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Introduction to MAT 402
Parker Glynn-Adey
University of Toronto, Mississauga
January 7, 2020
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
What is Geometry?
Etymologically, measurement of the Earth.
Shapes: topology, combinatorics
Structure: graph theory, tiling, crystallography
Symmetry: group theory, representation theory
Measurement: length, area, metrics
... and much, much, more.
Question
What’s special about geometry?
Tangible! Playful! Colourful!
Where does this course lead? (Top dozen posters)
A Celebration of Classical GeometryFields Institute on April 25th 2020
Where does this course lead? (Top five videos)
Math in Action Journal
Grade Distribution
Articles 10% + 15% 25%Wiki Improvement 10× 1% 10%Poster + Video Presentation 15%Midterm 20%Exam 30%
The Euclid Project
The Euclid Project
Euclid’s Elements was the standard introduction to geometry,number theory, and mathematics, from antiquity until moderntimes.
We are going to read it and write about it.
The Euclid Project
Euclid’s Elements was the standard introduction to geometry,number theory, and mathematics, from antiquity until moderntimes. We are going to read it and write about it.
The Explorations
The Explorations
During the Explorations part of the course,we will explore classical geometry post-Euclid.
The explorations will feature problems, puzzles, and tricks. Thepurpose of the Explorations is to develop your sense of the richnessof geometry. There is a rich body of folk lore geometry.
The Explorations
During the Explorations part of the course,we will explore classical geometry post-Euclid.
The explorations will feature problems, puzzles, and tricks. Thepurpose of the Explorations is to develop your sense of the richnessof geometry.
There is a rich body of folk lore geometry.
The Explorations
During the Explorations part of the course,we will explore classical geometry post-Euclid.
The explorations will feature problems, puzzles, and tricks. Thepurpose of the Explorations is to develop your sense of the richnessof geometry. There is a rich body of folk lore geometry.
(2,3,6) Kaleidoscope
Circle Limit III – Escher, 1959
Tangible Mathematics
Martin Schilling 1864 → Brown University 1973 → Smithsonian
Tangible Mathematics
Martin Schilling 1864 → Brown University 1973 → Smithsonian
Mural Mosaic in The Alhambra – Escher, 1922
Geometry: Art, Education, Research #GEAR2020
Friday October 9th to Sunday October 11th 2020 @ BIRSparker.glynn.adey@utoronto.ca
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