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Design Note #2: Oriented Triangles

This is inspired by the Izzi puzzle, which is composed of squares. I learned about it from Professor Mark Saul of the The Center for Mathematical Talent at NYU, who developed beautiful mathematical content for i2camp.org. The Izzi puzzle consists of squares that have bisected edges that are combinations of black and white.

On my teaching blog, I explored the idea of using equilateral triangles. You need only 24 pieces to have one of each possible triangle, and they can be assembled into a hexagon. The challenge is to match all edges.

Below is the one I created in acrylic. The picture is a hexagon, but not a solution.

I created them initially using etching to create a lighter color. But I’m not a fan of etching unless it is really necessary. For one thing, it is slow. But I’ve also found that there is usually a more aesthetically pleasing alternative using low power cut lines. The new version will be available soon in our store.

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Design Note #1: the Arbor Circle


An arbor is a small group of trees. I think of it as smaller than a forest, bigger than a grove. Ann Arbor (A2 to locals) loves its trees, and the co-founders of Ann Arbor named their new tree town after their wives, who shared a first name.

Like many of our designs, the Arbor Letter design has mathematical inspiration that has connections to nature. If you look carefully at the trees, you’ll note they are self-similar. Whenever a branch forms, the branch is a copy of the tree, reduced in scale. So the trees are fractals.

At first, we were taken with large (12”) diameter designs that we hung on the wall. But with a loop added, it makes a beautiful, delicate ornament. We make the design in a variety of sizes, and have written software for composing variations in the shape, positioning, and number of trees.

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A shared hobby created

I’ve had a few careers, all of them motivated by curiosity. Flying airplanes, writing software, financial engineering all provided a creative outlet, but as jobs go, that creativity was necessarily narrowly focused. I always enjoyed teaching, and figured I might take it up when I had explored enough other careers. To my surprise, I discovered teaching high school was the job that really indulged my creative side in the most general way. I taught high school math, physics, and computer science. Teaching computer science in particular enabled me to explore a trove of interesting problems to solve with the students. We wrote games in Scratch, constructed enormous structures in Minecraft using Python and Javascript, and sketched dynamic and interactive visualizations with Processing (and later p5.js).

Processing was especially inspiring. I used its pdf library to algorithmically generate drawings. It was this, combined with a visit to Ann Arbor’s MakerWorks, that ultimately led to Cherry Arbor Design.

MakerWorks has an array of maker tools, but I was drawn to the laser cutter, because I could see how the drawings created in Processing could be turned into precise wood or acrylic representations.  When I brought my creations home, Heidi was immediately intrigued with the possibilities. We started having our date nights at MakerWorks (yep, we’re nerds), creating earrings and other small items from thin cherry and maple boards, colorful acrylic, and Baltic birch plywood. Eventually, so that we could have unlimited access, we decided to buy a laser cutter. I still do most of my work with Processing and pf.js, while Heidi prefers Affinity Designer, an alternative to Adobe Illustrator.

Today, Heidi and I spend much of our time together making things, and further developing our design skills. We are all about nonstop learning, so at the moment, we’re taking a PhotoShop class at the local community college.