**Mathematical World**

Volume: 18;
2002;
123 pp;
Softcover

MSC: Primary 00; 26; 51; 86;

Print ISBN: 978-0-8218-3255-4

Product Code: MAWRLD/18

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

**Electronic ISBN: 978-1-4704-1193-0
Product Code: MAWRLD/18.E**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

#### Supplemental Materials

# Portraits of the Earth: A Mathematician Looks at Maps

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*Timothy G. Feeman*

“Every map is a tool, a product of human effort and creativity, that represents some aspects of our world or universe … [This] course was powered by the belief that by exploring the mathematical ideas involved in creating and analyzing maps, students would see how mathematics could help them to understand and explain their world.”

—from the Preface

Portraits of the Earth exemplifies the AMS's mission to bring the power
and vitality of mathematical thought to the nonexpert. It is designed to teach
students to think logically and to analyze the technical information that they
so readily encounter every day.

Maps are exciting, visual tools that we encounter on a daily basis: from
street maps to maps of the world accompanying news stories to geologic maps
depicting the underground structure of the earth. This book explores the
mathematical ideas involved in creating and analyzing maps, a topic that is
rarely discussed in undergraduate courses. It is the first modern book to
present the famous problem of mapping the earth in a style that is highly
readable and mathematically accessible to most students. Feeman's writing is
inviting to the novice, yet also interesting to readers with more mathematical
experience. Through the visual context of maps and mapmaking, students will see
how contemporary mathematics can help them to understand and explain the
world.

Topics explored are the shape and size of the earth, basic spherical
geometry, and why one can't make a perfect flat map of the planet. The author
discusses different attributes that maps can have and determines mathematically
how to design maps that have the desired features. The distortions that arise
in making world maps are quantitatively analyzed. There is an in-depth
discussion on the design of numerous map projections—both historical and
contemporary—as well as conformal and equal-area maps. Feeman looks at
how basic map designs can be modified to produce maps with any center, and he
indicates how to generalize methods to produce maps of arbitrary surfaces of
revolution. Also included are end-of-chapter exercises and laboratory projects.
Particularly interesting is a chapter that explains how to use Maple®
add-on software to make maps from geographic data points.

This book would make an excellent text for a basic undergraduate mathematics
or geography course and would be especially appealing to the teacher who is
interested in exciting visual applications in the classroom. It would also
serve nicely as supplementary reading for a course in calculus, linear algebra,
or differential geometry. Prerequisites include a solid grasp of trigonometry
and basic calculus.

#### Readership

Undergraduates and graduate students studying mathematics and geography; general mathematical audience.

#### Reviews & Endorsements

The book is interesting, informative, and well organized … a very good introduction to the mathematics of map projections.

-- FOCUS on Geography

I became hooked on this book … interesting, entertaining, mathematical, and, so … labor of love … Includes necessary details without getting bogged down in small details or putting in so much that it would turn off non-math majors. The writing is formal and engaging. The book can be used in a formal course with a group of students, independent study with one student, or just by a professor who wishes to learn more … Worth special note are the historical references throughout the book … This human side of the subject helps to motivate the origins of the results … by adding these personalities and the problems that they worked on, the subject comes alive … highly enjoyable book. I recommend this for yourselves, for your bookshelves, and for your students.

-- MAA Online

#### Table of Contents

# Table of Contents

## Portraits of the Earth: A Mathematician Looks at Maps

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface xi12 free
- Chapter 1. Geodesy – measuring the earth 116 free
- Chapter 2. Map projections 1126
- Chapter 3. Scale factors 1732
- Chapter 4. Distances and shortest paths on the sphere 2338
- Chapter 5. Angles, triangles, and area on a sphere 2944
- Chapter 6. Curvature of surfaces 3550
- Chapter 7. Classical projections 4156
- Chapter 8. Equal-area maps 4964
- Chapter 9. Conformal maps 6176
- Chapter 10. Analysis of map distortion 6984
- Chapter 11. Oblique perspectives 7994
- Chapter 12. Other worlds: Maps of surfaces of revolution 87102
- Appendix A. Aspects of thematic cartography: Symbohzation, data classification, and thematic maps 97112
- Appendix B. Laboratory Projects 107122
- Appendix C. Portraits of the earth: How the maps in this book were produced 115130
- Bibliography 119134
- Index 121136
- Back Cover Back Cover1141