Peter Kagey

OEIS triangle for sequence A301626.

OEIS sequence A301626 by Rémy Sigrist (March 2018).

(Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)

A CNC pyramid in wood

Some essentially 2D CNC designs

I learned how to use a CNC machine and wrote G-code today for the first time.

OEIS triangle for sequence A223538.

OEIS sequence A223538 by Tilman Piesk (March 2013).

(Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)

A face distorted through a picture taken through a stained-glass icosahedron.

Funhouse mirror icosahedron selfie made possible by @joshmillard.bsky.social

Also, coincidentally, I’m in Portland right now, and this morning I went with my friend to a “reading in the garden” event at Leach Botanical Garden in SE, and I gently forced him to read this article!

We Need To Rewild The Internet  | NOEMA The internet has become an extractive and fragile monoculture. But we can revitalize it using lessons learned by ecologists.

Have you seen this? Maybe my favorite article I’ve read this year! www.noemamag.com/we-need-to-r...

And never forget that the Wikipedia page for scratch and sniff begins with the words "Scratch and sniff technology ..."

Stamp Encore — Stamps Forever Vote for the stamp you want to bring back!

Cast your vote for the USPS to bring back the SCRATCH AND SNIFF "Frozen Treats" stamp.

Photo of the inside of our studio it’s a two-story high room with white walls and a white ceiling and a giant aluminum biomorphic undulating cellularly perforated sculpture standing in the middle

We’re opening up our studio to visitors on August 16th. Mark your calendars! We will have demos, you can shop our jewelry + puzzles, and also get sneak peaks of various sculpture projects we’re working on (in Catskill, NY)

Am I tempted to travel to Austria just for the purpose of climbing through a 97 m³ spatial net? 😏

berliner-playequipment.com/us/referenze...

Jacaranda Season in Los Angeles In Los Angeles, our protests have been acts of hope and courage, full of moments of joyful resistance expressed by dancing, singing, and blessings.

This article is from a month ago, but still gives me hope.

“Hope is a verb—an action we have to do.”

Last night, Sierra and I saw the Yeah Yeah Yeahs at the Orpheum and Karen O reminded us how strong the community in LA can be during this time of adversity for our city.

🚫🧊

Just this past month, I've been working with Pontus von Brömssen and Bert Dobbelaere on analogous problems for other space-filling polyhedra. Here are all of the ways of placing 4 cells (each 1/12 of a rhombic dodecahedron) of the rhombic pyramidal honeycomb face-to-face.

oeis.org/A385274

Mirad qué preciosidad nos comparte @peterkagey.com a partir de una fotografía que realicé en Valencia y a la que dediqué un #MicrorrelatoMatemático

La belleza de las #matemáticas ⬇️

The 187 possible shapes that can be formed from 5 of the Valencia tiles. Las 187 posibles formas que se pueden formar a partir de 5 fichas de Valencia.

Hay 187 formas posibles que se pueden formar a partir de 5 de estas fichas.

Up to rotation and translation, there are 3 distinct tiles, 4 connected components of two tiles, 15 of three tiles, 47 of four tiles, and 187 components of five tiles, shown here.

Want to guess how many there are for six, seven, and eight tiles?

Guessing a permutation in a way analogous to Wordle Let $w$ be a permutation of $\{1,2,\dots,n\}$ chosen uniformly at random. You have to determine $w$ by successively guessing permutations $v_1, v_2, \dots$. After each guess $v_j$ you are told wher...

I wish that MathOverflow treated everyone like Richard Stanley: ask a simple but rich question, get lots of upvotes and no snarky comments.

I’m guessing that you’re pointing out that the first bucket is 7 years while the rest are 5, so it’s likely wrong to conclude that the youngest bucket actually had a higher rate of turnout than the people in the second youngest bucket.

At first glance this looks pretty good to me! I’m curious to hear your gripes!

Always happy to chat more about any of this too! 😊

Problem 31, which asks about ways of tiling grids with various tile designs.

A few others (e.g. Problems 31, 79, 132) have answers or bounds now because I've worked on the problem.

For example, Problem 31 is discussed in my JIS paper with Bill Keehn, "Counting Tilings of the n × m Grid, Cylinder, and Torus."

Problem 17, which asks about ways of placing queens on a n x n chessboard to maximize number of available moves.

Some of the problems have answers or bounds now because I've asked about them (e.g. Problem 1, Problem 17, Problem 110)

Problem 53, which asks about convexity classes of n-gons.

Also, some of the problems, such as Problems 30, 53, 107, and 108, have solutions that were either already known or found after I wrote the problem down.

Problem 68, which asks about mazes on the square grid.

For example, the main problem in Problem 68 is definitely *not* open, although some subquestions might be.

If we close off the start/end of the maze, then we get a bijection with spanning trees on a grid graph, so counting the mazes is at most a step away from a standard result.

This is a good question! I said, "mathematicians might not know the answers to," because I haven't done a deep dive on existing literature for most of these problems, so I don't always have a great deal of confidence that they're open. Sometimes I call this "Open(ish) Problems Collection"

Some of these innocuous-sounding questions even made their way into my PhD dissertation, and I'm really proud of the fact that when non-experts ask me about my research, I can give them problems that they can really understand and start thinking about.

You can see the whole collection here!

Problem 48 from my Open Problems Collection which asks about the number of folds it takes to fold a strip of equilateral triangles down into a single triangle.

This collection has 130+ questions that mathematicians might not know the answers to, but that a 10–14 year old can think deeply about (and potentially even solve!)

(Here's the specific problem that the student was working on.)

A pencil, paper, and a partially folded piece of paper folded into a strip of equilateral triangles.

Last week, I was a faculty member at Camp Conway, a math camp for ~10–14 year olds outside of Los Angeles, CA.

The campers have time during their day to think about whatever they want, and I just got an email that a camper has been thinking about a problem from my "Open Problems Collection."

A New Pyramid-Like Shape Always Lands the Same Side Up | Quanta Magazine A tetrahedron is the simplest Platonic solid. Mathematicians have now made one that’s stable only on one side, confirming a decades-old conjecture.

"In the end, the work on monostable tetrahedra didn’t involve any particularly sophisticated math, according to Richard Schwartz of Brown University. But, he said, it’s important to ask this kind of question in the first place. It’s the kind of problem that’s often easiest to overlook."

I got to fully participate in not ranking Cuomo!

In L.A., Protesters Practice the Politics of Jesus What is oftentimes characterized as violent protest is, in fact, usually just disruptive.

I’ve written something for @sojo.net about what’s been happening in LA: sojo.net/articles/opi...

We see the logic of domination at work, and we’ve got to reject it and commit to the brave politics of care instead.