## Science Rendezvous!

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!

## 2014 Mentoring

I’ve added a page about the mentoring project that I’m working on with three Gr. 12 students this semester. I’ll be updating the page as we go. For more information see Mentoring — 2014. From the introductory remarks:

The plan for the semester is an ambitious one. We’re going to understand the structure of all the regular convex polytopes in all dimensions, and build up a intuition for dimensions greater than three. We’ll spend most of our time learning the tools we need to understand how a geometric object can be pieced together. These tools will include vectors, metric spaces, symmetry groups, and simplicial complexes. I’m taking a very broad view of what constitutes a tool and counts as information about a space. The final result of the project will be a poster presentation about the solids and some 3-dimensional “nets” of the 4-dimemsional solids (the simplex, cube, cross-polytope, and 24-cell).

I can’t resist saying things about hyperbolic geometry. Therefore, if we get to the end of the proposed project, we’ll take a stab at using out high brow high dimensional intuition to understand the Gieseking manifold. There is more than enough stuff to say about the platonic solids, so we’ll see how far we get.

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