Methods of GeometryJohn Wiley & Sons, 10.01.2000 - 486 Seiten A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: * Ample exercises designed to promote effective problem-solvingstrategies * Insight into novel uses of Euclidean geometry * More than 300 figures accompanying definitions and proofs * A comprehensive and annotated bibliography * Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department. |
Im Buch
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Seite viii
... Desargues ' theorem 165 5.4 Ceva's theorem 171 5.5 Trigonometry 177 5.6 Vector products 186 5.7 Centroid 193 5.8 Orthocenter 196 5.9 Incenter and excenters 199 5.10 Euler line and Feuerbach circle 204 5.11 Exercises 211 6 Plane ...
... Desargues ' theorem 165 5.4 Ceva's theorem 171 5.5 Trigonometry 177 5.6 Vector products 186 5.7 Centroid 193 5.8 Orthocenter 196 5.9 Incenter and excenters 199 5.10 Euler line and Feuerbach circle 204 5.11 Exercises 211 6 Plane ...
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Inhalt
Introduction | 1 |
Foundations | 19 |
Elementary Euclidean geometry | 55 |
Exercises on elementary geometry | 128 |
Some triangle and circle geometry | 158 |
Plane isometries and similarities | 232 |
Three dimensional isometries and similarities | 295 |
Symmetry | 327 |
XV | 372 |
39 | 390 |
Appendix A Equivalence relations | 423 |
Vector and matrix algebra | 429 |
Bibliography | 443 |
463 | |
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4-center AABC algebra altitude analogous analyze angle parameter axes axioms axis bijection bisector called Ceva's theorem chapter circle classes classify collinear composition compute Concepts congruent conjugacy conjugacy class conjugate Consider construct coordinate system Corollary corresponding defined deltahedra Desargues determine dihedral edges equations Euclidean geometry Euler example Exercise faces finite fixpoint formula frieze group function fundamental translation geometry glide reflection group of figure half turn hence identity integer interior intersect inverse isometry group isomorphic lattice points lemma line g linear mathematics matrix midpoint noncollinear orthocenter orthogonal orthogonal matrix parallel parallel axiom parallelogram perpendicular plane isometries polygonal regions polyhedra polyhedron previous paragraph Proof prove ratio real number regular result rotation segment similarity Suppose symmetry group tangent tetrahedron theory there's three-dimensional transformation transformational geometry triangle upper bound V₁ vector vertex vertices wallpaper groups wallpaper pattern x₁