# Math 510 Foundations of Geometry

Document Sample

```					Math 510: Foundations of Geometry
Spring 2005

COURSE SYLLABUS
Instructor: Dr. Paul Brock

E-mail: pwbrock@sciences.sdsu.edu

Office: GMCS 510

Office phone: 594-6835

Office Hours: 1:00 PM – 4:50 PM Friday

Text: Geometry: Theorems and Constructions, 2001, A. Berele

Chapter1: Congruent Triangles
Chapter2: Parallel Lines (Existence and Uniqueness)
Chapter3: Area (Theorems of Pythagoras and Heron)
Chapter4: Similar Triangles
Chapter5: Circles (Arcs and Angles)
Chapter6: Regular Polygons (Constructability)
Chapter7: Triangles and Circles (Circumcircles, Incircles, Excircles)
Chapter8: Medians (Center of gravity, Complementary Triangles)
Chapter9: Altitudes (The Euler Line, The Nine-Point Circle)
Chapter11: Constructions with Indirect Elements

This course is designed to provide students with the necessary training to teach geometry
at the high school level. The goal of the instructor is to present a complete course in
geometry that includes a comprehensive survey of the concepts and theorems that the
students will eventually teach to others, together with more advanced topics that expose
the students to the rich history of geometrical literature. Such advanced topics include
many well-known results concerning triangles such as Euler’s theorem, Ceva’s theorem,
and the problem of Fagnano. The more elementary topics include congruent triangles,
parallel lines, area, similar triangles, circles, and transformations in the plane. Topics
are introduced and explained in an abstract framework of definitions, postulates and
theorems, but an attempt is made to exhibit applications of these ideas to the solutions of
real-world problems.