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.
