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
4 by 4 grid
 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

Symmetries of an equilateral triangle.
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
What about higher dimensions?
Maps and Coordinates for Surfaces:
Flatland, The Earth and The Torus.
torus_coord.gif
torus_coord1.gif

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