Softcover ISBN:  9780821889855 
Product Code:  MCL/9 
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AMS Member Price:  $44.00 
eBook ISBN:  9780821891063 
EPUB ISBN:  9781470468446 
Product Code:  MCL/9.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9780821889855 
eBook: ISBN:  9780821891063 
Product Code:  MCL/9.B 
List Price:  $105.00 $80.00 
MAA Member Price:  $94.50 $72.00 
AMS Member Price:  $84.00 $64.00 
Softcover ISBN:  9780821889855 
Product Code:  MCL/9 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9780821891063 
EPUB ISBN:  9781470468446 
Product Code:  MCL/9.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9780821889855 
eBook ISBN:  9780821891063 
Product Code:  MCL/9.B 
List Price:  $105.00 $80.00 
MAA Member Price:  $94.50 $72.00 
AMS Member Price:  $84.00 $64.00 

Book DetailsMSRI Mathematical Circles LibraryVolume: 9; 2012; 127 ppMSC: Primary 97
Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation.
Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry.
The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority.
This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Titles in this series are copublished with the Mathematical Sciences Research Institute (MSRI).
ReadershipUndergraduate students interested in geometry and secondary education.

Table of Contents

Chapters

Title page

Plane geometry

Contents

Acknowledgments

Preface

Introduction to the student

Congruent figures

Axioms, theorems and proofs

Area measure

Angle measure

Similar figures

Trigonometric ratios

Circle measure

Perspective geometry

The axioms

Guidelines for the instructor

Hilbert’s axioms

Bibliography

Index


Additional Material

Reviews

An interesting and singular approach of the Euclidean geometry is contained in this book ... [The] book covers all the topics listed in the common core state standards for high school synthetic geometry ... [T]he didactical approach of the large collection of problems, solutions and geometrical constructions is very important to consider it as a good textbook for teaching and learning synthetic geometry.
Mauro Garcia Pupo, Zentralblatt MATH


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 Book Details
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Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation.
Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry.
The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority.
This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Titles in this series are copublished with the Mathematical Sciences Research Institute (MSRI).
Undergraduate students interested in geometry and secondary education.

Chapters

Title page

Plane geometry

Contents

Acknowledgments

Preface

Introduction to the student

Congruent figures

Axioms, theorems and proofs

Area measure

Angle measure

Similar figures

Trigonometric ratios

Circle measure

Perspective geometry

The axioms

Guidelines for the instructor

Hilbert’s axioms

Bibliography

Index

An interesting and singular approach of the Euclidean geometry is contained in this book ... [The] book covers all the topics listed in the common core state standards for high school synthetic geometry ... [T]he didactical approach of the large collection of problems, solutions and geometrical constructions is very important to consider it as a good textbook for teaching and learning synthetic geometry.
Mauro Garcia Pupo, Zentralblatt MATH