A Full Axiomatic Development of High School Geometry

A Full Axiomatic Development of High School Geometry
Author :
Publisher : Springer Nature
Total Pages : 140
Release :
ISBN-10 : 9783031235252
ISBN-13 : 3031235258
Rating : 4/5 (258 Downloads)

Book Synopsis A Full Axiomatic Development of High School Geometry by : David M. Clark

Download or read book A Full Axiomatic Development of High School Geometry written by David M. Clark and published by Springer Nature. This book was released on 2023-02-13 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


A Full Axiomatic Development of High School Geometry Related Books

A Full Axiomatic Development of High School Geometry
Language: en
Pages: 140
Authors: David M. Clark
Categories: Mathematics
Type: BOOK - Published: 2023-02-13 - Publisher: Springer Nature

DOWNLOAD EBOOK

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: Euclid and Beyond
Language: en
Pages: 535
Authors: Robin Hartshorne
Categories: Mathematics
Type: BOOK - Published: 2013-11-11 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements lead
Axiomatic Geometry
Language: en
Pages: 490
Authors: John M. Lee
Categories: Mathematics
Type: BOOK - Published: 2013-04-10 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a fi
Euclidean Geometry
Language: en
Pages: 157
Authors: David M. Clark
Categories: Mathematics
Type: BOOK - Published: 2012-06-26 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean g
A Vector Space Approach to Geometry
Language: en
Pages: 417
Authors: Melvin Hausner
Categories: Mathematics
Type: BOOK - Published: 2018-10-17 - Publisher: Courier Dover Publications

DOWNLOAD EBOOK

A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other