# A Periodic Table, Linkages, and Dance Squared

Welcome to this week’s Math Munch!

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. I wonder what a multiplicative persistence is?

Next 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!

### 12 responses »

• This video was soooo fascinating and would have never ever thought that all that came from one single square and the way it all went back into place again!!!

1. I thought that it was really cool how you can do so much using just basic shapes – squares and triangles and also a little bit of symmetry! I never knew you could create so many different shapes and patterns just by using a square. This way the square was separated into different parts then swapped around to create a square was really impressive and interesting to watch.

2. WOW!!!!!!! That video was Awesome! I can not believe all those shapes came from that ordinary square. I showed all my family and they thought it was Amazing! I’ve been on plenty of math sites and none of them have as cool as stuff on math munch. Keep posting stuff like this please!

• Hi Lilyana,
I love reading your comments! I’m glad you liked the video. I, too, thought that it was just fabulous. It made me want to make something like that of my own—maybe a video, or a flipbook, or a collage. Simple shapes shown in remarkable new ways. Also, it makes me happy that you shared the video with your family, because I think that sharing math is the best!
I promise we’ll keep posting cool stuff. Thanks for commenting and do come back by soon!
Justin

3. those shapes that the square makes is cool because when there were triangles and small squares I got confused how that it can fit like tthat

4. I really liked the dancing squares for the fact that all this happened from little squares, triangles and rectangles from the beginning square! I never really though how those three shapes are connected.

5. The dancing squares put a smile to my face. It’s pretty cool how Rene is 92 and still enjoys these kind of things. Most 90 year olds I know sure don’t care about stuff like this.

6. The fact that all of those shapes were formed with a single square is very intriguing! I really enjoyed this video.

• I’m glad you enjoyed it, Ibraar!
Justin

7. This is really cool. It represents how dividing and colliding can be so unique. Uniqueness of Canadians!!!!!!!!!!!!!!!!!!!!!!!!!! XD