Overview
Description
Axiom systems, models, independence, consistency; incidence, distance, betweenness, congruence, convexity; inequalities, quadrilaterals, limit triangles, the non-Euclidean geometry of Bolyai-Lobatchevsky.
Requirements
Prerequisites
MATH 373
Original catalog text
Prerequisites
Prerequisite(s): MATH 373.
Units
Lecture3
Learning Outcomes
- prove properties of lines, angles, and circles from the Euclidean axioms.
- prove properties of lines, angles and circles in non-Euclidean geometry.?
- distinguish between geometric properties that depend on the Euclidean parallel postulate and those that are independent of any parallel postulate assumptions.
- describe the logical consistency of geometries using models.