Recent Advances in Geometric Inequalities

'For the immediate future, however, this book should be (possibly chained!) in every university and college library, and, yes, in the library of every school which is intent on improving its mathematics teaching.' The Americal Mathematical Monthly, December 1991 'This book should make interesting reading for philosophers of mathematics, if they want to observe how mathematical ideas really develop.' Advances in Mathematics, 86, 1991

• The Existence of a Triangle.- Duality between Geometric Inequalities and Inequalities for Positive Numbers.- Homogeneous Symmetric Polynomial Geometric Inequalities.- Duality between Different Triangle Inequalities and Triangle Inequalities with (R, r, s).- Transformations for the Angles of a Triangle.- Some Trigonometric Inequalities.- Some Other Transformations.- Convex Functions and Geometric Inequalities.- Miscellaneous Inequalities with Elements of a Triangle.- Special Triangles.- Triangle and Point.- Inequalities with Several Triangles.- The Möbius-Neuberg and the Möbius-Pompeiu Theorems.- Inequalities for Quadrilaterals.- Inequalities for Polygons.- Inequalities for a Circle.- Particular Inequalities in Plane Geometry.- Inequalities for Simplexes in En (n ? 2).- Inequalities for Tetrahedra.- Other Inequalities in En (n ? 2).