Recent Advances in Geometric Inequalities

✍ Scribed by D. S. Mitrinović, J. E. Pečarić, V. Volenec (auth.)

• Publisher: Springer Netherlands
• Year: 1989
• Tongue: English
• Leaves: 728
• Series: Mathematics and Its Applications 28
• Edition: 1
• Category: Library

✦ Synopsis

`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

✦ Table of Contents

Front Matter....Pages i-xix
The Existence of a Triangle....Pages 1-25
Duality between Geometric Inequalities and Inequalities for Positive Numbers....Pages 26-36
Homogeneous Symmetric Polynomial Geometric Inequalities....Pages 37-48
Duality between Different Triangle Inequalities and Triangle Inequalities with (R, r, s)....Pages 49-63
Transformations for the Angles of a Triangle....Pages 64-73
Some Trigonometric Inequalities....Pages 74-100
Some Other Transformations....Pages 101-120
Convex Functions and Geometric Inequalities....Pages 121-143
Miscellaneous Inequalities with Elements of a Triangle....Pages 144-231
Special Triangles....Pages 232-277
Triangle and Point....Pages 278-339
Inequalities with Several Triangles....Pages 340-384
The Möbius-Neuberg and the Möbius-Pompeiu Theorems....Pages 385-400
Inequalities for Quadrilaterals....Pages 401-411
Inequalities for Polygons....Pages 412-432
Inequalities for a Circle....Pages 433-442
Particular Inequalities in Plane Geometry....Pages 443-462
Inequalities for Simplexes in E n (n ≥ 2)....Pages 463-544
Inequalities for Tetrahedra....Pages 545-575
Other Inequalities in E n (n ≥ 2)....Pages 576-676
Back Matter....Pages 677-710

✦ Subjects

Geometry