LEADER 04868nam 22006735 450 001 9910460109603321 005 20210107025714.0 010 $a0-691-02795-1 010 $a1-282-56922-8 010 $a1-4008-3389-2 024 7 $a10.1515/9781400833894 035 $a(CKB)2670000000067315 035 $a(EBL)537701 035 $a(OCoLC)638860600 035 $a(SSID)ssj0000437999 035 $a(PQKBManifestationID)11315296 035 $a(PQKBTitleCode)TC0000437999 035 $a(PQKBWorkID)10451522 035 $a(PQKB)10763366 035 $a(OCoLC)899265909 035 $a(MdBmJHUP)muse36717 035 $a(DE-B1597)446894 035 $a(OCoLC)973400920 035 $a(OCoLC)979577117 035 $a(DE-B1597)9781400833894 035 $a(MiAaPQ)EBC537701 035 $a(PPN)19924846X$9sudoc 035 $a(PPN)187954658 035 $a(EXLCZ)992670000000067315 100 $a20190708d2010 fg 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn Imaginary Tale $eThe Story of ?-1 /$fPaul J. Nahin 205 $aWith a New preface by the author 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2010] 210 4$dİ2010 215 $a1 online resource (294 p.) 225 0 $aPrinceton Science Library ;$v42 300 $aIncludes indexes. 300 $aOn t.p. "[the square root of minus one]" appears as a radical over "-1". 311 $a1-4008-8129-3 311 $a0-691-14600-4 327 $t Frontmatter -- $tA Note to the Reader -- $tContents -- $tIllustrations -- $tPreface to the Paperback Edition -- $tPreface -- $tIntroduction -- $tCHAPTER ONE The Puzzles of Imaginary Numbers -- $tCHAPTER TWO. A First Try at Understanding the Geometry of ?-1 -- $tCHAPTER THREE. The Puzzles Start to Clear -- $tCHAPTER FOUR. Using Complex Numbers -- $tCHAPTER FIVE. More Uses of Complex Numbers -- $tCHAPTER SIX. Wizard Mathematics -- $tCHAPTER SEVEN. The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory -- $tAPPENDIX A. The Fundamental Theorem of Algebra -- $tAPPENDIX B. The Complex Roots of a Transcendental Equation -- $tAPPENDIX C. (?-1)(?-1) to 135 Decimal Places, and How It Was Computed -- $tAPPENDIX D. Solving Clausen's Puzzle -- $tAPPENDIX E. Deriving the Differential Equation for the Phase-Shift Oscillator -- $tAPPENDIX F. The Value of the Gamma Function on the Critical Line -- $tNotes -- $tName Index -- $tSubject Index -- $tAcknowledgments 330 $aToday complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them.In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times.Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.Some images inside the book are unavailable due to digital copyright restrictions. 410 0$aPrinceton Science Library 606 $aNumbers, Complex 608 $aElectronic books. 615 0$aNumbers, Complex. 676 $a515.9 700 $aNahin$b Paul J., $048655 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910460109603321 996 $aAn Imaginary Tale$92466657 997 $aUNINA