Presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning Applications to physics, engineering, and economics Ideal for use at the junior and senior undergraduate level, with wide appeal to students, teachers, professional mathematicians, and puzzle enthusiasts
Author(s): Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov
Edition: 1
Year: 2005
Language: English
Pages: 277
Cover
......Page 1
Title: Geometric Problems on Maxima and Minima......Page 4
Copyright
......Page 5
Contents......Page 6
Preface......Page 8
1.1 Employing Geometric Transformations......Page 14
EXERCISES......Page 28
1.2 Employing Algebraic Inequalities......Page 32
EXERCISES......Page 37
1.3 Employing Calculus......Page 40
EXERCISES......Page 49
1.4 The Method of Partial Variation......Page 51
EXERCISES......Page 60
1.5 The Tangency Principle......Page 61
EXERCISES......Page 73
2.1 Isoperimetric Problems......Page 76
EXERCISES......Page 83
2.2 Extremal Points in Triangle and Tetrahedron......Page 85
EXERCISES......Page 91
2.3 Malfatti’s Problems......Page 93
EXERCISES......Page 100
2.4 Extremal Combinatorial Geometry Problems......Page 101
EXERCISES......Page 105
3.1 Triangle Inequality......Page 108
3.2 Selected Geometric Inequalities......Page 109
3.3 MaxMin and MinMax......Page 111
3.4 Area and Perimeter......Page 112
3.6 Broken Lines......Page 114
3.7 Distribution of Points......Page 115
3.8 Coverings......Page 117
4.1 Employing Geometric Transformations......Page 118
4.2 Employing Algebraic Inequalities......Page 137
4.3 Employing Calculus......Page 149
4.4 The Method of Partial Variation......Page 164
4.5 The Tangency Principle......Page 174
4.6 Isoperimetric Problems......Page 182
4.7 Extremal Points in Triangle and Tetrahedron......Page 189
4.8 Malfatti’s Problems......Page 198
4.9 Extremal Combinatorial Geometry Problems......Page 201
4.10 Triangle Inequality......Page 210
4.11 Selected Geometric Inequalities......Page 213
4.12 MaxMin and MinMax......Page 225
4.13 Area and Perimeter......Page 228
4.14 Polygons in a Square......Page 246
4.15 Broken Lines......Page 250
4.16 Distribution of Points......Page 253
4.17 Coverings......Page 263
Notation......Page 268
Glossary of Terms......Page 270
Bibliography......Page 276
