Real Algebraic Geometry

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered). Table of Contents Real Algebraic Geometry ISBN 9783642362422 ISBN 9783642362439 Publisher's Foreword Foreword Contents Chapter 1 Introduction Chapter 2 Geometry of Conic Sections Chapter 3 The Physics of Conic Sections and Ellipsoids Chapter 4 Projective Geometry Chapter 5 Complex Algebraic Curves Chapter 6 A Problem for School Pupils Appendix A* Into How Many Parts Do n Lines Divide the Plane? Editors' Comments on Gudkov's Conjecture