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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Σελίδα viii
... Rotations 254 Structure theorem 258 Glide reflections 261 Isometries and orthogonal matrices 262 Classifying isometries 267 Similarities 276 Exercises 281 7 Three dimensional isometries and similarities 7.1 Isometries 296 7.2 as CONTENTS.
... Rotations 254 Structure theorem 258 Glide reflections 261 Isometries and orthogonal matrices 262 Classifying isometries 267 Similarities 276 Exercises 281 7 Three dimensional isometries and similarities 7.1 Isometries 296 7.2 as CONTENTS.
Σελίδα ix
... rotations 306' 7.4 Glide and rotary reflections 309 7.5 Classifying isometries 312 7.6 Similarities 315 7.7 Exercises 317 8 Symmetry 8.1 Polygonal symmetry 336 8.2 Friezes 344 8.3 Wallpaper ornaments 355 8.4 Polyhedra 381 8.5 Exercises ...
... rotations 306' 7.4 Glide and rotary reflections 309 7.5 Classifying isometries 312 7.6 Similarities 315 7.7 Exercises 317 8 Symmetry 8.1 Polygonal symmetry 336 8.2 Friezes 344 8.3 Wallpaper ornaments 355 8.4 Polyhedra 381 8.5 Exercises ...
Σελίδα 2
... rotate the bowl 180° about its axis, it appears the same. This bowl is about five inches deep and ten in diameter. The artist had to distort the images on its curved inner surface so they would look right when viewed from above! Figures ...
... rotate the bowl 180° about its axis, it appears the same. This bowl is about five inches deep and ten in diameter. The artist had to distort the images on its curved inner surface so they would look right when viewed from above! Figures ...
Σελίδα 13
... Rotating a milk carton 180° about its vertical axis doesn't change it: The carton displays twofold rotational symmetry. Chapter 8 is a thorough introduction to symmetry theory and some of its applications, particularly in art and design ...
... Rotating a milk carton 180° about its vertical axis doesn't change it: The carton displays twofold rotational symmetry. Chapter 8 is a thorough introduction to symmetry theory and some of its applications, particularly in art and design ...
Σελίδα 111
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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