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Dave Jensen Profile picture
Dave Jensen
@DaveJensenMath
Mathematician at the University of Kentucky. Opinions expressed are my own and do not reflect the university, college, or department
Jan 18, 2022 • 20 tweets • 5 min read
This thing is a SQUARED RECTANGLE, a rectangle made up of smaller squares, no 2 of which have the same size. In this 🧵, I'll explain what these things have to do with electrical circuits and graph (co)homology. 1/20

image source: mathblag.wordpress.com/2012/07/21/squ… If you like to play with these things, a few questions to think about:

1. Can you build a squared square?
2. How about a squared rectangle with rational edge lengths, but the smaller squares have irrational edge lengths?
3. Is there a 3d version of a squared rectangle?
2/20
Nov 21, 2021 • 6 tweets • 2 min read
Quite happy with my expository article in the December Notices of the @amermathsoc, Chip Firing and Algebraic Curves. It's only 7 pages and written for a general math audience, so I encourage you to read it, but here's a short thread. 1/6

ams.org/journals/notic… The chip firing game is played with stacks of poker chips on the vertices of a graph. There is only 1 move: you pick a vertex to "fire", which means that the vertex gives 1 chip to each of its neighbors. Here's a web version of the game. 2/6

thedollargame.io/game/level/100…
Nov 9, 2021 • 7 tweets • 2 min read
CW: suicide, the holocaust

Yesterday was the birthday of Felix Hausdorff. Hausdorff made many important contributions to mathematics, but that is not what this thread is about. 1/7 Included here is an English translation of Hausdorff's farewell letter, excerpted from the book Mathematicians Under the Nazis, by Sanford Segal. It is very difficult to read, but I encourage you to do so if you're comfortable. 2/7
Jul 25, 2021 • 14 tweets • 4 min read
Our Penrose quilt is finished, after only 2 years! We make a lot of math quilts with the students in the Math Lab, but this quilt is by (and for) just me and my partner. In this 🧵 I discuss some of the math behind this quilt. 1/14 Image Most quilt patterns are periodic. For example, imagine you have 2 copies of this hexagon quilt, and you lay them on top of each other so that the hexes line up. If you take the top one and shift it a few inches to the left, the hexes will still line up. That's periodicity. 2/14 Image
Dec 31, 2020 • 10 tweets • 4 min read
Our most recent mathematical quilt is (finally) finished, and it is SO PRETTY! This one is a multiplication table (also called a Cayley table) for the symmetric group on 4 letters. Let's talk about it! 1/10 The warm colors (yellow, orange, and red) represent even permutations, so this 12x12 block is a multiplication table for the alternating group. 2/10