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 91.
Σελίδα 6
... prove that? Another way to phrase the same question is to consider the following alternatives to steps 5 to 8: 5.' draw gl/h through U, 6.' locate T' =g n P'Y. Condition TU // h is equivalent to equation T= T', which says that the two ...
... prove that? Another way to phrase the same question is to consider the following alternatives to steps 5 to 8: 5.' draw gl/h through U, 6.' locate T' =g n P'Y. Condition TU // h is equivalent to equation T= T', which says that the two ...
Σελίδα 7
... prove that TII/l h in figure 1.1.7. You may find the proof roundabout and unnecessarily complicated. There's ... proved by Gérard Desargues two centuries before, played a central role in this study. Several forms of his result are ...
... prove that TII/l h in figure 1.1.7. You may find the proof roundabout and unnecessarily complicated. There's ... proved by Gérard Desargues two centuries before, played a central role in this study. Several forms of his result are ...
Σελίδα 8
... Proving Tl] // h It's stated with difi'erent notation, so you need to work out the correspondence between points in ... proved? Desargues' theorem has entered this argument three times. Its various. 9 This proof should really verify that ...
... Proving Tl] // h It's stated with difi'erent notation, so you need to work out the correspondence between points in ... proved? Desargues' theorem has entered this argument three times. Its various. 9 This proof should really verify that ...
Σελίδα 12
... prove. Recently, researchers have intensely studied compound soap bubbles. For example, how do four of these with a given total volume abut each other about a common point so that their total area is minimized? 51M10 contains non ...
... prove. Recently, researchers have intensely studied compound soap bubbles. For example, how do four of these with a given total volume abut each other about a common point so that their total area is minimized? 51M10 contains non ...
Σελίδα 25
... prove the triangle congruences without referring to any diagram—your argument would be hard to understand but nevertheless correct. However, before proceeding with the step It follows that CA = CY+ YA = BZ + ZA = AB, you'd need to check ...
... prove the triangle congruences without referring to any diagram—your argument would be hard to understand but nevertheless correct. However, before proceeding with the step It follows that CA = CY+ YA = BZ + ZA = AB, you'd need to check ...
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