hlascs (@) uwec.edu
Each problem I solved became a rule, which served afterwards to solve other problems.
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.
- Use interactive geometry software to make geometric conjectures.
- Understand axiomatic thinking.
- Write geometric proofs.
- Create a wikibook of important axioms, theorems, and proofs.
- Updates to the wikibook
- Weekly group quizzes
- Two projects
- Two in-class exams
- Final exam
- Geometry & Symmetry by Kinsey, Moore, & Prassidis, 2011
- Euclid Elements (with applets)
- Geometry software
- 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
- Triangle congruence and similarity: A Common-Core-compatible approach
- Geometry and Proof (Battista and Clements)