A Mathematical Exploration of Map Projections

C.M. Linton

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English

American Mathematical Society
31 December 2025

Applied mathematics; Cartography, map-making & projections

Series: Dolciani Mathematical Expositions

How are maps created? What is the process that enables a location on the Earth's surface to become a point on a sheet of paper? The answer lies in map projections. This book provides a highly readable account of the theory that underpins all major map projections, starting from the concept of map distortion, which all flat maps necessarily possess. The engaging exposition is enhanced by the extensive use of diagrams, including over sixty maps. The opening chapters set the scene, covering the mathematical background, the notion of map distortion and the classification of map projections. The book then turns its attention to the different types of projection, including cylindrical, azimuthal, and conical projections. Following a modern analytic approach, the author uses the tools of multivariable calculus to derive the equations defining these map projections. The book ends with a chapter utilizing complex variables to study conformal projections, and a final summary chapter to wrap up the material. Each chapter is interwoven with a compelling historical narrative enriching the text.

A Mathematical Exploration of Map Projections assumes only a prior knowledge of elementary calculus, and is an excellent resource for anyone curious about the mathematics underlying map projections.

By: C.M. Linton
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 229mm, Width: 152mm,
ISBN: 9781470482022
ISBN 10: 1470482029
Series: Dolciani Mathematical Expositions
Pages: 187
Publication Date: 31 December 2025
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Forthcoming

Geometry and coordinates Map distortion Types of projection Basic cylindrical projections Psuedocylindrical projections Oblique cylindrical projections Azimuthal projections Conic projections Pseudoconic and polyconic projections Other projections Conformal projections using complex variables Final thoughts Trigonometric formulas Bibliography Index

C. M. Linton, Loughborough University, UK.