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I’ve been going through my old Twitter saves, when I came across this one which was no longer available, but which intrigued me!

The post is now gone from Twitter, but I found it via the WaybackMachine.

Prove that if all the coefficients of the quadratic equation \[ax^2 + bx + c = 0\] are odd integers, then the roots of the equation cannot be rational.

Want a hint for solving the problem? Highlight the following hidden text:

Write down \(1^2, 3^2, 5^2\) and \(7^2\) mod \(8\).

Use this together with the quadratic formula.

This problem comes fromThe USSR Olympiad Problem Book (1962) by D. O. Shklarsky. The whole book can be found digitally on archive.org.

One of the earliest laser cutting projects I ever considered was when I was a graduate student: making a stellated dodecahedron. When I got to Harvey Mudd College and had the opportunity to use the laser cutter in the Makerspace for the first time, it was one of the first things I attempted.

My initial method for securing the faces together didn’t work very well, so I ended up using the pieces and some Scotch tape to hold it together (with lots of tissue in the inside for some added structural integrity!)

On my second iteration, I bought some small hinges in bulk for 8¢/ea, and used a hinged construction. (I believe these are the same hinges that Alex Kontorovich used in his excavated truncated cuboctahedron in Polyplane.)

Here are some photos I made of the build process.

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Here are some more pictures of the piece that was in the 2025 exhibition:

I was going through some old saved tweets during my move to Bluesky, and my favorite tweets to come across were those that mean something different to me know than they did when I saved them. In particular, this tweet from 2021 shows that 2021 JMM Exhibition of Mathematical Art catalog, and little did I know that just three years later, I’d be making art and finding my own pieces in the 2024 and 2025 versions.

I recreated Dan Bach’s photo with the catalogs from the Exhibitions that I took part in.

JMM 2024

You can read about my piece in the 2024 exhibition on my post “Triangle Center Patterns“:

Triangle Center Patterns

Here’s the video, which really ought to be viewed in 4K!

And you can read more about the piece on the Bridges website for the 2024 exhibition.

JMM 2025

My friend and former colleague Francis Su kindly posted about my 2025 piece when he saw it at JMM:

I made some projections of this shape in Mathematica in order to plot on my AxiDrawV3 pen plotter.

You can read more about this piece on the Bridges website for the 2025 exhibition.