|1-Rigid Plane Geometry||26/||27/Introduction/
Pythagorean theorem The puzzle problem
Regular polygons. 1 figure tilings.
|28/Tangrams/ regular 1 figure tilings
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
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
|3 Inversion. Projective Geometry. Topology of Planar Networks||9/More Similarity Applied
Projections:Orthogonal vs. Central. Coincidences
Networks in the plane (sphere).
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 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.
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.
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.