The Doctrine of Triangles: A History of Modern Trigonometry - Softcover

Van Brummelen, Glen

Softcover

ISBN 10: 0691270430 ISBN 13: 9780691270432

Publisher: Princeton University Press, 2025

Synopsis

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth

The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology.

Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry’s participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms.

A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry’s rich historical past full circle into the modern era.

About this title

About the Author

Glen Van Brummelen is dean of the faculty of natural and applied sciences at Trinity Western University, and a historian of mathematics and astronomy. His many books include The Mathematics of the Heavens and the Earth: The Early History of Trigonometry and Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry (both Princeton).

Edition details

• Publisher: Princeton University Press
• Publication date: 2025
• Language: English
• ISBN 10: 0691270430
• ISBN 13: 9780691270432
• Binding: Paperback
• Number of pages: 392