## 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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## Quotes from “What if?” by Emily Clader

Posted in Math, Teaching and Learning by pgadey on 2019/05/23

I had to share these fantastic quotes from Emily Clader‘s piece “What If?: Mathematics, Creative Writing, and Play” in Journal of Humanistic Mathematics. The whole piece is great, and I encourage you to read it.

Mathematics … is a language, a set of structures through which ideas can be given both order and aesthetics. Like any language, it is capable of describing the world as one sees it, revealing patterns and properties that are often difficult to articulate without the right vocabulary. Yet also, like a language, mathematics can be used to explore the fantastic, the fictional, the conceivable but unreal. In providing an appropriate lexicon, mathematics gives form to our imagination of other worlds

Herein lies the true creative potential of mathematics. The precision of its language permits one to create a detailed imaginative picture of possible objects, possible structures, and possible worlds that do not, in practice,exist. Anything that can be conceived can be explored with as much rigor as the sensory world — indeed, even more so.

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## 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!

## Three-Dimensional Kaleidoscope

Posted in Math by pgadey on 2019/05/05

My highschool student, Lukas Boelling, made this three-dimensional icosahedral/dodecahedral kaleidoscope with his dad, @eric_boelling. Lukas based his models off this excellent paper: Alice through Looking Glass after Looking Glass: The Mathematics of Mirrors and Kaleidoscopes by Roe Goodman. Stay tuned for more models!

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