MAA Minicourse 2014
Visualizing projective geometry through photographs and perspective drawings

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Annalisa Crannell, Professor of Mathematics
Franklin and Marshall College

Marc Frantz, Research Associate
Southwestern University

Fumiko Futamura, Associate Professor of Mathematics
Southwestern University

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.)


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
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

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