Map of the World: An Introduction to Mathematical Geodesy

Martin Vermeer and Antti Rasila

Publisher:

CRC Press

Publication Date:

2019

Number of Pages:

289

Format:

Hardcover

Price:

99.95

ISBN:

9780367217730

Category:

Textbook

MAA Review
Table of Contents

[Reviewed by

Tom Schulte

, on

12/22/2019

]

This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application.

Generally, math is often stated without proof and developed through episodic sections in chapters that can largely be considered standalone. This results in the introduction of complex numbers and quaternions as well as the dot product and other vector fundamentals. Even exponential and logarithmic functions are introduced as potentially new to the reader. However, calculus and ODEs are expected to be in the ken of the same reader in a chapter that introduces tensor calculus to support describing theories of surfaces from Riemann and Gauss.

Basically, this is an application of complex analysis touching on numeric methods for approximation with significant spherical trigonometry and related topics. The theory and practice of projections of our home ellipsoid of revolution become a lesson and reference guide that can lead to such practical determinations as:

Lambert is best suited for a country extending in the East-West direction (Estonia), whereas Gauss-Krüger is best for a country extending in the North-South direction (like Finland). The conformal azimuthal projection known as the oblique stereographic projection is suitable for a country in the shape of a square (the Netherlands).

This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. As a textbook, it is either an adjunct source for lecture material or needs a supporting text.

In the classroom or not, this is a concise review of the theory and development of coordinate reference systems. Such models saw significant changes even in the Twentieth Century as touched on here with some of the many acronyms defined in the text:

The old European system ED50 was created in the 1950s by uniting the geodetic triangle networks of Western Europe. As the computations surface, the Hayford or International Ellipsoid was chosen, which the IUCG accepted already in 1924, and which differs significantly from the GRS80 ellipsoid. Also, the triangulation network of Finland was computed on the Hayford ellipsoid…

Finland often gets special attention in this work based on a 2014 Finnish edition which has a good translation.

Then, leaving the bounds of this world, significant content stretches to the astronomic, specifically “Precession, nutation, and the torques exerted by the Sun and Moon on the Earth’s equatorial bulge.” This includes sidereal time and an entire chapter on “The orbital motion of satellites.”

Tom Schulte (Tom.G.Schulte@gmail.com) watches the stars and tracks satellites, with the Heavens Above app recommended in this book, from Mandeville, Louisiana.

See the publisher's web page.

Tags:

Textbooks