Trigonometry has always been an underappreciated branch of
mathematics. It has a reputation as a dry and difficult subject, a
glorified form of geometry complicated by tedious computation. In
this book, Eli Maor draws on his remarkable talents as 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 compelling blend of history,
biography, and mathematics. He presents both a survey of the main
elements of trigonometry and a unique account of its vital
contribution to science and social development. Woven together in a
tapestry of entertaining stories, scientific curiosities, and
educational insights, the book more than lives up to the title
"Trigonometric Delights."
Maor, whose previous books have demystified the concept of
infinity and the unusual number "e," begins 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 colorful 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 four thousand years of trigonometric history. We
meet, for instance, the Renaissance scholar Regiomontanus, who is
rumored to have been poisoned for insulting a colleague, and Maria
Agnesi, an eighteenth-century Italian genius who gave up
mathematics to work with the poor--but not before she investigated
a special curve that, due to mistranslation, bears the unfortunate
name "the witch of Agnesi." The book is richly illustrated,
including rare prints from the author's own collection.
"Trigonometric Delights" will change forever our view of a once
dreaded subject.
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