Modern Geometry

Professor of Mathematics at Montana State University. Nationally known in the field of Geometry.

1. Geometry Through the Ages.
Greek Geometry Before Euclid. Euclid and the Elements. Neutral Geometry. Famous Open Problems in Geometry.
2. Topics in Euclidean Geometry.
Elementary Constructions. Exploring Relationships Between Objects. Formal Geometric Proof.
3. Other Geometries.
The Concept of Parallelism. Points, Lines, and Curves in Poincare?s Model of Hyperbolic Space. Polygons in Hyberbolic Space.
4. Transformation Geometry.
An Analytic Model of the Euclidean Plane. Representing Linear Transformations in 2-space with Matrices. The Direct Isometries: Translations and Rotations. Indirect Isometries: Reflections. Composition and Analysis of Transformations. Other Linear Transformations.
5. Fractal Geometry.
Introduction to Self-similarity. Fractal Dimension. Iterated Function Systems. From Order to Chaos. The Mandelbrot Set.
6. Projective Geometry.
Elements of Perspective Drawing. Introduction to Projective Geometry. The Cross Ratio. Applications of the Cross Ratio. Matrix Methods for 3-point Perspective Transformations. Applications of Geometry in Remote Sensing. Applications of Geometry in Terrain Rendering.
Index.