**AMS/MAA Textbooks**

Volume: 26;
2015;
559 pp;
Hardcover

**Print ISBN: 978-1-93951-208-6
Product Code: TEXT/26**

List Price: $77.00

AMS Member Price: $57.75

MAA Member Price: $57.75

**Electronic ISBN: 978-1-61444-619-4
Product Code: TEXT/26.E**

List Price: $50.00

AMS Member Price: $37.50

MAA Member Price: $37.50

# Thinking Geometrically: A Survey of Geometries

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*Thomas Q. Sibley*

MAA Press: An Imprint of the American Mathematical Society

This is a well written and comprehensive survey
of college geometry that would serve a wide variety of courses for
both mathematics majors and mathematics education majors. Great care
and attention is spent on developing visual insights and geometric
intuition while stressing the logical structure, historical
development, and deep interconnectedness of the ideas. Students with
less mathematical preparation than upper-division mathematics majors
can successfully study the topics needed for the preparation of high
school teachers.

There is a multitude of exercises and projects in
those chapters developing all aspects of geometric thinking for these
students as well as for more advanced students. These chapters include
Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry,
Transformational Geometry, and Symmetry. Topics in the other chapters,
including Non-Euclidean Geometry, Projective Geometry, Finite
Geometry, Differential Geometry, and Discrete Geometry, provide a
broader view of geometry. The different chapters are as independent as
possible, while the text still manages to highlight the many
connections between topics.

The text is self-contained, including
appendices with the material in Euclid's first book and a high school
axiomatic system as well as Hilbert's axioms. Appendices give brief
summaries of the parts of linear algebra and multivariable calculus
needed for certain chapters. While some chapters use the language of
groups, no prior experience with abstract algebra is presumed. The
text will support an approach emphasizing dynamical geometry software
without being tied to any particular software.

An instructor's manual for this title is available
electronically. Please send email to textbooks@ams.org for more
information.

#### Reviews & Endorsements

This also visually very appealing book offers a wealth of geometric information together with the historical background. The author takes the reader onto a long and engrossing journey to 11 well-selected basic sites of classical and modern geometry. Geometric intuition and facility in proofs are developed. Visualization by the use of dynamic geometry software is included in many exercises and projects.

-- Zentrallblatt

# Table of Contents

## Thinking Geometrically: A Survey of Geometries

Table of Contents pages: 1 2

- Cover cov11
- Half title i3
- Copyright ii4
- Title iii5
- Series iv6
- Contents vii9
- Preface xv17
- 1 Euclidean Geometry 127
- 2 Axiomatic Systems 6793
- 3 Analytic Geometry 97123
- 4 Non-Euclidean Geometries 151177
- 5 Transformational Geometry 195221
- 6 Symmetry 261287
- 7 Projective Geometry 317343
- 8 Finite Geometries 373399
- 9 Differential Geometry 409435

Table of Contents pages: 1 2