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.

Contents

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)