**MSRI Mathematical Circles Library**

Volume: 9;
2012;
127 pp;
Softcover

MSC: Primary 97;

Print ISBN: 978-0-8218-8985-5

Product Code: MCL/9

List Price: $39.00

AMS Member Price: $31.20

MAA Member Price: $35.10

**Electronic ISBN: 978-0-8218-9106-3
Product Code: MCL/9.E**

List Price: $39.00

AMS Member Price: $31.20

MAA Member Price: $35.10

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# Euclidean Geometry: A Guided Inquiry Approach

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*David M. Clark*

A co-publication of the AMS and the Mathematical Sciences Research Institute

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 co-published with the Mathematical Sciences Research Institute (MSRI).

#### Readership

Undergraduate students interested in geometry and secondary education.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Euclidean Geometry: A Guided Inquiry Approach

- Cover Cover11
- Title page iii4
- Plane geometry v6
- Contents vii8
- Acknowledgments ix10
- Preface xi12
- Introduction to the student xxiii24
- Congruent figures 126
- Axioms, theorems and proofs 1742
- Area measure 2752
- Angle measure 3964
- Similar figures 4974
- Trigonometric ratios 6388
- Circle measure 7196
- Perspective geometry 83108
- The axioms 103128
- Guidelines for the instructor 115140
- Hilbert’s axioms 121146
- Bibliography 123148
- Index 125150
- Back Cover Back Cover1157