LEADER 04544nam 22005535 450 001 9910484745603321 005 20200705105334.0 010 $a3-662-61053-1 024 7 $a10.1007/978-3-662-61053-4 035 $a(CKB)4920000000496061 035 $a(DE-He213)978-3-662-61053-4 035 $a(MiAaPQ)EBC6181499 035 $a(PPN)243758820 035 $a(EXLCZ)994920000000496061 100 $a20200421d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Universe of Quadrics /$fby Boris Odehnal, Hellmuth Stachel, Georg Glaeser 205 $a1st ed. 2020. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2020. 215 $a1 online resource (VIII, 606 p. 1 illus.) 311 $a3-662-61052-3 320 $aIncludes bibliographical references and index. 327 $a1 Introduction -- 2 Quadrics in Euclidean 3-space -- 3 Linear algebraic approach to quadrics -- 4 Projective and affine quadrics -- 5 Pencils of quadrics -- 6 Cubic and quartic space curves as intersections of quadrics -- 7 Confocal quadrics -- 8 Special problems -- 9 Quadrics and Differential Geometry -- 10 Line Geometry, Sphere Geometry, Kinematics -- 11 Some generalizations of quadrics -- References -- Index. 330 $aThe Universe of Quadrics This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective, affine, and metrical properties, covering both Euclidean and non-Euclidean geometries. While the history of conics is more than two thousand years old, the theory of quadrics began to develop approximately three hundred years ago. Quadrics play a fundamental role in numerous fields of mathematics and physics, their applications ranging from mechanical engineering, architecture, astronomy, and design to computer graphics. This text will be invaluable to undergraduate and graduate mathematics students, those in adjacent fields of study, and anyone with a deeper interest in geometry. Complemented with about three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises. The Authors Boris Odehnal, born in 1973, got his PhD and habilitation in geometry at the Vienna University of Technology. 2011?2012 professor at the Dresden University of Technology. Since 2012, he has held the position of senior lecturer in geometry at the University of Applied Arts Vienna. He is the author of several dozens of publications on geometry. Hellmuth Stachel, born in 1942, got his PhD and habilitation in geometry in Graz. In 1978, he became full professor at the Mining University Leoben, and from 1980?2011, he was full professor of geometry at the Vienna University of Technology. He has coauthored several books on mathematics and computational geometry and more than 160 articles on geometry. Georg Glaeser, born in 1955, got his PhD and habilitation in geometry at the Vienna University of Technology. Since 1998, he is full professor of geometry at the University of Applied Arts Vienna. He is the author and coauthor of more than twenty books on geometry, mathematics, computational geometry, computer graphics, and photography. 606 $aGeometry 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aGeometry. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aGeometry. 615 24$aApplications of Mathematics. 676 $a516.5 700 $aOdehnal$b Boris$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756118 702 $aStachel$b Hellmuth$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGlaeser$b Georg$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484745603321 996 $aThe Universe of Quadrics$92052279 997 $aUNINA