Author: peterkagey

How many distinct constructions can be made with a straightedge and compass if we draw \(n\) lines and circles? Describing a straightedge-and-compass construction Initially we start with two points, which we call \((0,0)\) and \((1,0)\). At each step, we can do one of two things: We get new points whenever lines intersect with lines, lines…

Ever since Bill Keehn and I started writing our paper, “Counting Tilings of the 𝑛 × 𝑚 Grid, Cylinder, and Torus,” I’ve been noticing and taking photos of tiles that I see that exhibit interesting symmetries. My wife will sometimes kid on the square: “Whenever you take your phone out to take a picture of…

A few weeks ago I was going through my saved tweets, and I saw this one from Math Lady Hazel which reminded me of a story from early 2017 that I played a small part in. In January 2017, reddit user Teblefer asked the following question: Two people are sharing a plate of nachos. They…

At the beginning of April, I posted two animations related to hexagons inscribed inside of an equilateral triangle. Here I discuss a bit about the origin of these animations and give code so that you can reproduce these on your own. Gathering 4 Gardner gift exchange I first stumbled across this idea at the beginning…

In February 2024, I attended the Gathering 4 Gardner in Atlanta (G4G15), which has a tradition of a gift exchange, where you bring 170 copies of a small gift, and in turn you get a small gift from all of the exchange participants. One of these gifts, a set of 3D-printed fractals from Hideki Tsuiki…

You know that feeling when someone expresses a feeling that you have better than you ever could figure out how to articulate it? While archiving my old liked tweets, I noticed that Yan Zhang had done it. Twice. I wanted to make sure that I copied these notes down so that I could still reference…