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Description
This 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.
Publication Date
2017
Publisher
Mark Barsamian
City
Athens
Keywords
Axiomatic Geometry, Euclidean Geometry, College Geometry, Introduction to Proofs
Disciplines
Geometry and Topology
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Barsamian, Mark, "Introduction to Axiomatic Geometry" (2017). OHIO Open Faculty Textbooks. 1.
https://ohioopen.library.ohio.edu/opentextbooks/1
Comments
This 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.)
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.