MARC record from Internet Archive

LEADER: 06315cam 2200937 a 4500
001 ocm29310868
003 OCoLC
005 20191013195034.0
008 931028s1994 njua b 001 0 eng
010 $a 93039003
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020 $a0691033900
020 $a9780691033907
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035 $a(OCoLC)29310868$z(OCoLC)32092566$z(OCoLC)1000665080
050 00 $aQA247.5$b.M33 1994
080 0 $a510.37(091
082 00 $a512/.73$220
084 $a31.01$2bcl
084 $aMAT 001n$2stub
084 $aMAT 100f$2stub
084 $aMAT 109f$2stub
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084 $a11-03$2msc
084 $a17,1$2ssgn
088 $a93-39003
100 1 $aMaor, Eli.
245 10 $aE :$bthe story of a number /$cEli Maor.
260 $aPrinceton, N.J. :$bPrinceton University Press,$c℗♭1994.
300 $axiv, 223 pages :$billustrations ;$c25 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
504 $aIncludes bibliographical references (pages 213-215) and index.
520 $aThe story of [pi] has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well: despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the book describes the story of e from a human as well as a mathematical perspective. In a sense, it is the story of an entire period in the history of mathematics, from the early seventeenth to the late nineteenth century, with the invention of calculus at its center. Many of the players who took part in this story are here brought to life. Among them are John Napier, the eccentric religious activist who invented logarithms and - unknowingly - came within a hair's breadth of discovering e; William Oughtred, the inventor of the slide rule, who lived a frugal and unhealthful life and died at the age of 86, reportedly of joy when hearing of the restoration of King Charles II to the throne of England; Newton and his bitter priority dispute with Leibniz over the invention of the calculus, a conflict that impeded British mathematics for more than a century; and Jacob Bernoulli, who asked that a logarithmic spiral be engraved on his tombstone - but a linear spiral was engraved instead! The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics - from the law of compound interest to the shape of a hanging chain, from the area under a hyperbola to Euler's famous formula e[superscript i[pi]] = -1, from the inner structure of a nautilus shell to Bach's equal-tempered scale and to the art of M.C. Escher. The book ends with an account of the discovery of transcendental numbers, an event that paved the way for Cantor's revolutionary ideas about infinity. No knowledge of calculus is assumed, and the few places where calculus is used are fully explained.
505 0 $a1. John Napier, 1614 -- 2. Recognition -- 3. Financial Matters -- 4. To the Limit, If It Exists -- 5. Forefathers of the Calculus -- 6. Prelude to Breakthrough -- 7. Squaring the Hyperbola -- 8. The Birth of a New Science -- 9. The Great Controversy -- 10. e[superscript x]: The Function That Equals its Own Derivative -- 11. e[superscript theta]: Spira Mirabilis -- 12. (e[superscript x] + e[superscript -x])/2: The Hanging Chain -- 13. e[superscript ix]: "The Most Famous of All Formulas" -- 14. e[superscript x + iy]: The Imaginary Becomes Real -- 15. But What Kind of Number Is It? -- App. 1. Some Additional Remarks on Napier's Logarithms -- App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity] -- App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus -- App. 4. The Inverse Relation between lim (b[superscript h] -- 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0 -- App. 5. An Alternative Definition of the Logarithmic Function.
505 0 $aApp. 6. Two Properties of the Logarithmic Spiral -- App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions -- App. 8. e to One Hundred Decimal Places.
650 0 $ae (The number)
650 02 $aMathematics$xhistory.
650 7 $ae (The number)$2fast$0(OCoLC)fst01185011
650 7 $aGeschichte$2gnd
650 7 $ae$gZahl$2gnd
650 17 $ae (wiskunde)$2gtt
650 7 $aMathe matiques$xHistoire.$2ram
650 7 $aNombres, The orie des.$2ram
650 7 $ae (le nombre)$2ram
650 7 $aNombres transcendants.$2ram
650 07 $aGeschichte.$2swd
650 07 $ae (Zahl)$2swd
653 0 $aNumber theory
856 41 $3Table of contents$uhttp://catdir.loc.gov/catdir/toc/prin031/93039003.html
856 41 $3Table of contents$uhttp://www.gbv.de/dms/bowker/toc/9780691033907.pdf
856 41 $3Table of contents$uhttp://www.gbv.de/dms/hbz/toc/ht006172490.pdf
856 42 $3Publisher description$uhttp://catdir.loc.gov/catdir/description/prin031/93039003.html
856 42 $uhttp://www.zentralblatt-math.org/zmath/en/search/?an=0805.01001$3Inhaltstext
938 $aBaker and Taylor$bBTCP$n93039003$c$24.95
938 $aYBP Library Services$bYANK$n573801
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948 $hNO HOLDINGS IN P4A - 1500 OTHER HOLDINGS