A Full Axiomatic Development of High School Geometry

by David M. Clark, Samrat Pathania

Overview

This textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content of high school geometry. It begins with a set of points, a measure of distance between pairs of points and ten simple axioms. From there the notions of length, area and angle measure, along with congruence and similarity, are carefully defined and their properties proven as theorems. It concludes with a proof of the consistency of the axioms used and a full description of their models. It is provided in guided inquiry (inquiry-based) format with the intention that students will be active learners, proving the theorems and presenting their proofs to their class with the instructor as a mentor and a guide.

The book is written for graduate and advanced undergraduate students interested in teaching secondary school mathematics, for pure math majors interested in learning about the foundations of geometry, for faculty preparing future secondary school teachers and as a reference for any professional mathematician. It is written with the hope of anchoring K-12 geometry in solid modern mathematics, thereby fortifying the teaching of secondary and tertiary geometry with a deep understanding of the subject.

Product Details

ISBN-13:	9783031235276
Publisher:	Springer International Publishing
Publication date:	02/25/2023
Edition description:	1st ed. 2023
Pages:	134
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

David Clark holds the rank of SUNY Distinguished Professor Emeritus at the State University of New York, New Paltz. He has published many articles and two books in universal algebra, mathematical logic, topological dualities and evolutionary computation. David has authored two other guided inquiry textbooks for future teachers, a real analysis text and an elementary text on Euclidean geometry. He is a founding editor of the Journal of Inquiry-Based Learning in Mathematics which publishes guided inquiry manuals for a wide range of courses.

Samrat Pathania is a former software engineer who currently teaches mathematics, physics, and computer science at Wallkill High School in Wallkill, New York. He is a New York State Master Teacher Emeritus and co-founder of the Educator Collective for Environmental Justice. Samrat is a passionate advocate for inquiry-based and climate solutions-centered STEM education, inside and outside the classroom. He has presented many talks and workshops on practical climate solutions. He lives in New Paltz, NY with his family in a net-zero home.

Table of Contents

Foundational Principles.- Neutral Geometry.- Similar Figures.- Area Measure.- Angle Measure.- Trigonometry.- Circle Measure.- Consistency and Models.- Appendix A: Axioms.- Appendix B: MCL #9.- Appendix C: Font Guide.- Appendix D: Theorem Index.- Appendix E: Notation Index.- Bibliography.- Index.

Editorial Reviews

The book is an excellent resource for geometry.” (Tara D. Taylor, Mathematical Reviews, July, 2024)

“The book A Full Axiomatic Development of High School Geometry focuses on the top tier in a sequence of four educational tiers of geometry beginning in preschool and primary grades, where young children gain their first experiences with abstract shapes through definitions and an assortment of geometry facts. … this book is likely to be of interest to many future secondary mathematics teachers in training.” (Frederic Morneau-Guérin, MAA Reviews, July 15, 2023)

From the Publisher