MATH 5200/7200
Review for Exam 3

For the exam you should understand all of the homework problems. For GSP problems I could ask you to explain in words how you would do a hyperbolic GSP construction. For questions on axioms and basic theorems in hyperbolic or spherical geometry, I could ask you to discuss a definition, axiom, or theorem in Euclidean geometry, and how it changes in hyperbolic or spherical geometry.

Summary of topics by class meetings, October 24 - November 21 (Homeworks 14 - 19)

A. Trigonometry

Friday 10/24: Definition of sine and cosine.

Monday 10/27: Trig formulas - area, law of cosines, law of sines. Homework 14 due (trig formulas).

Wednesday 10/29: Addition formulas for sine and cosine.

Friday 10/31 Fall Break

Monday 11/3: Surveying and navigation problems. Homework 15 due (trig applications and trig proofs).

Wednesday 11/5: Eratosthenes and the circumference of the Earth.

B. Hyperbolic geometry

Friday 11/ 17 (Mo Hendon): Introduction to hyperbolic geometry, the half-plane model. Length integral, shortest curve between two points. Homework 16 due (more trig proofs).

Monday 11/10: Hyperbolic GSP tools.

Wednesday 11/12: Hyperbolic constructions: equilateral triangle, regular quadrilateral, regular hexagon. Homework 17 due (hyperbolic GSP constructions).

Friday 11/14: Axioms and basic theorems in hyperbolic geometry, angle defect = area. Homework 18 due (discussion of axioms and basic theorems in hyperbolic geometry).

C. Spherical geometry

Monday 11/17: Spherical geometry, geodesic = arc of great circle, proof that angle excess = area.

Wednesday 11/19: Big triangles, angle excess for polygons, spherical Platonic solids.

Friday 11/21: Spherical dodecahedron, spherical icosahedron, axioms in spherical geometry. Homework 19 due (axioms and basic theorems in spherical geometry, angle excess formula for dodecahedron and icosahedron).