Methods of Geometry
John 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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Appendix A Equivalence relations
Appendix B Least upper bound principle
Appendix C Vector and matrix algebra
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