Revised: July 2009
Points, lines, planes, constructions; axiomatic structure of geometry and the nature of proof. Prerequisite: Math 321. Three semester hours
In this course you will be asked to:
1. Utilize information methods such as dot paper constructions, folding, and tracing to determine facts and relationships;
2. Study and develop fundamental ideas of Euclidean geometry based on measurement, parallelness and congruence;
3. Perform basic Euclidean constructions using traditional tools and the MiraTM;
4. Develop a system of facts and relationships concerning triangles, quadrilaterals, and other polygons;
5. Develop a system of facts and relationships concerning circles and circle parts;
6. Study and develop a system of facts and relationships concerning the measurement of length, area, surface area, and the Pythgorean Theorem;
7. Perform standard geometric constructions using The Geometer's SketchPadTM;
8. Develop an appreciation of formal deductive reasoning through pattern description, inductive reasoning, and the formulation of conjectures.
O'Daffer, P.G. & S.R. Clemens. Geometry: An Investigative Approach (2nd edition), 1992, Addison-Wesley.
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Chapter 1: A panoramic View of Geometry (1 day)
Introduction; Geometry in the physical world, as a mathematical system, as a formal axiomatic structure, and as a recreation
Chapter 2: Basic Ideas of Geometry (7 days)
Sets of points; The straight line; The plane; The angle; Simple closed curves and regions in the plane; Parallel, skew and intersecting lines; Triangles and Quadrilaterals
Chapter 3: Discovering Polygon Relationships (6 days)
Defining polygons; Symmetry in polygons; Constructions of polygons; Theorems about polygons
Chapter 5: Geometry in Three Dimensions (2 days)
Regular polyhedra; Symmetry in Space; Semiregular polyhedra
Chapter 6: Measurement-Length, Area, Volume (4 days)
Standard units of measurement; Metric units; English units; Length; Area; Volume and Capacity; Mass and Weight
Chapter 7 & 8: Motions in Geometry (6 days)
Translations; Rotations; Reflections; Combining transformations; Magnification
Supplement: Constructions (11 days)
Basic constructions; Properties of the triangle; General constructions; GeoSketchpad