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Glen Van Brummelen – Inspired by Math #18

Today I got to interview another great author of a Princeton University Press title. "Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry" is a delightful exploration of the techniques that ancient and medieval people from different cultures used to navigate and map the stars and the seas along with modern methods. There's a strong focus on the historical setting for these explorations. This setting brings the mathematics to life. I was very impressed to learn how very smart ancient astronomers and mathematicians were. Our twentyfirst century perception that we are smarter than our predecessors is simply not true. I was also delighted to learn an elegant variation of the familiar Pythagorean Theorem when applied to a sphere.

I thoroughly enjoyed getting exposed to this very elegant branch of mathematics and hope you too will catch some of Professor Van Brummelen's enthusiasm.

Chapter 1 of the book is available as a free PDF download.

About Glen Van Brummelen

From the Quest University Website:

Glen Van Brummelen, mathematics tutor, is a historian of mathematics, especially trigonometry and astronomy in ancient Greece and medieval Islam. He is past president of the Canadian Society for History and Philosophy of Mathematics, and senior fellow at the Dibner Institute for History of Science at MIT. In addition to authoring 30 scholarly and 10 encyclopedia articles, he is co-editor of "Mathematics and the Historian's Craft" (Springer) and recently published the first history of trigonometry in over a century with Princeton University Press called "The Mathematics of the Heavens and the Earth: The Early History of Trigonometry".

Glen has taught mathematics at small liberal arts colleges his entire career. He has taught over 30 different courses, including most traditional topics in math but also mathematics and music, mathematics and democracy, mathematics and computer graphics, spherical trigonometry (using a 19th-century textbook), and how to be an ancient astronomer. Several of his students have published their undergraduate research with him in recent years. In the summer he teaches the history of math regularly at MathPath, a math camp for bright 7th- and 8th-graders.

As if this wasn't enough, he keeps busy with his three very active kids of his own: Ariel (13), Matthew (9) and Andrew (5), all of whom will be mathematicians some day, and wife Heide (age unspecified). He is an avid soccer player, and played goal on the college team at his two previous colleges. He is undefeated at chess in the past 20 years, with a record of 2-0. Glen notes that "the key is to choose one's opponents carefully".

About "Heavenly Mathematics"

From the Princeton University Press Website:

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 images 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.

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  1. Trigonometric tables are to be found in a condensed cuneiform version on Plimpton 322 constructed in about 1700BC. What these tables lack can be calculated by applying the half angle formula. cotu +cosecu equals cot(u/2).

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