sayyoudefineapointwith coordinates(x,y),wherexandyare realnumbers.Thesoftwarestoresthisas(x+0i,y+0i).Inthepreviousexample,theintersectionpointisnothingbutoneofthesolutionsofasystemoftwoquadraticequations.Whenthecirclesceasetointersect,thesolutionsstillexist,butnowtheyplex.Andsoiseverythingthatdependsonthem.Wesimplyseeonthescreenonlytherealobjects,orifyoulike,theintersectionofa4-dimensionalspace(whereeachofthexandyaxeshas2degreesoffreedom)withtherealplane(noponents). Thecontinuityproblemissolvedbycursortracking.Puttingitsimply, Cinderellainterpretshowyoumove themouseasaguideforwhatthedesiredcontinuousmoveofobjectsis.Again,themanualprovidesthedetails. Letmenowrefertosomedisad- vantagesofCinderella.Theproblemis notwithwhatitcontains(atleastIwasunabletofindanybugorstrangebe- havior),butwithwhatismissing.TomeitisobviousthattheversionIplayedwith(version1.0)isimmatureandnotready(yet)fordistribution.Forexample,theonlywaytodefmeaconicinthisversionisbyspecifying5points.Thisisalmostuseless;normallyyou(andI)wouldliketodefine,say,anellipsebyits2focalpointsandthesumofdistancesfromthemtoeverypointontheellipse.(Or,say,byspecifyingthelengthsandpositionsofthe2axesoftheellipse.)Theauthorshaveassuredmethatthisisjustamatterofprovidingahumaninterface,andthatamorenaturalmechanismfordefiningconicsisplannedforanear-futurereleaseofthesoftware. Iwouldalsoliketoseeothertypesofentities,e.g.,higher-degreepolynomialsandeventrigonometricfunctions.Theauthorsclaimthatsomelimitedfunctionality(e.g.,notheorem-proving)foranyexternallydefinedfunction(e.g.,by Mathematica)willbeprovidedinversion2.0ofCinderella.Moreover,theau- thorspromisemoreflexibilitywiththelocusandanimationfeatures.(WithVer- sion1.0onlypointsandlinescanserveasmovers,roads,andtracers.)Anotherpromisedfeatureforthenextversionofthesoftwareisascriptinglanguagefortextualinput,batchfiles,logging,etc. Finally,Ihavemixedemotionsaboutthemanual.Ontheonehand,asmentionedabove,itscontentsareconciseandanized,andtheymakethesoftware-learningprocesssmoothandeasy.Ontheotherhand,ithas(tomytaste)twostylisticdrawbacks.First,itisabittooself-congratulatoryabouttheuseofthesophisticatedmathematicaltoolsintheimplementationofthesoftware.Second,itcontainsspellingerrorsandseemstorequireonemoreproofreading.Ibelievethatthesetwodrawbackscanbereadilyfixed.Letmeconcludewithagoodwordaboutthesoftwareinstallation:It'sapieceofcake.After~-0secondsorso,youcanplay. FacultyofComputerScienceTechnion--lsraelInstituteofTechnologyHaifa32000Israele-mail:barequet@cs.technion.ac.il Erratum Inhis"Rediscoveringafamilyofmeans"(MathematicalInteUigencer24(2002),no.2,58-65), StephenR.WassellbeginshisountwiththeuseofthearithmeticmeanbytheancientBabylonians.Readersmayhavebeensurprised,asIwas,bytheveryearlydategiven(andbyitsprecision). Onereader,RobertDavisofSouthernMethodistUniversity,wrotetoquerythisdating.ProfessorWassellthankshim,asdoI. WassellwasrelyingonanarticlebyMmsrconneSpiesser,whichhecited.PromptedbyProfessorDavis'squery,hewentbacktoSpiesserandfoundhehadmisreadher,takinganidentificationnumberforadate!
Hegivesthiscorrectedtextforthesentencefollowingequation(5)inhisarticle: Thearithmeticmean,thesimplestofthethree,wasknownandusedbytheBabylonians,perhapsasearlyas1900BCE. ForthishereferstoSpiesserandto
O.NeugebauerandA.Sachs,MathematicalCuneiformTexts,AmericanOrientalSociety,New Haven,CT,1945. TheEditor VOLUME24,NUMBER4,200275