A full axiomatic development of high school geometry / David M. Clark, Samrat Pathania.
Clark, David M., author.; Pathania, Samrat, author.
2023
QA461
Available Online

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Title A full axiomatic development of high school geometry / David M. Clark, Samrat Pathania.
Author Clark, David M., author.
ISBN 9783031235252 (electronic bk.)
3031235258 (electronic bk.)
303123524X
9783031235245
DOI https://doi.org/10.1007/978-3-031-23525-2
Published Cham, Switzerland : Springer, 2023.
Language English
Description 1 online resource (137 pages)
Item Number 10.1007/978-3-031-23525-2 doi
Call Number QA461
Dewey Decimal Classification 516.0071/2
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Pathania, Samrat, author.
Available in Other Form FULL AXIOMATIC DEVELOPMENT OF HIGH SCHOOL GEOMETRY.
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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. .

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