Mathematical World, Volume 18: Portraits of the Earth: A Mathematician Looks at Maps (Softcover)
Mathematical World, Volume 18: Portraits of the Earth: A Mathematician Looks at Maps (Softcover)
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From the back cover: "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."Students will explore:
- the shape of the earth
- the determination of latitude and longitude
- elementary spherical geometry
- the uses and computation of scale factors
- the design of optimal routes for air or sea navigation
- Gaussian curvature
- why one can't make a perfect flat map of the earth
- how to evaluate maps critically and analytically
- how to design atlas maps using both hand-drawn techniques and computer graphics software."
BRIEF CONTENTS
- Preface
- Chapter 1. Geodesy - measuring the earth
- Chapter 2. Map projections
- Chapter 3. Scale factors
- Chapter 4. Distances and shortest paths on the sphere
- Chapter 5. Angles, triangles, and area on a sphere
- Chapter 6. Curvature of surfaces
- Chapter 7. Classical projections
- Chapter 8. Equal-area maps
- Chapter 9. Conformal maps
- Chapter 10. Analysis of map distortions
- Chapter 11. Oblique perspectives
- Chapter 12. Other worlds: Maps of surfaces of revolution
- Appendix A. Aspects of thematic cartography: Symbolization, data classification, and thematic maps
- Appendix B. Laboratory Projects
- Appendix C. Navigation
- Bibliography
- Index
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PUBLISHER: American Mathematical Society
ISBN-13: 9780821832554
ISBN-10: 0821832557