Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 141: Euclidean Geometry
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Lecture(s) 
Sections 
Comments/Topics 
1 
Chapter 1 
Geometry, the five axioms of Euclid (have students read Chapter 1) 
5 
Chapter 2 
Logic, incidence geometry, models, affine and projective planes. 
3 
Chapter 3 
Hilbert’s axioms (add axiom 0: a line is a set of points.Proposition’s 3.2 proof is incorrect). 
3 
Chapter 4 
Neutral geometry. 
0 
Chapter 5 
(Have students read) 
1 
Chapter 6 
(Have students read selected sections) 
5 
Chapters 7 and 10 
Models and properties of hyperbolic geometry. 
2 
Spherical geometry. 

5 
Chapter 9 
Geometric symmetries and group theory. 
 Spherical geometry and trigonometry.Area of spherical triangle.Spherical barycenter, orthocenter, and incenter.Spherical Ceva’s theorem.(George A. Jennings, modern Geometry with Applications, Section 2, and online sources.)
 Advanced Euclidean geometry: Ceva’s theorem and its applications.The Euler line and the 9point circle.The Fermat point.Napoleon triangles. Morley’s theorem.(Sources: H.S.M. Coxeter, Geometry revisited, and multiple online sources [for instance, http://www.cuttheknot.org/goemetry.shtml])
 Have students explore hyperbolic geometry with NonEuclid, a hyperbolic geometry freeware developed by Joel Castellanos (currently at http://cs.unm.edu/~joel/NonEuclid/).Requirements: Javaenabled internet browser.A possible project is to experimentally verify that heights/medians/bisectors or a hyperbolic triangle are concurrent.
 Have students explore Euclidean geometry with Geometers Sketchpad or similar available online free software.