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  2. Matematik
  3. Geometri

A Full Axiomatic Development of High School Geometry

Af: David M. Clark, Samrat Pathania Engelsk Paperback

A Full Axiomatic Development of High School Geometry

Af: David M. Clark, Samrat Pathania Engelsk Paperback
Tjek vores konkurrenters priser
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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 134
ISBN-13: 9783031235276
Indbinding: Paperback
Udgave:
ISBN-10: 3031235274
Kategori: Geometri
Udg. Dato: 15 feb 2024
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer International Publishing AG
Oplagsdato: 15 feb 2024
Forfatter(e): David M. Clark, Samrat Pathania
Forfatter(e) David M. Clark, Samrat Pathania

Kategori Geometri

ISBN-13 9783031235276

Sprog Engelsk

Indbinding Paperback

Sider 134

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 15 feb 2024

Oplagsdato 15 feb 2024

Forlag Springer International Publishing AG

Kategori sammenhænge