57091 Geometry for High School Teachers, Spring 2009

This course is offered in support of our Master's program for secondary teachers and it will become one of the core courses for the program. The course will cover a variety of topics in Euclidean and non-Euclidean geometry with an emphasis on connections to high-school curriculum, problem-solving, examples, and applications. The topics covered may include:
• Affine Geometry (Ceva's Theorem; three altitudes, medians and bisectors of a triangle; center of masses; Menelaus' Theorem)
• Reflections, billiards, geometric problems on maxima and minima (Schwartz's triangle; Isoperimetric problem; Optical properties of ellipses and hyperbolas.)
• Inversions (General properties of Inversion; Appollonius' Problem)
• Projective Geometry (Desargues' theorem; Cross-ratios and invariance under projective transformations; Theorems of Pascal and Brianchon, including degenerate cases - Pappus' theorem and the dual statement)
• Spherical and Elliptic Geometries (Three altitudes, medians, and bisectors of a spherical triangle; Areas of spherical polygons and a proof of the Euler characteristic formula for convex polyhedra; Platonic solids; Duality principle in elliptic geometry)
• Elements of Hyperbolic Geometry (Klein's model of Lobachevsky's plane. Distances in Klein's model; Poincare's model.)
• Geometric Constructions

Flyer
Some of the in-service teachers taking this course will participate in Developing Leadership in School Mathematics Program funded by ODE. Pairs (or more) of teachers who are Secondary licensed and currently teaching Mathematics in the same building or district will take 6 graduate credit hours (3 credit hours is this course + 1 credit hour on-line pedagogy+ 2 credit hours in a follow-up Geometry course during the last two weeks of June). The tuition for these teachers will be covered by ODE. If you are interested, please, contact Dr. Judith Melillo at jmelillo [at] kent.edu

Jenya Soprunova, soprunova@math.kent.edu
Office hours: Tue 10:00 - 12:00, Wed 2:15-4:25 in MSB 219
Telephone: (330)672-9086
FAX: (330)672-2209

Lecture: W 4:25 - 7:05 in MSB 102

Handout
Statement on academic dishonesty