# Modern Geometry

Professor Hlas

hlascs (@) uwec.edu

Hibbard 530

*Each problem I solved became a rule, which served afterwards to solve other problems.*

—Rene Descartes

## Course Information

This course focuses on axiomatic thinking in Euclidean and non-Euclidean geometries. Emphasis will be on proof techniques, finite geometries, Euclidean constructions, transformations, spherical geometry, hyperbolic geometry, and geometry software.

More course information is posted on D2L.

### Goals

- Use interactive geometry software to make geometric conjectures.
- Understand axiomatic thinking.
- Write geometric proofs.
- Create a wikibook of important axioms, theorems, and proofs.

### Structure

- Updates to the wikibook
- Weekly group quizzes
- Two projects
- Two in-class exams
- Final exam

### Required

*Geometry & Symmetry*by Kinsey, Moore, & Prassidis, 2011- Euclid Elements (with applets)
- Geometry software
- Geometer's Sketchpad (via UWEC virtual lab)
- GeoGebra
- Spherical Easel
- NonEuclid

### Research background

- Lakatos, I. (1976).
*Proofs and refutations: The logic of mathematical discovery.*Cambridge, United Kingdom: Cambridge University Press. - Fawcett, H.P. (1938). The nature of proof: A description and evaluation fo certain procedures used in a senior high school to develop an understanding of the nature of proof.
*National Council of Teachers of Mathematics, Yearbook 13.*Reston, VA: NCTM. - Hyperbolic geometry in a high school geometry classroom (Donald, 2005)
- Finite geometries and axiomatics systems
- Isometries
- Triangle congruence and similarity: A Common-Core-compatible approach
- Geometry and Proof (Battista and Clements)