The number π
著者
書誌事項
The number π
American Mathematical Society, 2004
- タイトル別名
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Autour du nombre π
- タイトル読み
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The number pi
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注記
Includes bibliographical references (p. 313-317) and index
内容説明・目次
内容説明
'[In the book] we are dealing with a theme which cuts across the mathematics courses classically taught in the first four years of college. Thus it offers the reader the opportunity to learn, review and give long-term thought to the concepts covered in these programmes by following the guiding thread of this favoured number' - from the Preface. This is a clever, beautiful book. The authors trace the thread of pi through the long history of mathematics. In so doing, they touch upon many major subjects in mathematics: geometry (of course), number theory, Galois theory, probability, transcendental numbers, analysis, and, as their crown jewel, the theory of elliptic functions, which connects many of the other subjects.By this device, the authors provide a tour through mathematics, one that mathematicians of all levels, amateur or professional, may appreciate. In many cases, the tour visits well-known topics from particular special interest groups. Remarkably, pi is often found at the places of deepest beauty. The volume includes many exercises with detailed solutions. Anyone from undergraduate mathematics majors through university professors will find many things to enjoy in this book.
目次
- Measurement of the circle
- Wallis's formula and some others
- Euler, Euler again, always Euler
- Squaring the circle
- $pi$ and elliptic integrals
- Solutions to the exercises
- Bibliography
- Index
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