Overview

Written as a supplement to Marcel Berger’s popular two-volume set, Geometry I and II (Universitext), this book offers a comprehensive range of exercises, problems, and full solutions. Each chapter corresponds directly to one in the relevant volume, from which it also provides a summary of key ideas. Where the original Geometry volumes tend toward challenging problems without hints, this book offers a wide range of material that begins at an accessible level, and includes suggestions for nearly every problem. Bountiful in illustrations and complete in its coverage of topics from affine and projective spaces, to spheres and conics, Problems in Geometry is a valuable addition to studies in geometry at many levels.

Full Product Details

Author:   Marcel Berger ,  Silvio Levy ,  P. Pansu ,  J.-P. Berry
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 1st ed. 1984
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.860kg
ISBN:  

9781441928221

ISBN 10:   1441928227
Pages:   268
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Groups Operating on a Set: Nomenclature, Examples, Applications.- 2. Affine Spaces.- 3. Barycenters; the Universal Space.- 4. Projective Spaces.- 5. Affine-Projective Relationship: Applications.- 6. Projective Lines, Cross-Ratios, Homographies.- 7. Complexifications.- 8. More about Euclidean Vector Spaces.- 9. Euclidean Affine Spaces.- 10. Triangles, Spheres, and Circles.- 11. Convex Sets.- 12. Polytopes; Compact Convex Sets.- 13. Quadratic Forms.- 14. Projective Quadrics.- 15. Affine Quadrics.- 16. Projective Conics.- 17. Euclidean Conics.- 18. The Sphere for Its Own Sake.- 19. Elliptic and Hyperbolic Geometry.- 20. The Space of Spheres.- Suggestions and Hints.- Solutions.- 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10.- 11.- 12.- 13.- 14.- 15.- 16.- 17.- 18.- 19.- 20.

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