Parker Glynn-Adey

Science Rendezvous!

Posted in Math by pgadey on 2019/05/12

This year, at Science Rendezvous, we shared symmetry and geometry. These areas of math are very beautiful and full of lovely patterns. In particular, we focused on how to connect geometry and symmetry using group theory. This approach was pioneered by Donald Coxeter, one of the most famous mathematicians of the twentieth century, and former professor at the University of Toronto. The big theme of our display was the notion of symmetry groups. This talk Symmetry and Groups by Professor Raymond Flood of Gresham College gives a great introduction to this connection.

Lukas brought his kaleidoscope, and I got it on video!

We built models of the platonic solids from paper.
These solids are some of the most famous and beautiful objects in mathematics.
For more information, check out this Numberphile video. The paper models that we built were laser cut by Hot Pop Factory. They did a great job cutting and scoring the models. I am thrilled with the precision and accuracy we got.

Wallpaper patterns which tile the plane have very rigid symmetries.
It turns out that there are only seventeen types of symmetry possible.
By the way, I love this sort of theorem. Who would expect that there are exactly 17?!

We handed out some pages from this and online guide to symmetry and the wallpaper groups. Professor Dror Bar-Natan of the St. George Campus likes to collect examples of the wall papers. Here is a nice down-to-earth lecture “Glide Planes and Wallpaper Groups” about the wallpaper groups from Frank Hoffmann‘s course The Fascination of Crystals and Symmetry.

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