MATH 322

STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Revision of Approved Course

I. Name and Title of Course

Mathematics 322 Modern Geometry

II. Reasons for addition to present curricula.

Math 322. Modern Geometry was last revised in 1975. This document represents a revision of this course.

III. Major objectives of the Course

A. To provide the prospective mathematics teacher with an opportunity to broaden and deepen his/her understanding and experience with geometry.

B. To provide the prospective mathematics teacher with material which gives "reasan d'etre" for the study of geometry today -- illustrating its historical importance and its present day significance and relevance.

C. To provide a course which conforms with the current high school mathematics requirements in New York State.

D. To demonstrate the use of the Euclidean construction techniques in determining geometric figures from given elements.

E. To define similarity and isometry transformations in the plane and prove the basic theorems which relate these transformations to the elementary transformations.

IV. Topical Outline

A. Review of Elementary Geometry

1. Selected Definitions
2. Selected Statements and Theorems
3. Practice on past Regents Exams B. Euclidean Constructions 1. Basic Constructions. Tools in Euclidean Constructions
2. Geometric Loci
3. (Optional) Three famous unsolvable geometric constructions. C. Transformational Geometry. 1. Elementary Transformations
2. Elementary transformations, groups of translations, rotations, Isometries
3. Isometries of the plane a) Line reflections
b) Translations
c) Rotations
d) Glide reflections
e) Direct isometrics 4. Similarities of the plane a) Homotheties
b) Similarities 5. Applications of Isometries & Similarities D. Modern Synthetic Plane Geometry 1. Stewarts Theorem
2. Theorems of Menelaus and Ceva
3. Properties of the circumcircle, Incircle, & Excircles of a triangle
4. Properties of the medial & orthic triangles of a triangle
5. Nine point circle
6. Other topics E. Insight into other geometries 1. Historical developments of projective methods
2. Metric and non-metric geometries
3. Geometric systems and the creation of new mathematics V. Major Bibliography

Choquet, G., Geometry in a Modern Setting. Boston: Houghton Mifflin, 1969.

Coxeter, H.S.M., Introduction to Geometry. New York: John Wiley, 1969.

Dodge, C.W. Euclidean Geometry and Transformations. Reading, Mass.: AddisonWesley, 1974.

Eves, H.W., A Survey of Geometry, 2 Vols. Boston: Allyn and Bacon, 1972.

Hall, D.W., and S. Szabo, Plane Geometry, an Approach Through Isometrics. Englewood Cliffs, N.J.: Prentice-Hall, 1971.

Levy, L.S., Geometry: Modern Mathematics via the Euclidean Plane. Boston: Prindle, Weber & Schmidt, 1970.

Millman, R. and G. Parker, Geometry A Metric Approach with Models. New York: Springer-Verlag, 1981.

Moise, E., Geometry from an Advanced Standpoint. Reading, Mass.: Addison Wesley, 1974.

VI. Presentation and Evaluation

A. Presentation by means of lectures, discussions, and individual projects.

B. Evaluation by means of written exams, homework, and class participation.

C. Each instructor is individually responsible to publicly and explicitly state his methods of evaluation.

VII. Prerequisites:

MAT 270

VIII. Credit:

3 semester hours.

IX. Statement of Approval

This course proposal was examined in accord with recommended procedures and was approved by the Department of Mathematics on

_______________________________Chair, Department of mathematics

X. Catalog Description

Math 322. Modern Geometry

Euclidean Constructions; Transformational Geometry; Isometries Reflections, Translations: Rotations; Similarities in the Plane; Theorems of Menelaus and Ceva; Introduction to Projective Geometry.

XI. Statement of qualifications of faculty who will teach the course.

A masters degree in mathematics with special interest in the study of geometry