Catalogue


Heavenly mathematics : the forgotten art of spherical trigonometry /
Glen Van Brummelen.
imprint
Princeton, N.J. : Princeton University Press, c2013.
description
xvi, 192 p.
ISBN
0691148929 (hbk.), 9780691148922 (hbk.)
format(s)
Book
Holdings
More Details
imprint
Princeton, N.J. : Princeton University Press, c2013.
isbn
0691148929 (hbk.)
9780691148922 (hbk.)
contents note
Heavenly mathematics -- Exploring the sphere -- The ancient approach -- The medieval approach -- The modern approach: right-angled triangles -- The modern approach: oblique triangles -- Areas, angles, and polyhedra -- Stereographic projection -- Navigation.
catalogue key
8723942
 
Includes bibliographical references (p. [179]-188) and index.
A Look Inside
Excerpts
Flap Copy
"Written by the leading expert on the subject, this engaging book provides an in-depth historical introduction to spherical trigonometry. Heavenly Mathematics breathes new and interesting life into a topic that has been slumbering for far too long."--June Barrow-Green, associate editor of The Princeton Companion to Mathematics " Heavenly Mathematics is a very good book. It offers an interesting, accessible, and entertaining introduction to spherical trigonometry, which used to be a standard school topic but is now rarely studied. Interesting stories, engaging illustrations, and practical examples come together to enhance the reader's pleasure and understanding."--Fernando Q. Gouvêa, Colby College "Van Brummelen provides not only a wonderful historical treatment of spherical trigonometry but also a modern one that shows how the ancient and medieval methods were replaced by newer and simpler means of problem solving. Many students will find this a fascinating and worthwhile subject."--Victor J. Katz, editor of The Mathematics of Egypt, Mesopotamia, China, India, and Islam
Flap Copy
"This beautifully written book on an unusual topic, with its wealth of historical information about astronomy, navigation, and mathematics, is greatly to be welcomed."--Robin Wilson, president of the British Society for the History of Mathematics, author of Four Colors Suffice: How the Map Problem Was Solved "Written by the leading expert on the subject, this engaging book provides an in-depth historical introduction to spherical trigonometry. Heavenly Mathematics breathes new and interesting life into a topic that has been slumbering for far too long."--June Barrow-Green, associate editor of The Princeton Companion to Mathematics " Heavenly Mathematics is a very good book. It offers an interesting, accessible, and entertaining introduction to spherical trigonometry, which used to be a standard school topic but is now rarely studied. Interesting stories, engaging illustrations, and practical examples come together to enhance the reader's pleasure and understanding."--Fernando Q. Gouvêa, Colby College "Van Brummelen provides not only a wonderful historical treatment of spherical trigonometry but also a modern one that shows how the ancient and medieval methods were replaced by newer and simpler means of problem solving. Many students will find this a fascinating and worthwhile subject."--Victor J. Katz, editor of The Mathematics of Egypt, Mesopotamia, China, India, and Islam
Flap Copy
" Heavenly Mathematics is heavenly, is mathematics, and is so much more: history, astronomy, geography, and navigation replete with historical illustrations, elegant diagrams, and charming anecdotes. I haven't followed mathematical proofs with such delight in decades. If, as the author laments, spherical trigonometry was in danger of extinction, this book will give it a long-lasting reprieve."--David J. Helfand, president of the American Astronomical Society "This beautifully written book on an unusual topic, with its wealth of historical information about astronomy, navigation, and mathematics, is greatly to be welcomed."--Robin Wilson, president of the British Society for the History of Mathematics, author of Four Colors Suffice: How the Map Problem Was Solved "Written by the leading expert on the subject, this engaging book provides an in-depth historical introduction to spherical trigonometry. Heavenly Mathematics breathes new and interesting life into a topic that has been slumbering for far too long."--June Barrow-Green, associate editor of The Princeton Companion to Mathematics " Heavenly Mathematics is a very good book. It offers an interesting, accessible, and entertaining introduction to spherical trigonometry, which used to be a standard school topic but is now rarely studied. Interesting stories, engaging illustrations, and practical examples come together to enhance the reader's pleasure and understanding."--Fernando Q. Gouvêa, Colby College "Van Brummelen provides not only a wonderful historical treatment of spherical trigonometry but also a modern one that shows how the ancient and medieval methods were replaced by newer and simpler means of problem solving. Many students will find this a fascinating and worthwhile subject."--Victor J. Katz, editor of The Mathematics of Egypt, Mesopotamia, China, India, and Islam
Flap Copy
" Heavenly Mathematics is heavenly, is mathematics, and is so much more: history, astronomy, geography, and navigation replete with historical illustrations, elegant diagrams, and charming anecdotes. I haven't followed mathematical proofs with such delight in decades. If, as the author laments, spherical trigonometry was in danger of extinction, this book will give it a long-lasting reprieve."-- David J. Helfand, president of the American Astronomical Society "This beautifully written book on an unusual topic, with its wealth of historical information about astronomy, navigation, and mathematics, is greatly to be welcomed."-- Robin Wilson, president of the British Society for the History of Mathematics, author of Four Colors Suffice: How the Map Problem Was Solved "Written by the leading expert on the subject, this engaging book provides an in-depth historical introduction to spherical trigonometry. Heavenly Mathematics breathes new and interesting life into a topic that has been slumbering for far too long."-- June Barrow-Green, associate editor of The Princeton Companion to Mathematics " Heavenly Mathematics is a very good book. It offers an interesting, accessible, and entertaining introduction to spherical trigonometry, which used to be a standard school topic but is now rarely studied. Interesting stories, engaging illustrations, and practical examples come together to enhance the reader's pleasure and understanding."-- Fernando Q. Gouva, Colby College "Van Brummelen provides not only a wonderful historical treatment of spherical trigonometry but also a modern one that shows how the ancient and medieval methods were replaced by newer and simpler means of problem solving. Many students will find this a fascinating and worthwhile subject."-- Victor J. Katz, editor of The Mathematics of Egypt, Mesopotamia, China, India, and Islam
Full Text Reviews
Appeared in Choice on 2013-07-01:
Heavenly Mathematics is a truly enjoyable description of the somewhat forgotten science of spherical trigonometry. The typical undergraduate curriculum will only hint at this discipline via non-Euclidean geometry. Here, Van Brummelen (Quest Univ. Canada; The Mathematics of the Heavens and the Earth, CH, Aug'09, 46-6864) demonstrates how central the subject was to generations of navigators and geographers. Earth is roughly spherical, and the stars and planets appear to be constrained on a sphere to earthbound observers. Spherical trigonometry allows scientists/mathematicians to calculate positions and distances on the Earth and the heavens. As readers discover this discipline, they will also appreciate the beauty inherent in the topic. The book itself is well written with ample diagrams, photographs, and equations as well as reproductions/plates related to historical spherical trigonometry. The modern mathematics curriculum restricts students, except those at the upper levels, to a two-dimensional plane. As a result, students struggle when asked to transition to three dimensions. Van Brummelen's book invites readers to consider trigonometry in more than two dimensions, making it a useful supplement to a college geometry or trigonometry class. Summing Up: Highly recommended. All levels/libraries. J. T. Noonan Mount Vernon Nazarene University
Reviews
Review Quotes
" Heavenly Mathematics is a truly enjoyable description of the somewhat forgotten science of spherical trigonometry. . . . Van Brummelen's book invites readers to consider trigonometry in more than two dimensions, making it a useful supplement to a college geometry or trigonometry class."-- Choice
The present book is very well written; it leaves a clear impression that the author intended to endear--not merely present and teach--spherical trigonometry to the reader. Although not a history book, there are separate chapters shedding light on the approaches to the subject in the ancient, medieval, and modern times. There are also chapters on spherical geometry, polyhedra, stereographic projection and the art of navigation. The book is thoroughly illustrated and is a pleasant read. Chapters end with exercises; the appendices contain a long list of available and not so available textbooks and recommendations for further reading organized by individual chapters. The book made a valuable addition to my library. I freely recommend it to math teachers and curious high schoolers.
A beautiful popular book.
"A beautiful popular book."-- ThatsMaths.com
A no-nonsense introduction to spherical trigonometry.
Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun.
"Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun."-- R. Balashankar, Organiser
This item was reviewed in:
Choice, July 2013
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Main Description
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical photographs and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
Bowker Data Service Summary
This title traces the history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth.
Table of Contents
Prefacep. vii
Heavenly Mathematicsp. 1
Exploring the Spherep. 23
The Ancient Approachp. 42
The Medieval Approachp. 59
The Modern Approach: Right-Angled Trianglesp. 73
The Modern Approach: Oblique Trianglesp. 94
Areas, Angles, and Polyhedrap. 110
Stereographic Projectionp. 129
Navigating by the Starsp. 151
Ptolemy's Determination of the Sun's Positionp. 173
Textbooksp. 179
Further Readingp. 182
Indexp. 189
Table of Contents provided by Ingram. All Rights Reserved.

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