MAA Minicourse 2014
Visualizing projective geometry through photographs and perspective drawings
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Please give us feedback and/or feel free to ask us questions!

Annalisa Crannell, Professor of Mathematics
Franklin and Marshall College
https://edisk.fandm.edu/annalisa.crannell/
annalisa.crannell_at_fandm.edu

Marc Frantz, Research Associate
Southwestern University
marcfrantz10_at_gmail.com

Fumiko Futamura, Associate Professor of Mathematics
Southwestern University
http://people.southwestern.edu/~futamurf/
futamurf_at_southwestern.edu
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Minicourse Worksheets and Presentations

Wednesday January 15, 2:15-4:15 p.m.

DAY 1 (Desargues' Theorem)

Welcome!  Quick history of first Viewpoints, then of projective geometry.

“Drawing ART” puzzle: worksheet, presentation

Discover Desargues' theorem in small groups and through “Making an A” shadow worksheet, presentation

“L-collineation” puzzles, presentation: elations and homologies in perspective worksheet, presentation 

Concluding remarks (10 min.)

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Thursday January 16, 1-3 p.m.

DAY 2 (Numerical invariants)

The most under-appreciated theorem:  Discover Eves's theorem, Casey's theorem, the Casey angle, cross ratio (worksheet 1, worksheet 2, worksheet 3), and harmonic ratio through analyzing photographs in small groups, presentation

Geometric division: the relationship between cross ratio and slopes in perspective, presentation 


Supplemental Worksheets
Window Taping, the Aftermath
Drawing ART
Image of a Line
Geogebra lines and points
Extended Real Space
Desargues Proof
Of Meshes and Maps
Elation
Harmonic Homology
Geometric Division

Introduction to Harmonic Sets
Harmonic Sets in Music
Mapping L in two-point perspective
Mapping lines to points, lines to lines
Collineations in Perspective
From Perspectivities to Perspective Collineations
Periodic Collineations and Involutions
Translations and Dilations in Perspective
Introduction to Homogeneous Coordinates
Projective Collineations in Homogeneous Coordinates

Reprints
A Different Angle on Perspective
Drawing on Desargues
Hyperbola: Under Construction!
A Car Crash Solved - with a Swiss Army Knife