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 87.
Σελίδα 5
... Consider the image of a line g in the scene. It's formed by the intersections with e of all lines through 0 and points on g. Should O happen to fall on g, the image would be a single point on 8. Otherwise, it would be the intersection g ...
... Consider the image of a line g in the scene. It's formed by the intersections with e of all lines through 0 and points on g. Should O happen to fall on g, the image would be a single point on 8. Otherwise, it would be the intersection g ...
Σελίδα 6
... consider lines g on or parallel to y. For all those, g'// y; these g' all lie in the plane 6 // a through 0. Their vanishing points lie in the intersection h = 6 n e, a line in a parallel to y at the same distance from the ground as 0 ...
... consider lines g on or parallel to y. For all those, g'// y; these g' all lie in the plane 6 // a through 0. Their vanishing points lie in the intersection h = 6 n e, a line in a parallel to y at the same distance from the ground as 0 ...
Σελίδα 7
... Consider points A=A , B=B , and C= C on distinct lines I, m, and n, where l//n, asinfigure 1.1.8. Suppose AB intersects. A. B. at. N,. Bt'intersects. B. C. at. L,. and. CS4. intersects. CA at M. Then l/lm ifandonlyif L, M, and N fallona ...
... Consider points A=A , B=B , and C= C on distinct lines I, m, and n, where l//n, asinfigure 1.1.8. Suppose AB intersects. A. B. at. N,. Bt'intersects. B. C. at. L,. and. CS4. intersects. CA at M. Then l/lm ifandonlyif L, M, and N fallona ...
Σελίδα 9
... consider perspective questions. In exercise 5.11.13 you're invited to apply another form of the theorem to draw an analogous picture with an image plane that's vertical, but neither parallel nor perpendicular to any tile edge. The most ...
... consider perspective questions. In exercise 5.11.13 you're invited to apply another form of the theorem to draw an analogous picture with an image plane that's vertical, but neither parallel nor perpendicular to any tile edge. The most ...
Σελίδα 21
... 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.
... 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.
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