拉普拉斯小妖
2020-02-12 15:11:29
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.
