Methods of GeometryA 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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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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Häufige Begriffe und Wortgruppen
AABC algebra angle apply argument axes axioms axis base bisector called chapter circle classes classify composition compute Concepts congruent conjugate Consider consists construct contains Corollary corresponding defined definition derive Desargues describe detail determine developed distance distinct edges equations example Exercise faces figure fixed fixpoint formula four frieze function fundamental geometry given glide reflection half turn hence identity included interior intersect isometry isomorphic it's later lattice lemma length lies line g linear mathematics matrix measure methods opposite origin orthogonal matrix paragraph parallel parameter pattern perpendicular plane points polygonal polyhedra possible present problem Proof properties prove ratio region regular result rotation segment side similarity Suggestion Suppose symmetry group theorem theory three-dimensional transformation translation triangle unique vector vertices wallpaper groups
Bibliografische Informationen
| Titel | Methods of Geometry A Wiley-Interscience publication |
| Autor/in | James T. Smith |
| Ausgabe | illustriert, kommentiert |
| Verlag | John Wiley & Sons, 2000 |
| ISBN | 0471251836, 9780471251835 |
| Länge | 486 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |