MARC Record from Library of Congress

LEADER: 03584cam a22002897a 4500
001 2011279122
003 DLC
005 20120920102721.0
008 120716s2011 mauab b 001 0 eng d
010 $a 2011279122
020 $a9781453810576 (pbk.)
020 $a1453810579 (pbk.)
035 $a(OCoLC)ocn765912661
040 $aWCM$cWCM$dDLC
042 $alccopycat
050 00 $aQA241$b.G864 2011
082 00 $a512.7$223
100 1 $aGuthery, Scott B.
245 12 $aA motif of mathematics :$b[history and application of the mediant and the Farey sequence] /$cScott B. Guthery.
260 $aBoston :$bDocent Press,$cc2011.
300 $axx, 243 p :$bill., maps ;$c23 cm.
500 $aSubtitle from cover.
504 $aIncludes bibliographical references (p. 227-239) and index.
505 0 $aThe mediant. Non-arithemetised mathematics ; Ratio, proportion and fraction ; Definition of the mediant ; A sequence of vulgar fractions ; Nicolas Chuquet, and the règle des nombres moyens ; Rational approximation ; The mediant and the continued fraction ; John Wallis, Savilian Chair of Geometry ; Digit generation ; The Möbius transformation ; Mediant convergents ; The Simpson paradox ; A motif of mathematics -- History of the Farey sequence. Mr. R. Flitcon and question 281 ; Charles Haros, géomètre ; "Tables pour évaluer une fraction ordinaire ..." ; "Tables for evaluating a common fraction ..." ; The Farey sequence as the argument of a mathematical table ; "Instruction abrégée sur les nouvelles measures ..." ; Computing logarithms ; General purpose root finder ; Haros' publications ; The Bureau du Cadastre ; Grandes tables du Cadastre ; Sources of inspiration ; Bookends on the era of organized scientific computation ; Henry Goodwyn, Brewer and table maker ; The dispersal of Goodwyn's archive ; Goodwyn's publications ; "On the quotient arising from the division of an unit .." ; Goodwyn and the mediant property ; Decimalization of the pound sterling ; John Farey, geologist and musicologist ; "On a curious property of vulgar fractions" ; "Proof of a curious theorem regarding numbers" ; Delambre and Tilloch weigh in ; Farey's publications ; History's grudge against John Farey, Sr. --The table makers. Archibald's Mathematical table makers ; Lehmer's Guide to the tables in the theory of numbers ; Tables of tables ; Neville's tables ; The Farey series of order 1025 ; Reviews of The Farey series of order 1025 ; Solving Diophantine equations ; Rectangular-polar conversion tables ; Reviews of Rectangular-polar conversion tables ; Moritz Stern and Achille Brocot ; Gears and rational approximation -- Inventions and applications. Sampling algorithm ; Dithering algorithm ; Decimal-to-fraction conversion ; Analog-to-digital conversion ; Slash arithmetic and mediant rounding ; Patterns for weaving ; Networks of resistors -- The mediant and the Riemann hypothesis. Jérôme Franel, Chair for Mathematics in the French language ; "The Farey series and the prime numbers problem" ; A synopsis of Franel's proof ; "Remarks concerning the earlier paper by Mr. Franel" ; Neville's search for structure ; Capturing regularization -- Explorations and pereginations. The integer part function ; Mediant factorization ; The Mayer-Erdös constant ; Ocagne's recursion ; Primes and twin primes ; The fractional part function ; Final words -- Appendix A. Landau's proof of Franel's two dimensional integral -- Appendix B. "Some consequences of the Riemann hypothesis".
650 0 $aSeries, Farey.
650 0 $aContinued fractions.
650 0 $aNumber theory.