Tag Archives: discrete math

A Periodic Table, Linkages, and Dance Squared

Welcome to this week’s Math Munch!

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I like finding new ways of organizing information. That’s part of why I enjoy this Periodic Table of Mathematicians.

The letters in the table are the abbreviations of the chemical elements—like gold, helium, and iron—that are found on the usual periodic table. With a little creativity, they can also be abbreviations for the names of a bunch of celebrated mathematicians. Clicking on a square brings up the mathematician’s biography. I like guessing who might pop up!

The table was created by Erich Friedman, a mathematician who works at Stetson University in Florida. We’ve previously shared Erich’s holiday puzzles (here) and weight puzzles (here) and monthly research contest (here), but there’s even more to explore on his site. I’m partial to his Packing Center, which shows the best ways that have been found to pack shapes inside of other shapes. You might also enjoy his extensive listing of What’s Special About This Number?—a project in the same spirit as Tanya Khovanova’s Number Gossip.

A dense packing of 26 squares within a square that Erich discovered.

A dense packing of 26 squares within a square that Erich discovered.


I wonder what a multiplicative persistence is?

ttree_q150x150autoNext up, another Erik—Erik Demaine, whose work we’ve also often featured. What does he have for us this time? Some fantastic uncurling linkages, that’s what!

In 2000, Erik worked with Robert Connelly and Günter Rote to show that any wound-up 2D shape made of hinged sticks can be unwound without breaking, crossing, or lifting out of the plane. In the end, the shape must be convex, so that it doesn’t have any dents in it. For a while Erik and his colleagues thought that some linkages might be “locked” and unwinding some of the examples they created took months. You can find some great animations shared on the webpage that describes their result that locked linkages don’t in fact exist.

One thing that amazes me about Erik’s mathematical work is how young the problems are that he works on and solves. You might think a problem that can be put in terms of such simple ideas would have been around for a while, but in fact this problem of unwinding linkages was first posed only in the 1970s! It just goes to show that there are new simple math problems just waiting to be invented all the time.

Finally, I was so glad to run across this short film called Dance Squared. It was made by René Jodoin, a Canadian director and producer. Check out how much René expresses with just a simple square!

There’s a wonderful celebration of René titled When I Grow Up I Want To Be René Jodoin—written back in 2000 when René was “only” 80 years old. Now here’s 92! Making math is for people of all ages. You might also enjoy watching René’s Notes on a Triangle.

Bon appetit!

Reflection Sheet – A Periodic Table, Linkages, and Dance Squared