An Imaginary Tale：The Story of [the Square Root of Minus One]

Todaycomplexnumbershavesuchwidespreadpracticaluse--fromelectricalengineeringtoaeronautics--thatfewpeoplewouldexpectthestorybehindtheirderivationtobefilledwithadventureandenigma.InAnImaginaryTale,PaulNahintellsthe2000-year-oldhistoryofoneofmathematics'mostelusivenumbers,thesquarerootofminusone,alsoknownasi.Herecreatesthebafflingmathematicalproblemsthatconjureditup,andthecolorfulcharacterswhotriedtosolvethem.In1878,whentwobrothersstoleamathematicalpapyrusfromtheancientEgyptianburialsiteintheValleyofKings,theyledscholarstotheearliestknownoccurrenceofthesquarerootofanegativenumber.Thepapyrusofferedaspecificnumericalexampleofhowtocalculatethevolumeofatruncatedsquarepyramid,whichimpliedtheneedfori.Inthefirstcentury,themathematician-engineerHeronofAlexandriaencounteredIinaseparateproject,butfudgedthearithmetic;medievalmathematiciansstumbledupontheconceptwhilegrapplingwiththemeaningofnegativenumbers,butdismissedtheirsquarerootsasnonsense.BythetimeofDescartes,atheoreticalusefortheseelusivesquareroots--nowcalled"imaginarynumbers"--wassuspected,buteffortstosolvethemledtointense,bitterdebates.ThenotoriousifinallywonacceptanceandwasputtouseincomplexanalysisandtheoreticalphysicsinNapoleonictimes.Addressingreaderswithbothageneralandscholarlyinterestinmathematics,Nahinweavesintothisnarrativeentertaininghistoricalfactsandmathematicaldiscussions,includingtheapplicationofcomplexnumbersandfunctionstoimportantproblems,suchasKepler'slawsofplanetarymotionandacelectricalcircuits.Thisbookcanbereadasanengaginghistory,almostabiography,ofoneofthemostevasiveandpervasive"numbers"inallofmathematics.