Awards

• Short-listed for Choice 's Outstanding Academic Titles for 2013 2013
• Short-listed for BSHM Neumann Book Prize, British Society for the History of Mathematics 2013

Overview

Heavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth. Once at the heart of astronomy and ocean-going navigation for two millennia, the discipline was also a mainstay of mathematics education for centuries and taught widely until the 1950s. 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 of its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams. This unique compendium also features easy-to-use appendixes as well as exercises that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

Full Product Details

Author:   Glen Van Brummelen
Publisher:   Princeton University Press
Imprint:   Princeton University Press
Dimensions:   Width: 15.20cm , Height: 1.80cm , Length: 23.50cm
Weight:   0.340kg
ISBN:  

9780691175997

ISBN 10:   0691175993
Pages:   216
Publication Date:   04 April 2017
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In stock  
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Language:   English

Table of Contents

Preface vii 1 Heavenly Mathematics 1 2 Exploring the Sphere 23 3 The Ancient Approach 42 4 The Medieval Approach 59 5 The Modern Approach: Right- Angled Triangles 73 6 The Modern Approach: Oblique Triangles 94 7 Areas, Angles, and Polyhedra 110 8 Stereographic Projection 129 9 Navigating by the Stars 151 Appendix A. Ptolemy's Determination of the Sun's Position 173 Appendix B. Textbooks 179 Appendix C. Further Reading 182 Index 189

Reviews

One of Choice's Outstanding Academic Titles for 2013 Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics 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. --Alexander Bogomolny, CTK Insights A no-nonsense introduction to spherical trigonometry. --Book News, Inc. A beautiful popular book. --ThatsMaths.com 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 Heavenly Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry... As readers discover this discipline, they will also appreciate the beauty inherent in the topic. --Choice Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader. --Florin Diacu, Literary Review of Canada Van Brummelen has written a wonderful introduction ... that draws on the history of [spherical trigonometry] to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about. --Metascience [Heavenly Mathematics] is an excellent survey of spherical trigonometry... Simply an appreciation of a beautiful lost subject, with historical overtones... [D]istinguishable for its appealingly fresh style. --Mathematical Reviews [Heavenly Mathematics] is a lovely book to read... [A] wonderful introduction for anyone who wishes to learn more about this subject... I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it. --Mathematics Today Engaging, clear and not overly technical; you can safely lend this book to your friends in the history department... [Heavenly Mathematics] is excellent. --Zentralblatt MATH Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject. --Jan P. Hogendijk, Isis This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students. --Teresa Floyd, Mathematics Teacher Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins... Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative. --P.N. Ruane, Mathematical Gazette An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics. --Elizabeth Hamm, Aestimatio Critical Reviews in the History of Science

One of Choice's Outstanding Academic Titles for 2013 Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics 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. --Alexander Bogomolny, CTK Insights A no-nonsense introduction to spherical trigonometry. --Book News, Inc. A beautiful popular book. --ThatsMaths.com 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 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 Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader. --Florin Diacu, Literary Review of Canada Glen van Brummelen has written a wonderful introduction to the forgotten subject of spherical trigonometry that draws on the history of the subject to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about. He has succeeded in writing a book that is not intended for historians of science, but which historians of science will find little to complain about and indeed will surely enjoy reading. The book itself is handsomely produced with dozens of attractive illustrations and sold at an affordable price. If spherical trigonometry is ever to become a widely known subject again, this book will surely have played a major role in rescuing it from obscurity. --John M. Steele, Metascience This book is an excellent survey of spherical trigonometry, discussing and explaining many historic and modern applications in detail and giving full proofs for all theorems. The author has found the right conversational style for a very broad audience, like high school students and teachers of mathematics and amateur historians, who might also skip the proofs. A series of figures from old textbooks and photographs of historical teaching aids make the book very appealing. --Martin Funk, Mathematical Reviews This is a lovely book to read. I gained a great deal of satisfaction from working through the proofs and constructions, not least because the author has succeeded in convincing me that spherical trigonometry is not as hard as I once thought it was. The style and level of the book are definitely suited to those secondary school pupils who are prepared to follow the technical details, and perhaps try their hand at the very many exercises that are included. More generally, however, the book would provide a wonderful introduction for anyone who wishes to learn more about this subject. Having read the book, I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it. --Christopher Hollings, Mathematics Today The author's style is engaging, clear, and not overly technical; you can safely lend this book to your friends in the history department... [T]he book is excellent, and would be suited to a wide readership. Libraries (school and university) should give it serious consideration, and it is reasonably priced for private purchase. --Robert Dawson, Zentralblatt MATH Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject. --Jan P. Hogendijk, Isis This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students. --Teresa Floyd, Mathematics Teacher Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins... Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative. --P.N. Ruane, Mathematical Gazette An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics. --Elizabeth Hamm, Aestimatio Critical Reviews in the History of Science

One of Choice's Outstanding Academic Titles for 2013 Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics In this grand chronicle of the science behind the origins of our 4.6-billion-year-old Solar System, John Chambers and Jacqueline Mitton peruse everything from the giant collision thought to have formed our Moon to the nature of meteorites. --Rosalind Metcalfe, Nature 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. --Alexander Bogomolny, CTK Insights A no-nonsense introduction to spherical trigonometry. --Book News, Inc. A beautiful popular book. --ThatsMaths.com 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 Heavenly Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry... As readers discover this discipline, they will also appreciate the beauty inherent in the topic. --Choice Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader. --Florin Diacu, Literary Review of Canada Van Brummelen has written a wonderful introduction ... that draws on the history of [spherical trigonometry] to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about. --Metascience [Heavenly Mathematics] is an excellent survey of spherical trigonometry... Simply an appreciation of a beautiful lost subject, with historical overtones... [D]istinguishable for its appealingly fresh style. --Mathematical Reviews [Heavenly Mathematics] is a lovely book to read... [A] wonderful introduction for anyone who wishes to learn more about this subject... I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it. --Mathematics Today Engaging, clear and not overly technical; you can safely lend this book to your friends in the history department... [Heavenly Mathematics] is excellent. --Zentralblatt MATH Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject. --Jan P. Hogendijk, Isis This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students. --Teresa Floyd, Mathematics Teacher Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins... Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative. --P.N. Ruane, Mathematical Gazette An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics. --Elizabeth Hamm, Aestimatio Critical Reviews in the History of Science

An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics. --Elizabeth Hamm, Aestimatio Critical Reviews in the History of Science Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins. . . . Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative. --P.N. Ruane, Mathematical Gazette This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students. --Teresa Floyd, Mathematics Teacher Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject. --Jan P. Hogendijk, Isis Engaging, clear and not overly technical; you can safely lend this book to your friends in the history department. . . . [Heavenly Mathematics] is excellent. --Zentralblatt MATH [Heavenly Mathematics] is a lovely book to read. . . . [A] wonderful introduction for anyone who wishes to learn more about this subject. . . . I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it. --Mathematics Today [Heavenly Mathematics] is an excellent survey of spherical trigonometry. . . . Simply an appreciation of a beautiful lost subject, with historical overtones. . . . [D]istinguishable for its appealingly fresh style. --Mathematical Reviews Van Brummelen has written a wonderful introduction . . . that draws on the history of [spherical trigonometry] to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about. --Metascience Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader. --Florin Diacu, Literary Review of Canada Heavenly Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry. . . . As readers discover this discipline, they will also appreciate the beauty inherent in the topic. --Choice 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 A beautiful popular book. --ThatsMaths.com A no-nonsense introduction to spherical trigonometry. --Book News, Inc. 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. --Alexander Bogomolny, CTK Insights Once a mainstay of mathematics, spherical trigonometry no longer appears on school curricula. Here, Glen Van Brummelen reasserts the field's importance, sharing in illuminating detail how it figured in astronomy, cartography and our understanding of Earth's rotation. --Rosalind Metcalfe, Nature One of Choice's Outstanding Academic Titles for 2013Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics

Author Information

Glen Van Brummelen is coordinator of mathematics at Quest University Canada and former president of the Canadian Society for History and Philosophy of Mathematics. He won the 2016 Haimo Award for Distinguished College or University Teaching of Mathematics, awarded by the Mathematical Association of America, and the 2017 3M National Teaching Fellowship, awarded by the Society for Teaching and Learning in Higher Education.

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