MATH411: Foundations in Geometry

Course Description

Objectives

1. knowledge of the synthetic, investigative, and deductive approaches to Euclidean plane geometry.
   
   
2. knowledge of the historical and mathematical significance of the parallel postulate, including an introduction to a non-Euclidean geometry.
   
   
3. proficiency in the basic concepts of mathematical logic and their use in proofs.

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Grading Procedure

Attendance Policy

Course Outline

• Notation and Conventions (1 day)

  Basic terms; standard notation; construction vs. drawing
  
  

• Congruent Triangles (2 weeks)

  Fundamental ideas of geometric proof; triangle congruence theorems; special triangles; applications to constructionsl applications to inequalities
  
  

• Parallel Lines (2 weeks)

  Existance and uniqueness; applications; distance between parallel lines
  
  

• Area (1 week)

  Area formulas for triangles and quadrilaterals; Pythagorean Theorem; decomposition
  
  

• Similar Triangles (1 week)

  Basic theorems; applications to constructions
  
  

• Circles (2 weeks)

  Circles and tangents; arcs and angles; applications to constructions
  
  

• Regular Polygons (1 week)

  Constructability; basic theorems
  
  

• More on Triangles and Circles (4 weeks)

  Circumcircles; inscribed circles; classic circle problems; medians; altitudes; special points; Euler Line; Nine-Point Circle; classic triangle problems
  
  

• Supplement (2 weeks)

  Platonic solids, Euclidean and projective transformations and constructions using classical tools and computer software