Trigonometric Delights (Princeton Science Library)

Trigonometryhasalwaysbeenanunderappreciatedbranchofmathematics.Ithasareputationasadryanddifficultsubject,aglorifiedformofgeometrycomplicatedbytediouscomputation.Inthisbook,EliMaordrawsonhisremarkabletalentsasaguidetotheworldofnumberstodispelthatview.Rejectingtheusualariddescriptionsofsine,cosine,andtheirtrigonometricrelatives,hebringsthesubjecttolifeinacompellingblendofhistory,biography,andmathematics.Hepresentsbothasurveyofthemainelementsoftrigonometryandauniqueaccountofitsvitalcontributiontoscienceandsocialdevelopment.Woventogetherinatapestryofentertainingstories,scientificcuriosities,andeducationalinsights,thebookmorethanlivesuptothetitleTrigonometricDelights.Maor,whosepreviousbookshavedemystifiedtheconceptofinfinityandtheunusualnumber"e,"beginsbyexaminingthe"proto-trigonometry"oftheEgyptianpyramidbuilders.HeshowshowGreekastronomersdevelopedthefirsttruetrigonometry.Hetracestheslowemergenceofmodern,analyticaltrigonometry,recountingitscolorfuloriginsinRenaissanceEurope'squestformoreaccurateartillery,morepreciseclocks,andmorepleasingmusicalinstruments.Alongtheway,weseetrigonometryatworkin,forexample,thestruggleofthefamousmapmakerGerardusMercatortorepresentthecurvedearthonaflatsheetofpaper;weseehowM.C.Escherusedgeometricprogressionsinhisart;andwelearnhowthetoySpirographusesepicyclesandhypocycles.Maoralsosketchesthelivesofsomeoftheintriguingfigureswhohaveshapedfourthousandyearsoftrigonometrichistory.Wemeet,forinstance,theRenaissancescholarRegiomontanus,whoisrumoredtohavebeenpoisonedforinsultingacolleague,andMariaAgnesi,aneighteenth-centuryItaliangeniuswhogaveupmathematicstoworkwiththepoor--butnotbeforesheinvestigatedaspecialcurvethat,duetomistranslation,bearstheunfortunatename"thewitchofAgnesi."Thebookisrichlyillustrated,includingrareprintsfromtheauthor'sowncollection.TrigonometricDelightswillchangeforeverourviewofaoncedreadedsubject.