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. |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 48.
Σελίδα vii
... Euclid's Elements 29 Coordinate geometry 33 Foundation problem 35 Parallel axiom 37 Firm foundations 39 Geometry as pure mathematics 42 Exercises and projects 50 53 Incidence geometry 55 Ruler axiom and its consequences 57 Pasch's axiom ...
... Euclid's Elements 29 Coordinate geometry 33 Foundation problem 35 Parallel axiom 37 Firm foundations 39 Geometry as pure mathematics 42 Exercises and projects 50 53 Incidence geometry 55 Ruler axiom and its consequences 57 Pasch's axiom ...
Σελίδα 12
... Euclid's axiom, given a line g and a point P not on g, there's exactly one parallel to g through P. It can be shown that if Euclid's axiom failed but all the others held, then either there would always be more than one parallel to g ...
... Euclid's axiom, given a line g and a point P not on g, there's exactly one parallel to g through P. It can be shown that if Euclid's axiom failed but all the others held, then either there would always be more than one parallel to g ...
Σελίδα 21
... theorems contradicted Euclid's—even only slightly—would have been regarded as incorrect, hence useless. After nineteenth-century mathematicians began to consider nonEuclidean models, philosophers 2.1 GEOMETRY AS APPLIED MATHEMATICS 21.
... theorems contradicted Euclid's—even only slightly—would have been regarded as incorrect, hence useless. After nineteenth-century mathematicians began to consider nonEuclidean models, philosophers 2.1 GEOMETRY AS APPLIED MATHEMATICS 21.
Σελίδα 27
... Euclid, are particularly important for mathematics. A statement involving the concepts of the model is regarded as a theorem only after it has been rigorously proved from the axioms. This framework for organizing science was first ...
... Euclid, are particularly important for mathematics. A statement involving the concepts of the model is regarded as a theorem only after it has been rigorously proved from the axioms. This framework for organizing science was first ...
Σελίδα 28
... Euclid's are criticized in section 2.4. Jefferson gave no definitions. Until the nineteenth century an axiomatic model was not ordinarily applied to any subject area beyond that for which it was originally devised. To facilitate this ...
... Euclid's are criticized in section 2.4. Jefferson gave no definitions. Until the nineteenth century an axiomatic model was not ordinarily applied to any subject area beyond that for which it was originally devised. To facilitate this ...
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 |
Άλλες εκδόσεις - Προβολή όλων
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