Instructor


Jeffrey O. Bauer

107 Carhart Science

Phone: 402-375-7334

Email: jebauer1@wsc.edu


Course Description: A survey of geometries to include Euclidean, Transformation, Finite, and Coordinate geometries and how they relate to high school geometry.


Textbook: Modern Geometry. Thomas, David (2002). Brooks/Cole: Pacific Grove, CA. (ISBN: 0-534-36550-7)


Course Syllabus


Assignments


Supplemental Questions


Midterm


Final

Course Outline


  1. Introduction
    1. Developments
    2. Definition of Geometry
    3. Recent Issues
    4. National & State Standards
    5. Axiom Sets
  2. Finite Geometries
    1. Finite Geometries
    2. Four-Line & Four-Point Geometries
    3. Geometries of Fano & Young
    4. Geometries of Pappus & Desargues
    5. Other Finite Geometries
  3. Geometric Transformation
    1. Introduction
    2. Groups
    3. Euclidean Motion
    4. Homogeneeous Coordinates & Matrix Equations
    5. Group Properties
    6. Similarities
    7. Fractals
  4. Projective Geometry
    1. Fundamentals
    2. Postulation
    3. Duality
    4. Harmonic Sets
    5. Projective Transformations
    6. Equations of Transformations
    7. Conics
  5. Modern Euclidean Geometry
    1. Fundamentals
    2. Modern Synthetic Geometry
    3. Nine-Point Circle and Early 19th Century
    4. Recent Synthetic Geometry of the Triangle
    5. Applications of Synthetic Geometry
  6. Non-Euclidean Geometries
    1. Foundations
    2. Hyperbolic Geometry
    3. Ideal Points & Omega Triangles
    4. Quadrilaterals & Triangles
    5. Line Pairs & Area of Triangular Regions
    6. Curves
    7. Elliptic Geometry
    8. Spatial Geometry
  7. Nebraska K-12 Geometry Standards (Draft March 2009)