Geometry (Universitext) - Paperback

EAN (ISBN-13): 9783540434986
ISBN (ISBN-10): 3540434984
Hardcover
Paperback
Publishing year: 2013
Publisher: Springer Berlin Heidelberg

Book in our database since 2007-11-07T11:01:16-05:00 (New York)
Detail page last modified on 2024-03-17T09:58:49-04:00 (New York)
ISBN/EAN: 9783540434986

ISBN - alternate spelling:
3-540-43498-4, 978-3-540-43498-6
Alternate spelling and related search-keywords:
Book author: michel audin, michele audin, feuerbach
Book title: beyond geometry

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Information from Publisher

Author: Michele Audin
Title: Universitext; Geometry
Publisher: Springer; Springer Berlin
361 Pages
Publishing year: 2002-09-19
Berlin; Heidelberg; DE
Language: English
71,49 € (DE)

BC; Hardcover, Softcover / Mathematik/Geometrie; Geometrie; Verstehen; 51XX; 53XX; Area; Euclidean geometry; conics; differential geometry; projective geometry; quadrics; Geometry; EA

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 Pascal’s 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 aplane 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.