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 11
... define all relevant properties of these correspondences in terms of distance, their theory falls entirely in subclass 51F, metric geometry. These correspondences are special kinds of mathematical transformations, so this theory is also ...
... define all relevant properties of these correspondences in terms of distance, their theory falls entirely in subclass 51F, metric geometry. These correspondences are special kinds of mathematical transformations, so this theory is also ...
Σελίδα 26
... definition of the concepts used in a model and its theory, and the rigorous proof of theorems about the model ... define all the others from those. Similarly, among the theorems about the model are some that are specific to it ...
... definition of the concepts used in a model and its theory, and the rigorous proof of theorems about the model ... define all the others from those. Similarly, among the theorems about the model are some that are specific to it ...
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 30
... defines a right angle: If Q is on the segment PS, R is not on line PQ, and mi PQR = mARQS, then these two angles are right. No numerical angle measure is involved. Axiom 4 then says, if mZPQR = mARQS and mAP'Q'R' = mAR'Q'S' as infigure ...
... defines a right angle: If Q is on the segment PS, R is not on line PQ, and mi PQR = mARQS, then these two angles are right. No numerical angle measure is involved. Axiom 4 then says, if mZPQR = mARQS and mAP'Q'R' = mAR'Q'S' as infigure ...
Σελίδα 35
... Defining the real number system Rephrasing and augmenting Euclid's axioms As mentioned in section 2.4, Euclid didn't use numbers per se as lengths of line segments. He calculated with segments directly using integer arithmetic, and ...
... Defining the real number system Rephrasing and augmenting Euclid's axioms As mentioned in section 2.4, Euclid didn't use numbers per se as lengths of line segments. He calculated with segments directly using integer arithmetic, and ...
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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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