LEADER 05571nam 22005175 450 001 9910480073903321 005 20200704013633.0 010 $a1-4612-0929-3 024 7 $a10.1007/978-1-4612-0929-4 035 $a(CKB)3400000000089326 035 $a(SSID)ssj0000806453 035 $a(PQKBManifestationID)11458459 035 $a(PQKBTitleCode)TC0000806453 035 $a(PQKBWorkID)10750463 035 $a(PQKB)10821816 035 $a(DE-He213)978-1-4612-0929-4 035 $a(MiAaPQ)EBC3073433 035 $a(PPN)237993716 035 $a(EXLCZ)993400000000089326 100 $a20121227d1992 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGeometry of Surfaces$b[electronic resource] /$fby John Stillwell 205 $a1st ed. 1992. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1992. 215 $a1 online resource (XI, 236 p.) 225 1 $aUniversitext,$x0172-5939 300 $a"With 165 Figures." 311 $a0-387-97743-0 320 $aIncludes bibliographical references and index. 327 $a1. The Euclidean Plane -- 1.1 Approaches to Euclidean Geometry -- 1.2 Isometries -- 1.3 Rotations and Reflections -- 1.4 The Three Reflections Theorem -- 1.5 Orientation-Reversing Isometries -- 1.6 Distinctive Features of Euclidean Geometry -- 1.7 Discussion -- 2. Euclidean Surfaces -- 2.1 Euclid on Manifolds -- 2.2 The Cylinder -- 2.3 The Twisted Cylinder -- 2.4 The Torus and the Klein Bottle -- 2.5 Quotient Surfaces -- 2.6 A Nondiscontinuous Group -- 2.7 Euclidean Surfaces -- 2.8 Covering a Surface by the Plane -- 2.9 The Covering Isometry Group -- 2.10 Discussion -- 3. The Sphere -- 3.1 The Sphere S2 in ?3 -- 3.2 Rotations -- 3.3 Stereographic Projection -- 3.4 Inversion and the Complex Coordinate on the Sphere -- 3.5 Reflections and Rotations as Complex Functions -- 3.6 The Antipodal Map and the Elliptic Plane -- 3.7 Remarks on Groups, Spheres and Projective Spaces -- 3.8 The Area of a Triangle -- 3.9 The Regular Polyhedra -- 3.10 Discussion -- 4. The Hyperbolic Plane -- 4.1 Negative Curvature and the Half-Plane -- 4.2 The Half-Plane Model and the Conformai Disc Model -- 4.3 The Three Reflections Theorem -- 4.4 Isometries as Complex Functions -- 4.5 Geometric Description of Isometries -- 4.6 Classification of Isometries -- 4.7 The Area of a Triangle -- 4.8 The Projective Disc Model -- 4.9 Hyperbolic Space -- 4.10 Discussion -- 5. Hyperbolic Surfaces -- 5.1 Hyperbolic Surfaces and the Killing-Hopf Theorem -- 5.2 The Pseudosphere -- 5.3 The Punctured Sphere -- 5.4 Dense Lines on the Punctured Sphere -- 5.5 General Construction of Hyperbolic Surfaces from Polygons -- 5.6 Geometric Realization of Compact Surfaces -- 5.7 Completeness of Compact Geometric Surfaces -- 5.8 Compact Hyperbolic Surfaces -- 5.9 Discussion -- 6. Paths and Geodesies -- 6.1 Topological Classification of Surfaces -- 6.2 Geometric Classification of Surfaces -- 6.3 Paths and Homotopy -- 6.4 Lifting Paths and Lifting Homotopies -- 6.5 The Fundamental Group -- 6.6 Generators and Relations for the Fundamental Group -- 6.7 Fundamental Group and Genus -- 6.8 Closed Geodesic Paths -- 6.9 Classification of Closed Geodesic Paths -- 6.10 Discussion -- 7. Planar and Spherical Tessellations -- 7.1 Symmetric Tessellations -- 7.2 Conditions for a Polygon to Be a Fundamental Region -- 7.3 The Triangle Tessellations -- 7.4 Poincaré?s Theorem for Compact Polygons -- 7.5 Discussion -- 8. Tessellations of Compact Surfaces -- 8.1 Orbifolds and Desingularizations -- 8.2 Prom Desingularization to Symmetric Tessellation -- 8.3 Desingularizations as (Branched) Coverings -- 8.4 Some Methods of Desingularization -- 8.5 Reduction to a Permutation Problem -- 8.6 Solution of the Permutation Problem -- 8.7 Discussion -- References. 330 $aGeometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un­ til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba­ sic group theory (subgroups and cosets), and basic topology (open, closed, and compact sets). 410 0$aUniversitext,$x0172-5939 606 $aGeometry 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 615 0$aGeometry. 615 14$aGeometry. 676 $a516.3/62 700 $aStillwell$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut$041902 906 $aBOOK 912 $a9910480073903321 996 $aGeometry of surfaces$9382818 997 $aUNINA LEADER 02454nam 2200601Ia 450 001 9910450759903321 005 20200520144314.0 010 $a1-280-90837-8 010 $a9786610908370 010 $a0-85199-053-3 035 $a(CKB)1000000000344449 035 $a(EBL)301663 035 $a(OCoLC)476080819 035 $a(SSID)ssj0000148374 035 $a(PQKBManifestationID)11158490 035 $a(PQKBTitleCode)TC0000148374 035 $a(PQKBWorkID)10017261 035 $a(PQKB)11285038 035 $a(MiAaPQ)EBC301663 035 $a(MiAaPQ)EBC4949500 035 $a(Au-PeEL)EBL301663 035 $a(CaPaEBR)ebr10073612 035 $a(Au-PeEL)EBL4949500 035 $a(CaONFJC)MIL90837 035 $a(EXLCZ)991000000000344449 100 $a20040618d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEnvironmental impacts of sugar production$b[electronic resource] $ethe cultivation and processing of sugarcane and sugar beet /$fby Oliver D. Cheesman 210 $aCambridge, Mass. $cCABI International$d2004 215 $a1 online resource (269 p.) 300 $aDescription based upon print version of record. 311 $a0-85199-981-6 320 $aIncludes bibliographical references and index. 327 $aPreface; Foreword; 1 Background; 2 Overview; 3 Water Consumption; 4 Impacts on Water Quality and Aquatic Ecosystems; 5 Impacts on Terrestrial Biodiversity; 6 Impacts on Soils; 7 Atmospheric Impacts; 8 Use and Impacts of By-products; References; Appendices; Index 330 $aPressure from conservationists and increasing regulation, means that environmental considerations are increasingly important for the sugar industry. This book examines the environmental impacts of the sugar industry in relation to the cultivation of sugar crops (cane and beet) and the processing of the raw materials that they yield. 606 $aSugar crops$xEnvironmental aspects 606 $aAgriculture$xEnvironmental aspects 608 $aElectronic books. 615 0$aSugar crops$xEnvironmental aspects. 615 0$aAgriculture$xEnvironmental aspects. 676 $a633.6 700 $aCheesman$b Oliver$01030894 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910450759903321 996 $aEnvironmental impacts of sugar production$92448042 997 $aUNINA