A Full Axiomatic Development of High School Geometry
David M Clark author Samrat Pathania author
Format:Paperback
Publisher:Springer International Publishing AG
Published:15th Feb '24
Should be back in stock very soon
This paperback is available in another edition too:
- Hardback£49.99(9783031235245)
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.
“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)
“The book is an excellent resource for geometry.” (Tara D. Taylor, Mathematical Reviews, July, 2024)
ISBN: 9783031235276
Dimensions: unknown
Weight: unknown
134 pages
1st ed. 2023