Summer, 1997

Daily Topic Schedule

Monday Tuesday Wednesday Thursday
1-Rigid Plane Geometry 26/ 27/Introduction/

Pythagorean theorem The puzzle problem

Regular polygons. 1 figure tilings.

28/Tangrams/ regular 1 figure tilings

Equidecomposable Polygons

Symmetry & Isometry: Introduction

29/semiregular 2 figure tilings/
2 Rigid Space Geometry Planar and Space.


2/Generation of Isometries/ classification 3/Isometries and symmetries- generating tilings from more interesting figures.
Introduction to Space: cross sections and casting shadows. 
4/ Regular and semi-regular polyhedra

Symmetry in space

Begin Similarity and Orthogonal Projection

5/More on regular and semi-regular polyhedra
Space Isometries

3 Inversion. Projective Geometry. Topology of Planar Networks 9/More Similarity Applied

Projections:Orthogonal vs. Central. Coincidences

Networks in the plane (sphere).

10/Begin Inversion.

More on Projective geometry- The Projective Line & Point at Infinity.

The Euler Formula for the plane (sphere)

11/The Torus- flattened. Networks on the Torus.

Perspectivities and Projectivities.

Inversion - Circles and Lines.

12/Application of Inversion

Dimension - coordinates
The hypercube.

The Utility Problem.

4 Topology of the plane and space. Surfaces. Non-Euclidean Geometries 16/

The Color Problem

Non-Euclidean Geometry and inversion.

Perspective and projection in drawing.

17/ The Projective Plane
Finite Projective geometries.

Mathematical Models

Uncountably infinitely many points on a line segment.

Space Filling Curves- Fractals.

Begin: the Mobius Band and the Klein Bottle

18/More on Fractals

The Conics - Euclidean view.

Desargues Configurations

19/Closing -
Bianchon and Pascal Conic Configurations
The Conics - Projective View

Orientable and non-orientable surfaces.

Classification of Surfaces.

Turning the sphere inside out.

Handout- Some details on the five color theorem.

Overall Tentative Topic List

    1. Introduction.
      1. What is a Visual Argument?
    2. Planar Issues
      1. Points, lines and polygons.
      2. Planar Tilings
      3. Symmetry and Isometries.
    3. Introduction to Space.
      1. Polyhedra
      2. Isometries
    4. Magnification and Similarity
    5. Projective Geometry
      1. Configurations
      2. Duality
    6. Non-Euclidean Views
      1. Projective Geometry
      2. The Poincare Model
    7. Curves and Surfaces
      1. Continuity and Dimensions
      2. Accounting for Geometry (Planar and Non-Planar)
      3. Classification Problems
      4. Color Problems