LEADER 03722nam 2200613Ia 450 001 9910958498003321 005 20200520144314.0 010 $a0-88385-958-0 035 $a(CKB)2670000000205132 035 $a(EBL)3330414 035 $a(SSID)ssj0000667040 035 $a(PQKBManifestationID)11391341 035 $a(PQKBTitleCode)TC0000667040 035 $a(PQKBWorkID)10683940 035 $a(PQKB)10955798 035 $a(UkCbUP)CR9780883859582 035 $a(MiAaPQ)EBC3330414 035 $a(Au-PeEL)EBL3330414 035 $a(CaPaEBR)ebr10729385 035 $a(OCoLC)929120329 035 $a(RPAM)15827584 035 $a(EXLCZ)992670000000205132 100 $a20090918d2009 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric transformations$hIV$iCircular transformations /$fI.M. Yaglom ; translated by A. Shenitzer 205 $a1st ed. 210 $aWashington, D.C. $cMathematical Association of America$dc2009 215 $a1 online resource (viii, 285 pages) $cdigital, PDF file(s) 225 1 $aAnneli Lax new mathematical library ;$v44 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 08$a0-88385-648-4 327 $aReflections in a circle (inversion) -- Application of inversions to the solution of constructions -- Pencils of circles. The radical axis of two circles -- Inversion (concluding section) -- Axial circular transformations -- Non-Euclidean geometry of Lobachevskii?-Bolyai, or hyperbolic geometry -- Solutions. 330 $aThe familiar plane geometry of high school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincare? model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in high-school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems. 410 0$aAnneli Lax new mathematical library ;$vv. 44. 517 3 $aCircular transformations 606 $aInversions (Geometry) 606 $aGeometry, Modern 615 0$aInversions (Geometry) 615 0$aGeometry, Modern. 676 $a511.3/3 700 $aIAglom$b I. M$g(Isaak Moiseevich),$f1921-1988.$050559 701 $aShenitzer$b Abe$049807 712 02$aMathematical Association of America, 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910958498003321 996 $aGeometric transformations$94403474 997 $aUNINA