Geometry is the study of shape.

There’s been a renaissance in geometry over the last hundred years, with modern applications ranging from the large-scale structure of space-time, to the modelling of social networks like Facebook, to the computer graphics in video games and movies.

Donald Coxeter (1907-2003) was one of the greatest geometers in history. Coxeter is up there with giants like Euclid, Descartes, Riemann, and Bolyai. He was also, for about eighty of his ninety-six years, a Torontonian. We should celebrate having such a luminary in our city!

Coxeter studied polytopes, which are abstract generalizations of the polyhedra familiar to us in two or three dimensions.

You can readily measure Coxeter’s impact by the mathematical terms we use with his name: Coxeter group, Coxeter diagram (or Coxeter-Dynkin diagrams), Coxeter system, Coxeter number, Coxeter matrix, …  Most of us would be lucky to have even one mathematical construct named after us.

At the recent Nuit Blanche in Toronto this weekend, artist Nicola Verlato had an installation at OCAD which was a large mural inspired by the work of Coxeter and the great Toronto philosopher Marshall McLuhan. The work entitled The Merging featured several Coxeter polytopes. The featured image of the blog is her mural, and below is a teaser of the virtual reality installation.

If you happen to stroll down the north side of College Street in Toronto heading west towards Spadina, take a second and admire the geometric sculpture adorning the front of the Fields Institute. The piece is appropriately called Intuition.

For more on Coxeter, check out also Siobahn Robert’s biography, The King of Infinite Space.

Here is the trailer to the 2002 documentary on his life The Man Who Saved Geometry (full video available on Vimeo).

Anthony Bonato