Geometry: Ancient and ModernOxford University Press, 2001 - 313 páginas This is a guided tour of geometry, from Euclid through to algebraic geometry for students with little or no geometry studies. It shows how mathematicians use a variety of techniques to tackle problems, and links geometry to other branches of mathematics. It is a teaching text, with large numbers of exercises woven into the exposition. Topics covered include: ruler and compass constructions, transformations, triangle and circle theorems, classification of isometries and groups of isometries in dimensions 2 and 3, Platonic solids, conics, similarities, affine, projective and Mobius transformations, non-Euclidean geometry, projective geometry, and the beginnings of algebraic geometry. |
Contenido
Drawings and constructions | 12 |
Answers to exercises | 23 |
8 | 46 |
Triangles and triangle formulae | 52 |
Isometries of R2 | 82 |
Isometries of R | 116 |
533 | 147 |
Answers to exercises | 153 |
Infinity | 222 |
Complex geometry | 267 |
Answers to exercises | 297 |
| 301 | |
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AABC affine transformation angle axes axis called centre choose circle collinear common complex conic construct contains coordinates Corollary corresponding cubic curve cyclic deduce define Definition determine direct distance distinct easy edges elements ellipse equal equation example Exercise faces fact finite fixed points follows four geometry given gives going half-turn homogeneous hyperbola infinity invariant inverse isometry isomorphic joining Lemma length lies linear matrix means meet mid-point Möbius transformation Note obtain opposite orthogonal pair parallel permutation perpendicular plane polynomial projective Proof Proposition Prove reader reflection regular represented respectively result rotation sides similarity similarly subgroup suppose symmetry tangent theorem touches translation triangle vertices whence write zero