Geometry

1. Front Matter

   Pages i-vi

   PDF

2. Introduction

   • Michèle Audin

   Pages 1-5

3. Affine Geometry

   • Michèle Audin

   Pages 7-42

4. Euclidean Geometry, Generalities

   • Michèle Audin

   Pages 43-63

5. Euclidean Geometry in the Plane

   • Michèle Audin

   Pages 65-111

6. Euclidean Geometry in Space

   • Michèle Audin

   Pages 113-142

7. Projective Geometry

   • Michèle Audin

   Pages 143-182

8. Conics and Quadrics

   • Michèle Audin

   Pages 183-245

9. Curves, Envelopes, Evolutes

   • Michèle Audin

   Pages 247-267

10. Surfaces in 3-dimensional Space

    • Michèle Audin

    Pages 269-300

11. Back Matter

    Pages 301-360

    PDF

Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michèle Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces.
It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding.

• 51XX
• 53XX
• Area
• Euclidean geometry
• conics
• differential geometry
• projective geometry
• quadrics

From the reviews:

"With this book on geometry - an English translation of the French original published in 1998 - the author has without a doubt created a work which will crucially influence many generations of geometers to come. Audin knows how to combine clarity with modern methods of geometric thought, and one cannot help but notice the love for geometry on each and every page. ... As might be expected the author cites many French textbooks in the well thought our bibliography, yet does not shy from including som "humorous" works as well. Congratulations!"

H. Sachs in "Mathematical Reviews", 2003

"The book is to be welcomed. There are plenty of exercises and fort pages devoted to hints and solutions, and it is indeed advisable that the student works carefully through them in order to cement understanding. … Final year undergraduates or postgraduates will find this a valuable summary of geometry from an algebraic perspective." (Gerry Leversha, The Mathematical Gazette, March, 2005)

"This book, which has been published originally in French in 1998, gives a sound introduction into affine, Euclidean and projective geometry. … The book can be recommended unreservedly for upper undergraduates." (G. Kowol, Monatshefte für Mathematik, Vol. 143 (4), 2004)

"Everything is presented clearly and rigorously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master’s level to discover geometry and deepen their knowledge and understanding." (Serguey M. Pokas, Zentralblatt MATH, Vol. 1043 (18), 2004)

"This textbook deals with quite a host of classical geometric topics. … As a benefit each chapter ends with numerous interesting exercises and examples to be solved by the reader. Moreover at the end of the book hints forthe solution of these exercises are offered. …The book can be recommended to students at an upper undergraduate level having a good base of linear algebra … ." (A. Gfrerrer, IMN, Vol. 57 (193), 2003)

"Audin … writing for undergraduates who have some linear algebra, selects and unifies a range of topics that actually traverses a good deal of this terrain. … a solid introduction to many faces of modern geometry. … Summing Up: … Recommended. General readers; lower-division undergraduates through professionals." (D. V. Feldman, CHOICE, July, 2003)

"With this book on geometry … the author has without a doubt created a work which will crucially influence many generations of geometers to come. Audin knows how to combine clarity with modern methods of geometric thought, and one cannot help but notice the love for geometry on each and every page. … Congratulations!" (Hans Sachs, Mathematical Reviews, 2003 h)

"The book is addressed to students at upper undergraduate and Master’s level to discover geometry and deepen their knowledge and understanding, starting from linear algebra … . Each property is proved, examples and exercises illustrate the course content. Precise hints for most of the exercises are provided at the end of the book." (Zentralblatt für Didaktik der Mathematik, June, 2002)

• IRMA, Université Louis Pasteur, Strasbourg, France

  Michèle Audin

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