## Math 402. Non Euclidean Geometry

Instructor Syllabus

**Text:** M. Hvidsten, Geometry with Geometry Explorer (GEX)

Day-Week labels and text sections in [ ] precede topics.

**1 Geometry and the Axiomatic Method [Chapter 1] **

W1 [1.1] Greek Origins of Geometry

F1 [1.2] Thales and Pythagoras

M2 [1.4] Axiom Systems and Systems of Axioms

W2 [1.5] Consistency of axiomatic systems

F2 [1.5] Independence and Completeness

M3 Labor Day, No Class

W3 Quiz 1 and Introduction to Lab 1

F3 [1.7] A Computational Axiomatic System using GEX

**2 Euclidean Geometry **

M4 [Appendix A] Euclid's Elements, Book I

W4 [2.1] Absolute (neutral) Geometry, Exterior Angle Theory

F5 [2.2] Congruence, SAS, ASA, SSS, Pons Asinorum, Pasch

M4 [2.1] Parallels, 5th Postulate, Playfair, Propositions 28/29

W4 [2.5] Similarity, AAA, Altgeld Tower Project

F4 Quiz 2 and Birkhoff's Axioms begun [3.6]

**3 Analytic Geometry **

M6 [3.1, 3.2] Review of Cartesian Coordinates and Plane Vectors

W6 Lab 2 [3.3] Bezier Splines with Xfig

F6 [3.4] Pappus' proof of Pythagoras' Theorem and the Law of Cosines

M7 [3.4] Peripheral Angle Theorem, Law of Sines, Cross Ratios [cf 2.6]

W7 [3.6] The Cartesian Model of Euclid's Geometry (Birkhoff concluded)

F7 [7.1] The Poincare Disk Model of Non-Euclidean Geometry

M8 [7.2] The Klein Model of Non-Euclidean Geometry

W8 [7.8] Sphere Projections and Isomorphism of Models

F8 Midterm Hourly

**8 Transformation Subgroups of the Moebius Group. **

M9 [3.5] the complex plane, polar and cartesian representation

W9 [3.5] complext functions and conformal mappings

F9 discuss midterm and preview of the second half semester

The syllabus for weeks 10-15 consists of selections from chapters 8 and 9 of Hvidsten, student reports, field trips and review, as posted on the class calendar.

approved by R. Muncaster, August 24, 2005.