Martin Flashman's Courses- Math 103 Fall, 2003
Class Topic Notes and Outlines
Tuesday Thursday
8-26
Introduction to "Visual Math"
8-28
The Pythagorean Theorem

a2 + b2 = c2
9-2
Tangrams and Dissection Puzzles
9-4
Dissection Puzzles &
Scissors Congruent
(Equidecomposable)
Polygons

9-9
Dissection Theorem for Regular Polygons
BeginTilings of the Plane
9-11
Regular and Semi- regular Tilings of the Plane

9-16
Symmetries for a Single Polygon
Reflections and Rotations

9-18
Symmetries for a Frieze Pattern on a Strip
Translations and Glide Reflections

...|p|q|p|q|
p|q|p|q|p|q|p|...
...|d|b|d|
b|d|b|d|b|d|b|d|...
9-23
Symmetries for a Tiling of the Plane
Isometries of the Plane.

9-25
Isometries  in Symmetry Groups
and planar tilings.
Begin Space- Symmetries and Isometries
Rotations and Reflections

9-30
Spatial Objects:
Getting Familiar with The Platonic Solids.

10-2
Spatial Symmetry
The Platonic and Archimedean Solids
.
 Cubeoctahedron Rhombicubeoctahedron Icosidodecahedron
10-7
More on Solids. Connections between Polyhedra. Frameworks. Duality.

10-9
Similarity in the plane and space.

10-14
Geometric Sequences, Series and
Space Filling Curves

10-16
Space Filling Curves and
The Hypercube.

10-21
More Encounters with The Fourth Dimension

10-23
Maps and Coordinates for Surfaces:
Flatland, The Earth and The Torus.

10-28
Maps and Beginning Projective Geometry

10-30
Perspective and Projective Geometry

11-4
Perspective in Space and The Projective Plane

11-6
The Cone  and  The Conic Sections

11-11
Projective Geometry:
An Introduction to Desargues' Theorem

Projective Geometry:
Desargues' Theorem ,Duality, Pascal's Theorem and The Conics!

11-18
More Duality and Proofs.
What is possible and what is not!
Properties of Curves and Surfaces:
Geometric, projective, and topological.

V+R = E + 2
Appplications of the Euler Formula and a "Hard Problem":
What's possible and what's impossible!
The Color Problems on the plane, the sphere, and the torus...

Other Worlds and Surfaces:
A Non-euclidean Universe.

New adventures on the Mobius Band, the Klein Bottle, and
the Projective Plane.

Classification of Surfaces.

"New" Surfaces

12-11
Turning a sphere inside out.
Wrap Up for Course:
Some Last Remarks and Videos on
Flatland and Visual Mathematics
Project Fair