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A full axiomatic development of high school geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A full axiomatic development of high school geometryby David M. Clark, Samrat Pathania.
作者:	Clark, David M.
其他作者:	Pathania, Samrat.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xiv, 134 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	GeometryStudy and teaching (Secondary)
電子資源:	https://doi.org/10.1007/978-3-031-23525-2
ISBN:	9783031235252$q(electronic bk.)

A full axiomatic development of high school geometry
Clark, David M.

A full axiomatic development of high school geometry[electronic resource] /by David M. Clark, Samrat Pathania. - Cham :Springer International Publishing :2023. - xiv, 134 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783031235252$q(electronic bk.)

Standard No.: 10.1007/978-3-031-23525-2doiSubjects--Topical Terms:

545074
Geometry
--Study and teaching (Secondary)

LC Class. No.: QA461 / .C53 2023

Dewey Class. No.: 516.00712

A full axiomatic development of high school geometry
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505 0 $a 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.
520 $a 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.
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