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.

Autorentext

Marcel Berger is Ancien Professeur of the University of Paris and emeritus director of research at the Centre National de la Recherche Scientifique (CNRS), from 1979 to 1981 he was president of the French Mathematical Society and from 1985 to 1994 director of the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette.

Klappentext

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.

Inhalt

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.