I recently designed and made a string art cardioid sculpture, which is now hanging in our mathematics department’s window. It is made from laser-cut plywood and yarn. I wrote a “how-to” guide that includes templates for the laser-cut pieces. You can find the PDF document here. Enjoy!
Author: Dave Richeson
A Laser-Cut Tromino Puzzle
In my “intro-to-proofs” class, I like to have my students work on some induction problems that are not the usual proof of sums and products of integers. One lovely example is the following problem about tiling a grid with “trominoes” (three squares joined in an el-shape). Prove that for any n ≥ 1, a 2nx2n grid with…
The Unknotting Number is Not Additive
On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called “Unknotting number is not additive under connected sum” (and an updated version on September 15, 2025). In it, they surprised the mathematical community by giving a counterexample to a long-standing conjecture in knot theory. The story was picked up…
Mathematics Departments at Liberal Arts Colleges
I was looking for information about mathematics programs at other liberal arts colleges, so I put together this collection of links. I thought others might find it helpful, so I’m posting it here. (I actually asked ChatGPT to assemble this list. It did an OK, but not great, job. About 70% of the links were…
Magic Eye Image as an Animated GIF
I’ve been playing around with Magic Eye images lately. Yesterday, I had the idea of creating an animated gif that shows the identical magic eye image for each frame. At first, the image looks like TV static (remember TV static?), but by unfocusing your eyes, you can see an image amid the static. Here are…
Type Math on a Mac—Remapping My Keyboard
I use LaTeX to type mathematical documents. However, I often want to type mathematics when LaTeX is unavailable—for instance, in an email to a student, in a social media post, etc. To do so, I typically go to one of the many websites that offer “copy-and-paste” mathematical symbols, Greek letters, or subscript/superscripts. It is do-able…
Make a “Magic Eye” image using Excel
I’ve been on a weird kick lately making images using Excel. [Here’s one post. I hope to post more soon.] If you add a background color to each cell in a spreadsheet and resize the cell widths to make each one square, then you can zoom out so that each cell acts like a pixel…
Making the Mandelbrot Set with Excel
The Mandelbrot set is one of the most stunning geometric objects in all of mathematics. In this blog post, I will show how to generate the Mandelbrot set below using Excel. It is also an example of how you can use AI (I used ChatGPT) to help with a task like this. (Here is the…
Fold-and-Cut Turtle Tile
A few days ago, I posted templates showing how to fold a piece of paper so that you can cut out a hat or spectre tile in one cut. I decided to finish the trifecta: here’s a template to fold and cut a turtle tile.
Fold-and-Cut Hat and Spectre Tiles
In the late 1990s, Erik Demaine, Martin Demaine, and Anna Lubiw proved that any pattern made from straight line segments in the plane—connected or not—can be cut out of a piece of paper by first making some strategic folds and then making a single cut. This is the now-famous Fold-and-Cut Theorem. (See Erik Demaine’s website,…
David Richeson: Division by Zero 