Martin Flashman's Courses- Math 103 Spring, 2005
[Tentative] Class Topic Notes and Outlines
Work in Progress-

Subject to Change!

Tuesday Thursday
1-18-05
Introduction to "Visual Math"

1-20-05
The Pythagorean Theorem

a2 + b2 = c2

1-25
The Pythagorean Theorem (finished!)

 Tangrams and Dissection Puzzles BeginTilings of the Plane

2-1-05
Regular and Semi- regular Tilings of the Plane

2-3-05
Finish Semi-Regular Tilings
Symmetries
for a Single Polygon

Reflections and Rotations

2-8
Symmetries
for a Triangle

2-10
Symmetries for a Tiling of a Frieze and the Plane
...|p|q|p|q|p|q|p|q|p|q|p|...
...|d|b|d|b|d|b|d|b|d|b|d|...

2-15
Lab: WinGeometry and Surfing

2-17
Isometries in Symmetry Groups
and planar tilings.
Begin Space- Symmetries and Isometries
Rotations and Reflections

2-22
Isometries
Begin Space- How do we encounter space?
2-24
Finish Classification of Isometries in the Plane
Spatial Objects- How do we understand them?

3-2
Spatial Objects:
Getting Familiar with The Platonic Solids.
Counting in geometry and topology.
What are topological properties?

3-4
Counting on curves and in the plane.
Euler's Formula

V+R = E + 2
3-8
Appplications of the Euler Formula
"A Hard Problem"

What's possible and what's impossible!
The Utilities Problem and Complete Graphs
in the Plane!

3-8
Appplications of the Euler Formula
The Color Problems on the plane and  the sphere and ...
Creating a Klein Bottle

3-22
Maps and Coordinates for
Surfaces

Flatland, The Earth and The Torus.

3-24
Encounters with The Fourth Dimension
The Hypercube.
3-29
More on Surfaces
Adventures on the Mobius Band, the Klein Bottle, and
the Projective Plane !

"New" Surfaces and
The Classification of Surfaces

3-31
No Class
Cesar Chavez Day

4-5 (Finish 3-29)
"New" Surfaces and
The Classification of Surfaces
4-7
Similarity in the plane and space.

Geometric Sequences and Geometric Series
 Big Big

4-12
Space Filling Curves

4-14
Projective Geometry:
Cones and Conic Sections
Preliminaries for "Calculus"

4-19
Ch. 10.1 Some Historical Problems of Visualization:
The parabola and squares.
Visualizing Algebra, Motion and Change
Analytic geometry- Descartes and Fermat
10.2  Four Problems Connecting the visual to the Numerical
Motion and distance travelled; Motion and position; Tangent line; Area of a region.

4-21
10.2  Four Problems Connecting the visual to the Numerical
Motion and distance travelled; Motion and position; Tangent line; Area of a region.

10.3, 10.4:Newton: Tangent lines, velocity, and the derivative. 10.5, 10.6 Determining position and areas.
4-26
Calculus:
Putting concepts together with computations. 10.7
See notes from 4-21

Projective Geometry:
Desargues' Theorem and The Conics!

4-28
An Introduction to Desargues' Theorem
Perspective and Projective Geometry
5-3

Perspective in Space and The Projective Plane
5-5
Other Worlds and Surfaces:
A Non-euclidean Universe
5-5
Inventory
References are to Notes from Spring 2004

2-24
Spatial Objects:
Getting Familiar with The Platonic Solids.

2-26

The Platonic and Archimedean Solids.

 Cubeoctahedron Rhombicubeoctahedron Icosidodecahedro

3-2
More on Solids. Symmetry. Isometries in Space.

3-4
Connections between Polyhedra. Frameworks. Duality.
Similarity in the plane and space.

3-9

More on Similarity, Geometric Sequences, and Series

3-11
Space Filling Curves

3-23
Encounters with The Fourth Dimension
The Hypercube.

3-25
More on the Hypercube:Coordinates

Coordinates for the Hypercube and the Tower of Hanoi

*
*
*

*

 4-13 Other Surfaces- The Sphere and the Torus and Beyond: Adventures on the Mobius Band, the Klein Bottle, and the Projective Plane?

4-15
More on Surfaces

4-20
More on Surfaces
The Classification of Surfaces
"New" Surfaces

4-22
The Classification of Surfaces
Euler's Characteristic Number

"New" Surfaces
Cones and Conic Sections- Projective Geometry
4-27
More on the Conics
Projective Geometry:
An Introduction to Desargues' Theorem

4-29
Perspective and Projective Geometry

5-4
More about Perspective and the Projective Plane
5-6
Other Worlds and Surfaces:
A Non-euclidean Universe.

Turning a sphere inside out.

Maps and Projective Geometry

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

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

Some Historical Problems of Visualization: Ch. 10.1
The parabola and squares.
visualizing algebra
Motion and Change visualized
Analytic geometry- Descartes and Fermat
Four Problems Connecting the visual to the Numerical10.2
Motion and distance travelled
Motion and position.
Tangent line
Area of a region.

Newton: Tangent lines, velocity, and the derivative. 10.3, 10.4
Determining position and areas. 10.5, 10.6
Putting concepts together with computations. 10.7
1 -29-04 (old)
Dissection Puzzles &
Scissors Congruent (Equidecomposable) Polygons
Dissection Theorem for Regular Polygons