Geometry Textbook

by Mark Barsamian

I have developed a textbook for use in my one-semester Junior-level Axiomatic Geometry course at the Ohio University Main Campus in Athens, Ohio. My current work on the book includes both adding new material and revising the existing material.

The book presents Euclidean Geometry and was designed for a one-semester course preparing junior and senior level college students to teach high school Geometry. The book could also serve as a text for a junior level Introduction to Proofs course. (I have used it many times for MATH 3110 College Geometry at Ohio University in Athens. The webpage for my Geometry course can be reached at the following (link). The web page includes a schedule that shows how the book is used in the course.)

Axiom systems are introduced at the beginning of the book, and throughout the book there is a lot of discussion of how one structures a proof. The axiom system includes the existence of a distance function, coordinate functions, and an angle measurement function. It is significant that the axiom system does not include any axioms about area. Rather, similarity and area are developed in theorems. Throughout the book, the writing is meant to have a level of precision appropriate for a junior or senior level college math course.

Each chapter of the book ends with exercises that are organized by section. The Definitions and Theorems are numbered, and complete lists of them are presented in the Appendices. Throughout the PDF version of the book, most references are actually hyperlinks. That is, any reference to a numbered book section, or numbered definition or theorem, can be clicked on to take the reader to see that numbered item. Using the “back arrow” will take the reader back to where they were before.

Chapter 1:Axiom Systems
Chapter 2: Axiomatic Geometries
Chapter 3: Neutral Geometry I: The Axioms of Incidence and Distance
Chapter 4: Neutral Geometry II: More about the Axioms of Incidence and Distance
Chapter 5: Neutral Geometry III: The Separation Axiom
Chapter 6: Neutral Geometry IV: The Axioms of Angle Measurement
Chapter 7: Neutral Geometry V: The Axiom of Triangle Congruence
Chapter 8: Neutral Geometry VI: Circles
Chapter 9: Euclidean Geometry I: Triangles
Chapter 10: Euclidean Geometry II: Similarity
Chapter 11: Euclidean Geometry III: Area
Chapter 12: Euclidean Geometry IV: Circles
Chapter 13: Euclidean Geometry VI: Advanced Triangle Theorems
Chapter 14: The Circumference and Area of Circles
Chapter 15: Maps, Transformations, Isometries
Appendix 1: List of Definitions
Appendix 2: List of Theorems

The text is available through the Ohio University Open Library, at the following link: (Link to Barsamian Geometry Text)

Even though the book is available in electronic form for free, when I teach the course I require that students buy a print copy of the book. I have the book printed locally, and students buy it for $45. (I print the book in two volumes. Volume I contains all the Chapters, 1 - 15. Volume II contains the two appendices, which are the lists of Definitions and Theorems. The reason that I do this is that I allow students to use Volume II on quizzes and exams.)

(page maintained by Mark Barsamian, last updated October, 2019)