Trigonometry has always been the black sheep of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by its tedious computation. In this book, Eli Maor provides a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a blend of history, biography and mathematics. He presents both a survey of the main elements of trigonometry and an account of its vital contribution to science and social development. The author starts by examining the proto-trigonometry of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker, Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M.C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles. Maor also sketches the lives of some of the intriguing figures who have shaped 4000 years of trigonometric history. We meet the Renaissance master Regiomontanus, who is rumoured to have been poisoned for insulting a colleague, and Maria Agnesi, an 18th-century Italian genius who gave up mathematics to work with the poor - but not before she investigated a special curve that, due to a mistranslation, bears the unfortunate name the witch of Agnesi.