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 82.
Σελίδα 26
... definition of the concepts used in a model and its theory, and the rigorous proof of theorems about the model. Complicated concepts should be defined, and difficult theorems proved, from simpler ones. Imagine a careful exposition of a ...
... definition of the concepts used in a model and its theory, and the rigorous proof of theorems about the model. Complicated concepts should be defined, and difficult theorems proved, from simpler ones. Imagine a careful exposition of a ...
Σελίδα 28
... definitions, and proofs is useful in reporting the results, and can serve later as an effective framework for ... definitions. Euclid's are criticized in section 2.4. Jefferson gave no definitions. Until the nineteenth century an ...
... definitions, and proofs is useful in reporting the results, and can serve later as an effective framework for ... definitions. Euclid's are criticized in section 2.4. Jefferson gave no definitions. Until the nineteenth century an ...
Σελίδα 29
... define all geometric concepts used. Some of these "definitions” are vague, and it's not clear what's being defined in terms of what: for example, Euclid uses the term line for what we call line. 1. A point is that which has no part. 2. A ...
... define all geometric concepts used. Some of these "definitions” are vague, and it's not clear what's being defined in terms of what: for example, Euclid uses the term line for what we call line. 1. A point is that which has no part. 2. A ...
Σελίδα 32
... definitions so muddled, and why did he seem unaware that his axioms were so inadequate? There's a spectrum of interpretations. Many scholars now agree that the aspects of space constituting Euclid's subject matter included not all ...
... definitions so muddled, and why did he seem unaware that his axioms were so inadequate? There's a spectrum of interpretations. Many scholars now agree that the aspects of space constituting Euclid's subject matter included not all ...
Σελίδα 33
... definitions of the terms mentioned, but as clarifications. Russo suggests that Euclid, like today's mathematicians, left the initial concepts undefined, and Hellenistic scientists understood why. But by A.D. 400, when Greek science had ...
... definitions of the terms mentioned, but as clarifications. Russo suggests that Euclid, like today's mathematicians, left the initial concepts undefined, and Hellenistic scientists understood why. But by A.D. 400, when Greek science had ...
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