundred euros’ worth of curved tiles.

A "beautiful little problem" about rational roots of quadratic equations with odd coefficients.

Photos and stories about stellated dodecahedron model from the 2025 JMM art exhibition, which was inspired by early makerspace projects and built using plywood, 8¢ hinges and laser-cut faces

Recreating a 2021 tweet with JMM catalog photos and reflecting on my mathematical art in the 2024 and 2025 JMM exhibitions—photos, video, Bridges links, and pen-plotter/Mathematica projections.

FEND.

A Mathematica animation inspired by Robert Fathauer's cube-fractal timelapse and Ayliean's #MathArtMarch, exploring shifting cube fractals and transparent views.

A curated collection of saved video tweets showcasing Rafael Araujo’s geometric art, Keishiro Ueki’s hinged objects, Amy Goodchild’s Genuary illustrations, and Matt Pritchard’s optical illusion.

A set of saved video tweets: Matt Henderson’s triangle-center fractal that inspired my work, Josh Millard’s clip of Olivier Gomis woodworking, Pierre Thibault’s hypnotic topology loop, and Flávio Costa’s pen-plotter synced to Debussy.

Four saved video tweets: a cubic curve through nine points, a rubber-band dodecahedron fold, a rolling oloid (with student project), and a public LEGO build at the Tate Modern.

A curated archive of saved tweets featuring images of mathematical art, optical illusions, origami and paper models, Truchet designs, teaching resources, and other geometry- and math-related posts.

An M.C.

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 inspired by a tweet.

Step-by-step guide to creating animated math GIFs using LaTeX (TikZ) and ImageMagick — render each frame as a transparent PDF page, then convert to an animated GIF (example: randomized colored circles).

Exploring the math behind the @xorTriangles bot: generating XOR number triangles, characterizing rotationally symmetric seeds via linear algebra over Z/2, and connections to OEIS.

Exploration of Project Euler Problem 208's 'robot walks'—visual demos, interactive applet and code, Stack Exchange discussions, a Twitter bot that tweets walk patterns, and prints inspired by the paths.

A Pour La Science mention of my OEIS work and the 'anti' sum–product problem: sequences (A337655, A337946) whose addition and multiplication tables maximize distinct values (and in A337946 never overlap), with related OEIS explorations.

Explores Zimin words and bifixes in binary strings—counting words that begin with odd/even palindromes, related OEIS sequences, bijections, and pattern-avoidance results.

Explores OEIS A263135—maximal penny-to-penny contacts for n pennies on hexagonal-grid vertices—spiral packings, comparison with face-penny sequence A047932, and a conjectured difference (A216256) with an open-problem bounty.

Exploring OEIS sequence A278299 — the minimal polyomino sizes that allow an n-coloring with every pair of colors adjacent; origin, bounds, computations, and a playable solver.

An exploration of OEIS sequence A289523: greedily placing circles of area kπ so they don't overlap, with plots, spiral variants, and questions about linear bounds and packing density.

Exploration of OEIS A261865 — the least integer k whose square root has a multiple in (n,n+1); includes examples, plots, a conjectured density formula for values, and record-finding computations.

Interpreting Richard Guy’s 1971 letter to Neil Sloane and investigating his partition sequence A279197: corrected definition, Haskell code, and extended OEIS terms counting inseparable, self-conjugate 3-term arithmetic partitions of {1..3n}.

Part 2 of a three-part guide to @BotfonsNeedles.

Part 2 of a three-part guide to @BotfonsNeedles: using the Twitter API (tweepy) to post images, read and write tweets, and maintain a running Monte Carlo estimate of π.

Part 1 of a three-part guide to @BotfonsNeedles: simulating Buffon's needle in Python to estimate π and generating images in Python for a Twitter bot.

Exploring polytopes with lattice coordinates — counting polygons and polyhedra on square, triangular and higher-dimensional grids, surprising lattice examples and embeddings, OEIS sequence cataloging, and an applet illustrating the binomial formula for eq…

A Python tool that turns two-dimensional OEIS sequences into one-bit-per-pixel parity bitmaps — featuring a fractal from A279212, example images, downloadable code, and links to further exploration.

Counting LEGO brick towers: rules and generating-function proofs (including the 3^{n-1} formula for 1×2 bricks), symmetry and OEIS sequences, and notes on stability and overhang problems.

Photos and discussion of a 30×40 Truchet canvas print built from Truchet tiles on the truncated trihexagonal tiling, with notes on the 10 PRINT inspiration, Catalan connections for 2n-gons, and links to random-tiling bots and further reading.