CATALOG DESCRIPTION:

Math 01.202  Introduction to Geometry                                                                           3 s.h.

Prerequisites: Basic Algebra II

This course develops the fundamental concepts of Euclidean geometry from a modern point of view.
Its topics include sets, points, lines, space, betweeness, incidence, congruence, parallelism, similarity, transformations, volumes, and areas.  Non-Euclidean geometries are introduced.  Not open to mathematics majors.  Use of calculators is required. Students are expected to have completed an equivalent of Intermediate Algebra.
 

OBJECTIVES:

Students will be able to:

1. Discuss a variety of great geometric ideas in ways that transcend mathematics.
2. Use synthetic, analytic, and transformational techniques.
3. Discuss the similarities and differences between Euclidean and non-Euclidean geometries.
4. Apply the concepts of incidence, dimension, parallelism, congruency, similarity, self-similarity, perpendicularity, cardinality, and transformal geometry.
5. Use a variety of tools, physical models, and appropriate technology to develop and describe geometric concepts and relationships and their uses.
6. Demonstrate the kinds of proofs found in geometry.
7. Present written and oral arguments to justify conjectures and generalizations based on explorations.
 

CONTENT:

1. History of Geometry

Theorems and proof
Pythagorean Theorem
Golden Rectangle
Axioms

2. Geometric Constructions

Congruence, similarity, and incidence
Parallelism and perpendicularity
Polyhedra
Duality
Extenstions to higher dimensions

3. Symmetry, Transformations and Equivalences

Reflections, rotations, translations
Isometries and symmetries
Topological equivalence
Projections
Self-similarity and fractal geometry

4. Non-Euclidean Geometries

Axiomatic systems
Finite geometries
Spherical geometry
Hyperbolic geometry
Comparing euclidean and non-euclidean geometries
Concepts of infinities

TEXTBOOKS:

Edward B. Burger and Michael Starbird:  THE HEART OF MATHEMATICS, 2/E, Wiley, 2005.

L. Christine Kinsey and Teresa E. Moore: SYMMETRY, SHAPE, AND SPACE, Key Collegle, 2002.

Gary L. Musser and Lynn E. Trimpe: COLLEGE GEOMETRY: A PROBLEM SOLVING APPROACH WITH APPLICATIONS, PrenticeHall, Upper Saddle, NJ, 1994.