Geometric problems on maxima and minima:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2006
|
| Subjects: | |
| Online Access: | Table of contents only Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [263]-264) |
| Physical Description: | IX, 264 S. graph. Darst. |
| ISBN: | 0817635173 9780817635176 |
Staff View
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| 245 | 1 | 0 | |a Geometric problems on maxima and minima |c Titu Andreescu ; Oleg Mushkarov ; Luchezar Stoyanov |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2006 | |
| 300 | |a IX, 264 S. |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references (p. [263]-264) | ||
| 650 | 4 | |a Maxima and minima | |
| 650 | 4 | |a Geometry |v Problems, exercises, etc | |
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| 700 | 1 | |a Mushkarov, Oleg |e Verfasser |4 aut | |
| 700 | 1 | |a Stoyanov, Luchezar N. |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
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
vi Contents
4.5 The Tangency Principle 161
4.6 Isoperimetric Problems 169
4.7 Extremal Points in Triangle and Tetrahedron 176
4.8 Malfatti s Problems 185
4.9 Extremal Combinatorial Geometry Problems 188
4.10 Triangle Inequality 197
4.11 Selected Geometric Inequalities 200
4.12 MaxMin and MinMax 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
Glossary of Terms 257
Bibliography 263
|
| adam_txt |
Contents
Preface vii
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
vi Contents
4.5 The Tangency Principle 161
4.6 Isoperimetric Problems 169
4.7 Extremal Points in Triangle and Tetrahedron 176
4.8 Malfatti's Problems 185
4.9 Extremal Combinatorial Geometry Problems 188
4.10 Triangle Inequality 197
4.11 Selected Geometric Inequalities 200
4.12 MaxMin and MinMax 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
Glossary of Terms 257
Bibliography 263 |
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| index_date | 2024-07-02T16:44:20Z |
| indexdate | 2024-07-09T20:53:41Z |
| institution | BVB |
| isbn | 0817635173 9780817635176 |
| language | English |
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| spelling | Andreescu, Titu 1956- Verfasser (DE-588)12217805X aut Ekstremalni zadači v geometriata Geometric problems on maxima and minima Titu Andreescu ; Oleg Mushkarov ; Luchezar Stoyanov Boston [u.a.] Birkhäuser 2006 IX, 264 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. [263]-264) Maxima and minima Geometry Problems, exercises, etc Geometrie (DE-588)4020236-7 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Geometrie (DE-588)4020236-7 s DE-604 Mushkarov, Oleg Verfasser aut Stoyanov, Luchezar N. Verfasser aut http://www.loc.gov/catdir/toc/fy0610/2005935987.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0663/2005935987-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015476380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andreescu, Titu 1956- Mushkarov, Oleg Stoyanov, Luchezar N. Geometric problems on maxima and minima Maxima and minima Geometry Problems, exercises, etc Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4143389-0 |
| title | Geometric problems on maxima and minima |
| title_alt | Ekstremalni zadači v geometriata |
| title_auth | Geometric problems on maxima and minima |
| title_exact_search | Geometric problems on maxima and minima |
| title_exact_search_txtP | Geometric problems on maxima and minima |
| title_full | Geometric problems on maxima and minima Titu Andreescu ; Oleg Mushkarov ; Luchezar Stoyanov |
| title_fullStr | Geometric problems on maxima and minima Titu Andreescu ; Oleg Mushkarov ; Luchezar Stoyanov |
| title_full_unstemmed | Geometric problems on maxima and minima Titu Andreescu ; Oleg Mushkarov ; Luchezar Stoyanov |
| title_short | Geometric problems on maxima and minima |
| title_sort | geometric problems on maxima and minima |
| topic | Maxima and minima Geometry Problems, exercises, etc Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Maxima and minima Geometry Problems, exercises, etc Geometrie Aufgabensammlung |
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