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). |
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3 |
Chapter 4 |
Neutral geometry. |
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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. |
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|
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 9-point circle.The Fermat point.Napoleon triangles. Morley’s theorem.(Sources: H.S.M. Coxeter, Geometry revisited, and multiple online sources [for instance, http://www.cut-the-knot.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: Java-enabled 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.