It is well known that we can make a cardioid by drawing straight lines inside a circle. Simply choose one point on the circle’s boundary to be the base point. Then, connect points on the circle to the points twice as far away from the base point (measured along the circumference). If there are n…
Author: Dave Richeson
Connections with mathematical terms
I’ve been enjoying the New York Times Connections game. It is a word game with simple instructions: “Find groups of four items that have something in common.” That is, you want to group the 16 given words into four groups of four, with each group sharing some trait. Examples they give are: FISH: bass, salmon,…
Drawing a Celtic Knot
I decided to put together some activities for a gathering of math and computer science majors—puzzles, math crafts, etc. One of them was to draw a Celtic knot. I decided to write up a handout with the instructions. I thought I’d post it here. Enjoy! Here’s a printable pdf of the handout and the diamond-shaped…
Math class technology policy: Fall 2023 edition
I decided to address the use of technology—especially generative AI and large language models like ChatGPT and Bard—in the syllabi for my classes this fall. Here’s the current draft of my technology policy for my upcoming calculus classes. If you have thoughts or observations, leave them in the comments below. Also, feel free to copy,…
3D-Printable Aperiodic Monotiles and Aperiodic Monotile Coloring Book Pages
In March 2023, David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss thrilled the world when they announced their discovery of a family of aperiodic monotiles. These are tiles (imagine ceramic tiles you’d use on a decorative floor) that can cover an infinite plane, but unlike tiles made of rectangles, hexagons, equilateral triangles, and so…
Halloween craft: FLEX-A-GHOUL
Flexagons are a favorite mathematical craft. The original flexagon—the trihexaflexagon—appears to be a two-sided hexagon, but by performing a pinch flex move, the hexagon opens from the center displaying a hidden face. Continuing to pinch flex the shape and we see that the flexagon has three sides. That is not quite true, however. While it…
Preorders and Finite Topological Spaces
Today I tweeted that I had asked my topology students to find all of the different topologies of a two-point set and a three-point set. It turns out that there are three of the former and nine of the latter. (The sequence of the number of topologies for an n-point set begins 1 (for ),…
My Two-Day Crash Course in PGFPlots and TikZ
I will be teaching multivariable calculus in the fall. During the semester, I’ll have to make numerous figures in two-and three-dimensional space for exams and handouts. One of the things I wanted to do this summer was to learn how to use TikZ to create graphs and other graphics in my LaTeX documents. After a…
Essential Trigonometry for Calculus
My son is taking a calculus course in high school this year. While talking to him about his homework, I have come to realize that his knowledge of trigonometry is pretty weak. He said that they were supposed learn trigonometry last spring after the COVID-19 pandemic hit and school switched to fully online. Needless to…
Puzzle: Let’s (Un)Do the Twist!
Today, while walking our dog, I had an idea for the puzzle shown below. Here is a printable pdf. I hope you enjoy it. If you would like a hint as to how to solve the puzzle, read about this puzzle from the great puzzle master Sam Loyd; it was the inspiration for my puzzle.
David Richeson: Division by Zero 