Table of contents for Geometric problems on maxima and minima / Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov.


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1  Methods for Finding Geometric Extrema                            1
1.1  Employing Geometric Transformations .............           1
1.2  Employing Algebraic Inequalities . . . . . . . . . . . . . ...  19
1.3  Employing Calculus ........................                27
1.4  The Method of Partial Variation. . . . . . . . . . . . .  .  38
1.5  The Tangency Principle .....................         . .   48
2  Selected Types of Geometric Extremum Problems                   63
2.1 Isoperimetric Problems . . . . . . . . . . . . . . ..... . .  .  63
2.2  Extremal Points in Triangle and Tetrahedron . . . . . . . . ...  72
2.3  Malfatti's Problems  .......................           ..  80
2.4  Extremal Combinatorial Geometry Problems . . . . . . . ...  88
3  Miscellaneous                                                   95
3.1  Triangle Inequality  ........................              95
3.2  Selected Geometric Inequalities . . . . . . . . . . . . .....  96
3.3  MaxMin and MinMax .......................                  98
3.4  Area and Perimeter  ........................               99
3.5  Polygons in  a Square  .......................            101
3.6  Broken Lines  ..........................              .   101
3.7  Distribution of Points . . . . . . . ... .  . . . . . . . . . . . .  102
3.8  Coverings  .............................                  104
4  Hints and Solutions to the Exercises                           105
4.1  Employing Geometric Transformations . . . . . . . . . ....  105
4.2  Employing Algebraic Inequalities . . . . . . . . . . . .....  124
4.3  Employing Calculus ........................               136
4.4  The Method of Partial Variation  . . . . . . . . . . . . .....  151
4.5  The Tangency Principle  ..  ....................         161
4.6 Isoperimetric Problems.  . . . . . . . . . . . . .......... . . . . 169
4.7  Extremal Points in Triangle and Tetrahedron . . . . . . . . . ...  176
4.8  M alfatti's Problems  . .  . .  . .  . . .  . .  .  . .  . . .  .  . .  . ...  185
4.9  Extremal Combinatorial Geometry Problems . . . . . . . . ...  188
4.10 Triangle Inequality .................... ....... 197
4.11 Selected Geometric Inequalities . . . . . . . . . . . . . . . ...  200
4.12 MaxMinandMinMax ........................ 212
4.13  Area and Perimeter  .........................           215
4.14  Polygons in a Square  ...............     ........   .  233
4.15  Broken  Lines  ............................             237
4.16 Distribution of Points . . . . . . . . . . . . . . ..... .......  240
4.17  Coverings  ...................         ...........      250
Notation                                                         255



Library of Congress subject headings for this publication: Maxima and minima, Geometry Problems, exercises, etc