LEADER 04501nam 2200625 a 450 001 9910141013703321 005 20200520144314.0 010 $a9786613813619 010 $a9781282242494 010 $a1282242490 010 $a9781118032787 010 $a1118032780 010 $a9781118031032 010 $a1118031032 035 $a(CKB)2670000000077536 035 $a(EBL)675148 035 $a(OCoLC)710974981 035 $a(SSID)ssj0000485881 035 $a(PQKBManifestationID)11307184 035 $a(PQKBTitleCode)TC0000485881 035 $a(PQKBWorkID)10430209 035 $a(PQKB)10020888 035 $a(MiAaPQ)EBC675148 035 $a(PPN)250258927 035 $a(Perlego)2764533 035 $a(EXLCZ)992670000000077536 100 $a20110323d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMethods of geometry /$fJames T. Smith 210 $aNew York $cJohn Wiley & Sons$d2000 215 $a1 online resource (506 p.) 300 $a"A Wiley-Interscience publication"--t.p. 311 08$a9780471251835 311 08$a0471251836 320 $aIncludes bibliographical references and index. 327 $aMethods of Geometry; Contents; Preface; About the author; 1 Introduction; 1.1 Episodes; 1.2 Advanced geometry; 1.3 This book; 1.4 Reading about geometry; 1.5 Projects; 2 Foundations; 2.1 Geometry as applied mathematics; 2.2 Need for rigor; 2.3 Axiomatic method; 2.4 Euclid's Elements; 2.5 Coordinate geometry; 2.6 Foundation problem; 2.7 Parallel axiom; 2.8 Firm foundations; 2.9 Geometry as pure mathematics; 2.10 Exercises and projects; 3 Elementary Euclidean geometry; 3.1 Incidence geometry; 3.2 Ruler axiom and its consequences; 3.3 Pasch's axiom and the separation theorems 327 $a3.4 Angles and the protractor axioms3.5 Congruence; 3.6 Perpendicularity; 3.7 Parallel axiom and related theorems; 3.8 Area and Pythagoras' theorem; 3.9 Similarity; 3.10 Polyhedral volume; 3.11 Coordinate geometry; 3.12 Circles and spheres; 3.13 Arcs and trigonometric functions; 3.14 ?; 4 Exercises on elementary geometry; 4.1 Exercises on the incidence and ruler axioms; 4.2 Exercises related to Pasch's axiom; 4.3 Exercises on congruence and perpendicularity; 4.4 Exercises involving the parallel axiom; 4.5 Exercises on similarity and Pythagoras' theorem 327 $a4.6 Exercises on circles and spheres, part 14.7 Exercises on area; 4.8 Exercises on volume; 4.9 Exercises on circles and spheres, part 2; 4.10 Exercises on coordinate geometry; 5 Some triangle and circle geometry; 5.1 Four concurrence theorems; 5.2 Menelaus' theorem; 5.3 Desargues' theorem; 5.4 Ceva's theorem; 5.5 Trigonometry; 5.6 Vector products; 5.7 Centroid; 5.8 Orthocenter; 5.9 Incenter and excenters; 5.10 Euler line and Feuerbach circle; 5.11 Exercises; 6 Plane isometrles and similarities; 6.1 Transformations; 6.2 Isometries; 6.3 Reflections; 6.4 Translations; 6.5 Rotations 327 $a6.6 Structure theorem6.7 Glide reflections; 6.8 Isometries and orthogonal matrices; 6.9 Classifying isometries; 6.10 Similarities; 6.11 Exercises; 7 Three dimensional isometries and similarities; 7.1 Isometries; 7.2 Reflections; 7.3 Translations and rotations; 7.4 Glide and rotary reflections; 7.5 Classifying isometries; 7.6 Similarities; 7.7 Exercises; 8 Symmetry; 8.1 Polygonal symmetry; 8.2 Friezes; 8.3 Wallpaper ornaments; 8.4 Polyhedra; 8.5 Exercises; Appendix A Equivalence relations; Appendix B Least upper bound principle; Appendix C Vector and matrix algebra; Bibliography; Index 330 $aA practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An 606 $aGeometry 615 0$aGeometry. 676 $a516 700 $aSmith$b James T$0146063 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141013703321 996 $aMethods of geometry$92002607 997 $aUNINA