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 88.
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... concepts related to equivalence relations, described briefly in appendix A. Concepts related to transformations, their compositions and inverses, and transformation groups are developed in detail in section 6.1, but this book applies ...
... concepts related to equivalence relations, described briefly in appendix A. Concepts related to transformations, their compositions and inverses, and transformation groups are developed in detail in section 6.1, but this book applies ...
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James T. Smith. 1.3 This book Concepts Overview Two- and three-dimensional geometry Vector and matrix algebra for analytic geometry Equivalence relations and least upper bounds Familiar concepts and notation Numbering results, exercises ...
James T. Smith. 1.3 This book Concepts Overview Two- and three-dimensional geometry Vector and matrix algebra for analytic geometry Equivalence relations and least upper bounds Familiar concepts and notation Numbering results, exercises ...
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... concepts to study 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 ...
... concepts to study 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 ...
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... Concepts Survey literature You may want to spend some time reading about geometry in general— diverse parts of the outline in section 1.2—while you work through the foundations and elementary topics in chapters 2 and 3. That would be ...
... Concepts Survey literature You may want to spend some time reading about geometry in general— diverse parts of the outline in section 1.2—while you work through the foundations and elementary topics in chapters 2 and 3. That would be ...
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... Concepts Elementary geometry in school and university Conics and quadrics Geometric knowledge and physical experience Hyperbolic and elliptic area theory Perspective drawing Orthogonal projection Art Deco When pursuing geometry—or any ...
... Concepts Elementary geometry in school and university Conics and quadrics Geometric knowledge and physical experience Hyperbolic and elliptic area theory Perspective drawing Orthogonal projection Art Deco When pursuing geometry—or any ...
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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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