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AuthorBerger, Marcel. author
TitleProblems in Geometry [electronic resource] / by Marcel Berger, Pierre Pansu, Jean-Pic Berry, Xavier Saint-Raymond
ImprintNew York, NY : Springer New York : Imprint: Springer, 1984
Connect tohttp://dx.doi.org/10.1007/978-1-4757-1836-2
Descript VIII, 268 p. online resource

SUMMARY

The textbook Geometry, published in French by CEDICjFernand Nathan and in English by Springer-Verlag (scheduled for 1985) was very favorably reยญ ceived. Nevertheless, many readers found the text too concise and the exercises at the end of each chapter too difficult, and regretted the absence of any hints for the solution of the exercises. This book is intended to respond, at least in part, to these needs. The length of the textbook (which will be referred to as [B] throughout this book) and the volume of the material covered in it preclude any thought of publishing an expanded version, but we considered that it might prove both profitable and amusing to some of our readers to have detailed solutions to some of the exercises in the textbook. At the same time, we planned this book to be independent, at least to a certain extent, from the textbook; thus, we have provided summaries of each of its twenty chapters, condensing in a few pages and under the same titles the most important notions and results,used in the solution of the problems. The statement of the selected problems follows each summary, and they are numbered in order, with a reference to the corresponding place in [B]. These references are not meant as indications for the solutions of the problems. In the body of each summary there are frequent references to [B], and these can be helpful in elaborating a point which is discussed too cursorily in this book


CONTENT

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


Mathematics Geometry Mathematics Geometry



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