Ebook: Problems in Geometry
- Tags: Geometry
- Series: Problem Books in Mathematics
- Year: 1984
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
The textbook Geometry, published in French by CEDICjFernand Nathan and in English by Springer-Verlag (scheduled for 1985) was very favorably re 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:
Front Matter....Pages i-viii
Groups Operating on a Set: Nomenclature, Examples, Applications....Pages 1-10
Affine Spaces....Pages 11-17
Barycenters; the Universal Space....Pages 18-22
Projective Spaces....Pages 23-29
Affine-projective Relationship: Applications....Pages 30-34
Projective Lines, Cross-Ratios, Homographies....Pages 35-39
Complexifications....Pages 40-42
More about Euclidean Vector Spaces....Pages 43-50
Euclidean Affine Spaces....Pages 51-57
Triangles, Spheres, and Circles....Pages 58-65
Convex Sets....Pages 66-68
Polytopes; Compact Convex Sets....Pages 69-73
Quadratic Forms....Pages 74-78
Projective Quadrics....Pages 79-84
Affine Quadrics....Pages 85-92
Projective Conics....Pages 93-101
Euclidean Conics....Pages 102-105
The Sphere for Its Own Sake....Pages 106-113
Elliptic and Hyperbolic Geometry....Pages 114-119
The Space of Spheres....Pages 120-123
Back Matter....Pages 124-267
Content:
Front Matter....Pages i-viii
Groups Operating on a Set: Nomenclature, Examples, Applications....Pages 1-10
Affine Spaces....Pages 11-17
Barycenters; the Universal Space....Pages 18-22
Projective Spaces....Pages 23-29
Affine-projective Relationship: Applications....Pages 30-34
Projective Lines, Cross-Ratios, Homographies....Pages 35-39
Complexifications....Pages 40-42
More about Euclidean Vector Spaces....Pages 43-50
Euclidean Affine Spaces....Pages 51-57
Triangles, Spheres, and Circles....Pages 58-65
Convex Sets....Pages 66-68
Polytopes; Compact Convex Sets....Pages 69-73
Quadratic Forms....Pages 74-78
Projective Quadrics....Pages 79-84
Affine Quadrics....Pages 85-92
Projective Conics....Pages 93-101
Euclidean Conics....Pages 102-105
The Sphere for Its Own Sake....Pages 106-113
Elliptic and Hyperbolic Geometry....Pages 114-119
The Space of Spheres....Pages 120-123
Back Matter....Pages 124-267
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