MATH 5200/7200 Foundations of Geometry I
J. Wilson, Instructor, Summer 2010


Last modified on April 25, 2010

This is the web site page devoted to MATH 5200/7200 Foundations of Geometry I and MATH 7210 Foundations of Geometry II, at the University of Georgia, as led by Jim Wilson.

Course Description MATH 5200/7200 (from UGa Bulletin): Advanced Elementary Geometry for prospective teachers of secondary school mathematics: Axiom systems and models; the parallel postulate; neutral, Euclidean, and non-Euclidean geometries.

Course Description MATH 7210 (from UGa Bulletin): Further development of the axioms and models for Euclidean and non-Euclidean geometry; transformation geometry.

Prerequisites: MATH 3000 and MATH 3200 or equivalent.

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MATH 7200 Documentation

MATH 5200/7200 Syllabus - General information about the objectives and operation of the course.

MATH 5200/7200 Outline/Topics

Schedule Summer 2010

Prologue and Basic Notions -- Appendix and Chapter 0

Congruence, Constructions, and the Parallel Postulate -- Chapter 1

Circles -- Chapter 2

Area and the Pythagorean Theorem -- Chapter 3

Similarity -- Chapter 4

MATH 7210 Syllabus -

MATH 7210 Outline/Topics

Similarity - - Finish Chapter 4

Transformational Geometry -- Chapters 5 and 6

Non-Euclidean Geometry

Hyperbolic Geometry

Elliptic Geometry

Taxicab Geometry

Geometric Inversion

Problems and other topics

Students Enrolled



EMAT 5200/7200 Midterm Examination

MATH 7200 Midterm HTML (with solutions)

MATH 7200 Midterm PDF (without solutions)

EMAT 5200/7200 Final

EMAT 7200 Final Pool of Items


Jim's GSP Library

Some GSP based Lessons

History of Mathematics -- St. Andrews University

Challenge Problems

Supplemental Theorems


Libeskind's Axioms -- Appendix

Discussion Outline Section 1.1

Discussion Outline Section 1.2

Discussion Outline Section 1.3

Discussion Outline Section 1.4

Discussion Outline Section 2.1

Discussion Outline Section 2.2

Discussion Outline Section 2.3

Discussion Outline Section 3.1

Discussion Outline Section 3.2

Discussion Outline Section 3.3

Discussion Outline Section 4.1

Discussion Outline Section 4.2

Discussion Outline Section 4.3

Discussion Outline Section 4.4

Discussion Outline Section 4.5

Discussion Outline Section 5.1

Discussion Outline Section 5.2

Discussion Outline Section 5.3

Discussion Outline Section 5.4

TaxiCab Geometry


Hyperbolic Geometry

Libeskind Materials -- Chapter 1

Elliptic Geometry

Libeskind Materials -- Chapter 2


Taxicab Geometry

Libeskind Materials -- Chapter 3

Susan Sexton materials

Geometric Inversion

Libeskind Materials -- Inversion

Kyle Schultz materials

Pick's Theorem

Euclid's Postulates -- From MathWorld

Euclid's Postulates -- From Math Reference Project.

For those interested in a more rigorous approach, follow the Math Reference Project Axioms of Modern Mathematics

Hilbert's Axioms for Geometry

Equivalents to the parallel postulate. See also Scott Brodie's page on the Parallel Postulate and the Pythagorean Theorem

Pythagorean Triples

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