MATH 351 MODERN GEOMETRY

Course Syllabus

1. Ruler-Compass Constructions

a. Basic Euclidean Constructions

b. Techniques for Solving Construction Problems

c. Constructions Using Loci

1. Establishing Circles and Tangents

2. Solving Triangles Given the Parts

d. Constructions in Algebraic Geometry

1. Addition and Quadratic Forms

2. Similar Figures

e. Inversion Geometry with Invariants

1. Inverse of a point with respect to a circle

2. Inverse of a Set of Points

3. Invariant Sets and Points

2. Newton-Poincaire Model

a. Definition of Lobachevskian Two Space

b. The Basic Incidence Postulates

c. The Basic Metric Postulates

d. Constructions in Lobachevskian Geometry

e. Metric Lobachevskian Geometry

f. An Analytic Geometry for Lobachevskian Two Space

3. Isometries of Euclidean Two Space

a. Ruler-Compass Constructions for Transformations

b. Verification of Properties and Developments of Conjectures

c. Use of 3x3 Matrices

d. Invariant Points and Sets

e. Complete Characterization of Euclidean Transformations

Prerequisites: MATH 220

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