## The String Figure Mentorship

This week at the string mentorship we played with some nice figures. From left to right we are: Caroline Graham with Jacob’s Ladder, Parker Glynn-Adey a variant of the Well, Hillarey Tsui with Crow’s Feet, and Jacob Kikukawa with Wawu from Nauru Island.

## String Figure: Outrigged Canoe

As part of my current highschool mentorship project on string figures, I’m recording string figures that we study. Here are two views of the figure, Outrigged Canoe, which one looks better to you?

## Q8(b) from 2014 Final Winter

Exercise 8bAssume is an matrix with and has the property that each entry in the first row equals the sum of the entries in the column below it. Prove that .

## Two nice facts about games.

Since giving my talk last week about games, I’ve been on a bit of a mathematical gaming kick, and would like to share some of the gems I’ve come across. We’ll give a beautiful argument due to Gale about his game Chomp, and an exceedingly clever argument due to Hochberg, McDiarmid, and Saks which applies Sperner’s lemma to the Game of Y.

## Mathematics and Games (Kangaroo Math 2014)

On Sunday, March 23rd, 2014, I gave a talk to parents of kids writing the 2014 Kangaroo Math contest. The slides are available here: Kangaroo 2014 Slides. The content of the talk was a discussion of Tic-Tac-Toe in disguise, and a proof of the winning strategy for Nim.

Click more for further information.

## Dodecahedral Crafts

This evening I made some dodecahredral crafts to show my mentoring students. This week we’re proving that the dodecahderon actually exists, by constructing it explicitly. The model on the right illustrates our proof splendidly. For instructions, check out Laszlo Bardos’ site CutOutFoldUp.com. The dodecahedral calendar is from Marlies’ Crafts.

## 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.

## Singularities I.1

These are some notes that I’m writing up on Gromov’s papers on singularities of maps. This first post will look at some of the introductory material in: Singularities, Expanders and Topology of Maps. Pt 1. These notes will be a partial introduction to what is going on.

## Of Waists and Spheres

These are some notes that I’m writing up on Gromov‘s *waist inequality*. We’ll look at some standard material about the Borsuk-Ulam theorem and finish with a nice application of the inequality.

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