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 (52 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
An Axiomatic Development of the Number System for High School Students
Language: en
Pages: 45
Authors: William Rabinowitz
Categories: Axiomatic set theory
Type: BOOK - Published: 2002-05-01 - Publisher:

DOWNLOAD EBOOK

This book begins with the natural number system 1, 2, 3... and zero. The natural number is enlarged by adding fractions defined by four axioms. This is followed
Thinking Geometrically
Language: en
Pages: 586
Authors: Thomas Q. Sibley
Categories: Mathematics
Type: BOOK - Published: 2015-08-14 - Publisher: The Mathematical Association of America

DOWNLOAD EBOOK

Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for bot
The Number System
Language: en
Pages: 88
Authors: Bevan K. Youse
Categories: Arithmetic
Type: BOOK - Published: 1965 - Publisher:

DOWNLOAD EBOOK

Why Johnny Can't Add
Language: en
Pages: 208
Authors: Morris Kline
Categories: Mathematics
Type: BOOK - Published: 1974 - Publisher: Random House Incorporated

DOWNLOAD EBOOK

Briefly discusses the traditional mathematics formerly taught in American schools and views the language and weaknesses of the modern math curriculum