## 3D Printer Models for MAT 232

Posted in Computers, Math, Teaching and Learning by pgadey on 2019/11/07

This semester, I am teaching MAT 232 Multivariable Calculus. We often talk about level curves and use the saddle surface $z = x^2 - y^2$ as a key example. Every time it comes up, I ask students to stare at the part of their hand where the thumb meets the palm. Of course, they stare at me like I am crazy! This region of the hand is a good model for a saddle surface. If you start looking around at biological examples, you’ll see saddle surfaces everywhere.

I got interested in getting some 3D printed models of saddle surfaces to hand around the class. I found a great project 3D Printed Models for Multivariable Calculus put together by John Zweck. The STL files for the models are freely available, and I asked Reinhard Grassmann of the Continuum Robotics Lab if he could 3D print some models of saddle surfaces and the paraboloid $z = x^2 + y^2$ for me.

They arrived yesterday and they turned out GREAT! You can clearly see the level curves in one model, and the coordinate grid in another. They feel great to hold and are durable enough to hand around to a class of students.

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## MSLC Semina — Exploring Knights Tours

Posted in Math by pgadey on 2019/10/24

At the MSLC Seminar we had an “improvisational seminar” this week. We started off chit-chatting about various problems, and a theme emerged. One participant posed the following problem:

The game of Knight Placement is played on an 8×8 chessboard. Two players alternately take turns placing knights on the board. A move consists of adding a knight to the board, such that no knight is under attack. A player loses if they’re unable to place a knight. Who wins under optimal play?

I followed this question up with:

Suppose that the Queen of Chess has a garrison of twenty-five knights. The knights are kept on a 5×5 chessboard. One fine morning, the Queen shows up and orders the knights to all switch places, or be severely punished. Can every knight switch places simultaneously?

This got us thinking about knights tours. In a knight’s tour, a knight travels to every cell of a chessboard by visiting each square exactly once. Notice that if the 5×5 board has a knight’s tour, then the garrison can re-arrange themselves by each stepping along the tour.

We found a couple small boards with and without closed knight’s tours. Wikipedia turned our attention to this paper:

Allen J. Schwenk (1991). “Which Rectangular Chessboards Have a Knight’s Tour?” Mathematics Magazine: 325–332. (link)

Working through that paper might make a good session at MSLC Seminar. If anyone knows the history / providence of the puzzles above, I would be hear about them.

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## UTM Math Club — The Diamond System

Posted in Math by pgadey on 2019/10/09

I gave a string workshop at the UTM Math Club. It was very experimental. I wanted to highlight the algorithmic aspect of string figures. We were going to do the first bit of inoli’s Diamonds System.

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## Symmetry Groups at Science Unlimited

Posted in Math by pgadey on 2019/08/15

I gave a talk about symmetry groups at Science Unlimited 2019.
The slides are available here, for the curious.

## MSLC Summer Seminar

Posted in Math by pgadey on 2019/08/08

• May 30th “Derivation and applications of the gamma function” by David Salwinski
• June 6th “An Extension of Heron’s Formula” by Zohreh Shahbazi
• June 13th “What is Homology?” by Parker Glynn-Adey
• June 20th “Exploring Mathematics Learning Support Across Canadian Universities” by Rubina Shaik and Shrijan Rajkarnikar
• June 27th “Liouville numbers and irrationality measure” by David Salwinski
• July 4th “Representation theory” by Lisa Jeffery
• July 11th “Geodesics on Surfaces of Revolution” by Amanda Petcu
• July 18th “An (informal) Introduction to Model Theory and Skolem’s Paradox.” by Yasin Mobassir
• July 25th “Geometric Reflections” by Parker Glynn-Adey
• August 1st “The Inscribed Square Problem” by Amanda Petcu
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## Geometric Reflections

Posted in Math by pgadey on 2019/07/25

Kaleidoscopes create wonderful geometric patterns.
They are both beautiful and thought provoking.

There is something pleasing to a mystic in such a land of mirrors. For a mystic is one who holds that two worlds are better than one. In the highest sense, indeed, all thought is reflection — Chesterton

In this talk, I outlined the mathematical theory of kaleidoscopes.
We introduced Coxeter geometries, and classified them in the plane.

## Hyperbolic Visualizations!

Posted in Math by pgadey on 2019/07/15

Thanks to Vi Hart, Andrea Hawksley, Elisabetta A. Matsumoto, and Henry Segerman for making these amazing things!

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Posted in Math by pgadey on 2019/07/05

## The Nature of Things: Martin Gardner

Posted in Math by pgadey on 2019/06/03
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## The Quantum Gravity Topological Quantum Field Theory Blues by Scott Carter

Posted in Math by pgadey on 2019/05/24

Scott Carter has some poetry up on his website. He works on knotted surfaces, and I think this version is just great. Back in the day, I wanted to understand knotted surfaces and I remember looking at his work a bit.

I’ve been calculating
I said I’ve been calculating
calculating all night long
Got a quasi- triangular Hopf algebra
and I wrote down the coproduct wrong.

I’ve been integrating
integrating the whole day through
I said I’ve been integrating
integrating the whole day through
Got a Chern-Simons functional integral
and its convergent, too.

I’ve been writing down knot diagrams
converting them to braids
Using the Alexander isotopy
you know I’m not afraid
I’ve been
assigning modules
to each of these six strings
been doin’ it for weeks now
and I still don’t understand a thing.

I’ve got them old Quantum Gravity
Topological Quantum Field Theory Blues
I’ve got them old Quantum Gravity
Topological Quantum Field Theory Blues
And without NSF funding I think that you would, too.

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