A Full Axiomatic Development of High School Geometry

The textbook provides a complete axiomatic development of plane Euclidean geometry, covering points, distance, length, area, angle measure, congruence, and similarity, with proofs and models. It is designed for graduate and advanced undergraduate students, pure math majors, faculty preparing future teachers, and professionals. Its goal is to anchor K-12 geometry in solid modern mathematics, strengthening the teaching of secondary and tertiary geometry.

Format: Paperback / softback
Length: 134 pages
Publication date: 15 February 2024
Publisher: Springer International Publishing AG

This textbook offers a comprehensive and rigorous axiomatic treatment of the fundamental aspects of plane Euclidean geometry, which forms the core curriculum of high school geometry. It commences with a set of points, a distance measure between pairs of points, and ten simple axioms. From this foundation, the concepts of length, area, angle measure, congruence, and similarity are meticulously defined and their properties are established as theorems. The book concludes with a proof of the consistency of the axioms employed and a detailed description of their models. The text is designed in a guided inquiry format, encouraging students to actively engage in the learning process by proving theorems and presenting their proofs to their classmates under the guidance of an instructor. The book is intended for graduate and advanced undergraduate students who are interested in teaching secondary school mathematics, pure math majors who wish to delve into the foundations of geometry, faculty preparing future secondary school teachers, and as a reference for professional mathematicians. Its primary objective is to establish a solid foundation in modern mathematics for K-12 geometry, thereby enhancing the teaching of secondary and tertiary geometry with a profound understanding of the subject.

Weight: 237g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031235276
Edition number: 1st ed. 2023