Author | Audin, Michรจle. author |
---|---|
Title | Geometry [electronic resource] / by Michรจle Audin |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-642-56127-6 |
Descript | VI, 361 p. online resource |
1. This is a book -- 2. How to use this book -- 3. About the English edition -- 4. Acknowledgements -- I. Affine Geometry -- 1. Affine spaces -- 2. Affine mappings -- 3. Using affine mappings: three theorems in plane geometry -- 4. Appendix: a few words on barycenters -- 5. Appendix: the notion of convexity -- 6. Appendix: Cartesian coordinates in affine geometry -- Exercises and problems -- II. Euclidean Geometry, Generalities -- 1. Euclidean vector spaces, Euclidean affine spaces -- 2. The structure of isometries -- 3. The group of linear isometries -- Exercises and problems -- III. Euclidean Geometry in the Plane -- 1. Angles -- 2. Isometries and rigid motions in the plane -- 3. Plane similarities -- 4. Inversions and pencils of circles -- Exercises and problems -- IV. Euclidean Geometry in Space -- 1. Isometries and rigid motions in space -- 2. The vector product, with area computations -- 3. Spheres, spherical triangles -- 4. Polyhedra, Euler formula -- 5. Regular polyhedra -- Exercises and problems -- V. Projective Geometry -- 1. Projective spaces -- 2. Projective subspaces -- 3. Affine vs projective -- 4. Projective duality -- 5. Projective transformations -- 6. The cross-ratio -- 7. The complex proje ctive line and the circular group -- Exercises and problems -- VI. Conics and Quadrics -- 1. Affine quadrics and conics, generalities -- 2. Classification and properties of affine conics -- 3. Projective quadrics and conics -- 4. The cross-ratio of four points on a conic and Pascalโs theorem -- 5. Affine quadrics, via projective geometry -- 6. Euclidean conics, via projective geometry -- 7. Circles, inversions, pencils of circles -- 8. Appendix: a summary of quadratic forms -- Exercises and problems -- VII. Curves, Envelopes, Evolutes -- 1. The envelope of a family of lines in the plane -- 2. The curvature of a plane curve -- 3. Evolutes -- 4. Appendix: a few words on parametrized curves -- Exercises and problems -- VIII. Surfaces in 3-dimensional Space -- 1. Examples of surfaces in 3-dimensional space -- 2. Differential geometry of surfaces in space -- 3. Metric properties of surfaces in the Euclidean space -- 4. Appendix: a few formulas -- Exercises and problems -- VI -- VII -- VIII -- A few Hints and Solutions to Exercises -- I -- II -- III -- IV -- V