Methods of GeometryJohn Wiley & Sons, 1 Μαρ 2011 - 486 σελίδες 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. |
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Αποτελέσματα 1 - 5 από τα 71.
Σελίδα vii
... ' theorem 81 Similarity 89 Polyhedral volume 92 Coordinate geometry 100 Circles and spheres 106 Arcs and trigonometric functions 110 it 119 4 Exercises on elementary geometry 4.1 4.2 4.3 4.4 4.5. vii Methods of Geometry: Contents.
... ' theorem 81 Similarity 89 Polyhedral volume 92 Coordinate geometry 100 Circles and spheres 106 Arcs and trigonometric functions 110 it 119 4 Exercises on elementary geometry 4.1 4.2 4.3 4.4 4.5. vii Methods of Geometry: Contents.
Σελίδα ix
... Polyhedra 381 8.5 Exercises 407 Appendix A Equivalence relations Appendix B Least upper bound principle Appendix C Vector and matrix algebra Bibliography Index 295 327 423 425 429 443 463 This page intentionally left blank Preface This ...
... Polyhedra 381 8.5 Exercises 407 Appendix A Equivalence relations Appendix B Least upper bound principle Appendix C Vector and matrix algebra Bibliography Index 295 327 423 425 429 443 463 This page intentionally left blank Preface This ...
Σελίδα 9
... polyhedra Linear incidence geometry and ordered geometries; finite geometry Metric geometry and transformational geometry Geometric constructions Extremum problems Hyperbolic and elliptic non-Euclidean geometries Projective geometry and ...
... polyhedra Linear incidence geometry and ordered geometries; finite geometry Metric geometry and transformational geometry Geometric constructions Extremum problems Hyperbolic and elliptic non-Euclidean geometries Projective geometry and ...
Σελίδα 10
... polyhedra 52C. Discrete geometry Subclass 52A doesn't overlap this book much, although convex sets play major roles in chapters 3 and 8. In section 8.4, though, you'll study in detail many polyhedra—certain surfaces bounded by finitely ...
... polyhedra 52C. Discrete geometry Subclass 52A doesn't overlap this book much, although convex sets play major roles in chapters 3 and 8. In section 8.4, though, you'll study in detail many polyhedra—certain surfaces bounded by finitely ...
Σελίδα 14
... polyhedra and their symmetries. Appendices Analytic geometry is best pursued using vector and matrix algebra and the theory of systems of linear equations. For three and higher dimensions, they're virtually indispensable. Most students ...
... polyhedra and their symmetries. Appendices Analytic geometry is best pursued using vector and matrix algebra and the theory of systems of linear equations. For three and higher dimensions, they're virtually indispensable. Most students ...
Περιεχόμενα
1 | |
19 | |
3 Elementary Euclidean geometry | 53 |
4 Exercises on elementary geometry | 127 |
5 Some triangle and circle geometry | 157 |
6 Plane isometrles and similarities | 227 |
7 Three dimensional isometries and similarities | 295 |
8 Symmetry | 327 |
Appendix A Equivalence relations | 423 |
Appendix B Least upper bound principle | 425 |
Appendix C Vector and matrix algebra | 429 |
Bibliography | 443 |
Index | 463 |
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC algebra altitude analogous angle parameter apply AX YZ axiomatic axis bijection bisector called chapter circle classification collinear composition compute concepts congruent conjugacy conjugate Consider construct contains convex coordinate system Corollary corresponding define definition deltahedra Desargues dihedral dihedral angles distance edges equations Euclid Euclidean geometry example Exercise exterior angle theorem faces figure find finite first fixed fixpoint Flgure formula frieze group function glide reflection half turn hence Hilbert incidence axioms interior intersection isometry group isomorphic lemma line g linear mathematicians mathematics matrix methods midpoint noncollinear orthogonal orthogonal matrix parallel axiom parallelogram perpendicular plane isometries points polygonal region polyhedra polyhedron prism Proof prove radius ratio real number regular result rotation segment shown in figure similarity Suppose symmetry group tangent tetrahedron theorem theory there’s three-dimensional transformation transformational geometry triangle triangular undefined upper bound vector vertex vertices wallpaper groups