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
Approved: 2003-03-01 (revised 2011-07-01, )

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Euclidean and Non-Euclidean Geometry, Greenberg, 3rd Edition, $70
Search by ISBN on Amazon: 0716724464

Suggested Schedule:

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.

Additional Notes:

  1. 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.)
  2. 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])
  3. 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.
  4. Have students explore Euclidean geometry with Geometers Sketchpad or similar available online free software.