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