“Mathematical trigonometry has never received enough attention. It is a dull and challenging topic, a glorified variation of geometry made challenging by laborious computation. Eli Maor dispels that notion in this book using his exceptional skills as a teacher of the realm of numbers. He avoids the typical dry explanations of sine, cosine, and their trigonometric relations in favor of an engaging synthesis of history, biography, and mathematics. In addition to providing an overview of the fundamentals of trigonometry, he also provides a unique description of how important it is to both scientific and social progress. The book more than lives up to its title, Trigonometric Delights, because it is woven together in a tapestry of amusing tales, fascinating mathematical facts, and enlightening insights.
Maor begins by looking at the “proto-trigonometry” used by the Egyptian pyramid builders. Maor’s prior books have decoded the meaning of infinity and the strange number “e.” He demonstrates how Greek astronomers created the first true trigonometry. He describes the colorful beginnings of modern, analytical trigonometry and how it slowly emerged during Renaissance Europe’s drive for more precise clocks, cannons, and musical instruments. Along the way, we observe trigonometry in action, for instance, in the famous cartographer Gerardus Mercator’s struggle to depict the curved earth on a flat sheet of paper, in the use of geometric progressions in the artwork of M. C. Escher, and in the use of epicycles and hypercycles in the Spirograph toy.
The biographies of some of the fascinating people who have influenced the history of trigonometry throughout the past four thousand years are also sketched by Maor. We meet people like the Renaissance scholar Regiomontanus, who is said to have been poisoned for insulting a colleague, and Maria Agnesi, an Italian mathematician of the eighteenth century who gave up mathematics to help the poor—but not before she looked into a particular curve that, sadly, was given the unfortunate name “the witch of Agnesi” due to a mistranslation.” ” Richly illustrated, the book features rare prints from the author’s own collection. Trigonometric Delights will permanently alter how we perceive a once-dreaded topic.”