This course explores geometry from heuristic, axiomatic, and computational angles. Students examine ancient results, Euclid, non-Euclidean geometry via the Poincaré disk, and transformational geometry.
Demonstrate properties of types of finite plane symmetry groups.
Summarize contributions of pivotal geometers.
Prove Simple theorems of hyperbolic geometry.
Calculate distances, angle measures, and areas in the Poincaré Disk.
Construct objects in the Poincaré Disk.
Explain the significance of denying the fifth axiom of Euclid's Playfair's Postulate.
Represent direct and indirect isometries using matrix methods.
Represent geometric objects and linear transformations using matrices.
Identify the invariants of matrix transformations.
Analyze the compositions of linear transformations.
Demonstrate properties of isometries: reflections, rotations, translations, and glide reflections.
Euclidean Plane Geometry and Constructions
Perform basic constructions with straight-edge and compass.
Prove theorems in Euclidean Geometry.
Axiomatic Systems and Ancient and Neutral (Finite) Geometries
Prove elementary theorems in neutral geometry.
Demonstrate properties of components of axiomatic systems.
Solve elementary problems from Western and Non-Western sources.
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