# Mathy Clocks, Spirolaterals, and Mandalas

Welcome to this week’s Math Munch!

Hermann’s Abacus Clock. What time was I working on this post?

A few months ago, the Math Munch team got an email from retired mathematician Hermann Hoch with a lead to his amazing website full of (among other things)… clocks! One of the things Hermann does with his spare time in retirement is make creative math-y clocks using html. He calls them “html5 experiments”– and they really do take math art to the next level!

There are many fascinating clocks on Hermann’s site. (Be careful, or you might spend too much time watching the seconds go by!) One of my favorites is a clock he calls the Mondriaan Clock. The display is inspired by the art of Dutch painter Piet Mondriaan, who was known for his paintings of overlapping squares and rectangles in primary colors. The clock also comes with the exciting prompt– “wait until time creates golden ratios for us”! At what time will one of the rectangles in the image have dimensions that approximate the Golden Ratio? Hermann says that this question isn’t easy– he hasn’t even found all of the times himself! (And I’m sure he’d love to know– post your ideas in the comments below.)

Next up, I’ve been obsessed with Spirolaterals lately. What’s a Spirolateral, you ask? It’s a shape made by drawing segments of different lengths (say, 2, 3, and 4) one after another in a cycle (say, right, up, left, and down) until the shape closes up (or doesn’t, and you know it never will). If you follow those instructions (drawing on grid paper helps), you make this flower-like shape:

You can make Spirolaterals (or Loop-de-Loops, as they’re also called) with any numbers and using any turning angle. This Spirolateral uses three numbers and a turning angle of 90 degrees. (See the square corners?) But what if you use four numbers? Five numbers? Thirteen numbers? You can try drawing by hand- and then coloring them in, to make a beautiful mathematical creation. The Spirolateral below uses the first 50 digits of pi!

But you also don’t have to draw them by hand. The two Spirolaterals shown here were both drawn using a computer program! My favorite program for drawing Spirolaterals with 90 degree turns is this one, made by Chris Lusto. He gives great instructions and allows you to use as many numbers as you like!

But what if you wanted to make a Spirolateral with a… 109 degree turn? Wouldn’t that be cool! Well, yes, it is cool–

You can make this and other crazy Spirolaterals at this awesome website, brought to us by The Mathenaeum.

Finally, I leave you with this mesmerizing video of Dearing Wang drawing a Mandala. If you thought you’d never use your skills with a straight-edge and compass you worked so hard to develop in Geometry class– think twice. And for you straight-edge and compass nerds, keep an eye out for his pentagon construction! Is it perfect??

Bon appetit!

How long did it take me to make this post? (Hint: This clock tells time in base 6!)

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