When least is best: how mathematicians discovered many clever ways to make things as small (or as large) as possible
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton University Press
2004
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 370 S. graph. Darst. |
| ISBN: | 0691070784 |
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| 245 | 1 | 0 | |a When least is best |b how mathematicians discovered many clever ways to make things as small (or as large) as possible |c Paul J. Nahin |
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Record in the Search Index
| _version_ | 1804130211742089216 |
|---|---|
| adam_text | PAUL J. NAHIN IS HOW MATHEMATICIANS DISCOVERED MANY CLEVER WAYS TO MAKE
THINGS AS SMALL (OR AS LARGE) AS POSSIBLE EST CONTENTS PREFACE XIII X*
MINIMUMS, MAXIMUMS, DERIVATIVES, AND COMPUTERS L 1.1 INTRODUCTION 1 1.2
WHEN DERIVATIVES DON T WORK 4 1.3 USING ALGEBRA TO FIND MINIMUMS 5 1.4 A
CIVIL ENGINEERING PROBLEM 9 1.5 THE AM-GM INEQUALITY 13 1.6 DERIVATIVES
FROM PHYSICS 20 1.7 MINIMIZING WITH A COMPUTER 24 2. THE FIRST EXTREMAL
PROBLEMS 37 2.1 THE ANCIENT CONFUSION OF LENGTH AND AREA 37 2.2 DIDO S
PROBLEM AND THE ISOPERIMETRIC QUOTIENT 45 2.3 STEINER S SOLUTION TO
DIDO S PROBLEM 56 2.4 HOW STEINER STUMBLED 59 2.5 A HARD PROBLEM WITH
AN EASY SOLUTION 62 2.6 FAGNANO S PROBLEM 65 3. MEDIEVAL MAXIMIZATION
AND SOME MODERN TWISTS 71 3.1 THE REGIOMONTANUS PROBLEM 71 3.2 THE
SATURN PROBLEM 11 3.3 THE ENVELOPE-FOLDING PROBLEM 79 X CONTENTS 3.4 THE
PIPE-AND-CORNER PROBLEM 85 3.5 REGIOMONTANUS REDUX 89 3.6 THE MUDDY
WHEEL PROBLEM 94 4. THE FORGOTTEN WAR OF DESCARTES AND FERMAT 99 4.1 TWO
VERY DIFFERENT MEN 99 4.2 SNELL S LAW 101 4.3 FERMAT, TANGENT LINES, AND
EXTREMA 109 4.4 THE BIRTH OF THE DERIVATIVE 114 4.5 DERIVATIVES AND
TANGENTS 120 4.6 SNELL S LAW AND THE PRINCIPLE OF LEAST TIME 127 4.7 A
POPULAR TEXTBOOK PROBLEM 134 4.8 SNELL S LAW AND THE RAINBOW 137 5.
CALCULUS STEPS FORWARD, CENTER STAGE 140 5.1 THE DERIVATIVE: CONTROVERSY
AND TRIUMPH 140 5.2 PAINTINGS AGAIN, AND KEPLER S WINE BARREL 147 5.3
THE MAILABLE PACKAGE PARADOX 149 5.4 PROJECTILE MOTION IN A
GRAVITATIONAL FIELD 152 5.5 THE PERFECT BASKETBALL SHOT 158 5.6 HALLEY S
GUNNERY PROBLEM 165 5.7 DE L HOSPITAL AND HIS PULLEY PROBLEM, AND A NEW
MINIMUM PRINCIPLE 171 5.8 DERIVATIVES AND THE RAINBOW 179 6. BEYOND
CALCULUS 200 6.1 GALILEO S PROBLEM 200 6.2 THE BRACHISTOCHRONE PROBLEM
210 6.3 COMPARING GALILEO AND BERNOULLI 221 6.4 THE EULER-LAGRANGE
EQUATION 231 6.5 THE STRAIGHT LINE AND THE BRACHISTOCHRONE 238 6.6
GALILEO S HANGING CHAIN 240 CONTENTS XI 6.7 THE CATENARY AGAIN 247 6.8
THE ISOPERIMETRIC PROBLEM, SOLVED (AT LAST!) 251 6.9 MINIMAL AREA
SURFACES, PLATEAU S PROBLEM, AND SOAP BUBBLES 259 6.10 THE HUMAN SIDE OF
MINIMAL AREA SURFACES 271 7. THE MODERN AGE BEGINS 279 7.1 THE
FERMAT/STEINER PROBLEM 279 7.2 DIGGING THE OPTIMAL TRENCH, PAVING THE
SHORTEST MAIL ROUTE, AND LEAST-COST PATHS THROUGH DIRECTED GRAPHS 286
7.3 THE TRAVELING SALESMAN PROBLEM 293 7.4 MINIMIZING WITH INEQUALITIES
(LINEAR PROGRAMMING) 295 7.5 MINIMIZING BY WORKING BACKWARDS (DYNAMIC
PROGRAMMING) 312 APPENDIX A. THE AM-GM INEQUALITY 331 APPENDIX B. THE
AM-QM INEQUALITY, AND JENSEN S INEQUALITY 334 APPENDIX C. THE SAGACITY
OF THE BEES 342 APPENDIX D. EVERY CONVEX FIGURE HAS A PERIMETER
BISECTOR 345 APPENDIX E. THE GRAVITATIONAL FREE-FALL DESCENT TIME ALONG
A CIRCLE 347 APPENDIX F. THE AREA ENCLOSED BY A CLOSED CURVE 352
APPENDIX G. BELTRAMI S IDENTITY 359 APPENDIX H. THE LAST WORD ON THE
LOST FISHERMAN PROBLEM 361 ACKNOWLEDGMENTS 365 INDEX 367
|
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| author | Nahin, Paul J. 1940- |
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| author_facet | Nahin, Paul J. 1940- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte gnd |
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| id | DE-604.BV017391530 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:17:26Z |
| institution | BVB |
| isbn | 0691070784 |
| language | English |
| lccn | 2003055537 |
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| physical | XVIII, 370 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | Princeton University Press |
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| spelling | Nahin, Paul J. 1940- Verfasser (DE-588)136816614 aut When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible Paul J. Nahin Princeton [u.a.] Princeton University Press 2004 XVIII, 370 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geschichte gnd rswk-swf Calcul infinitésimal ram Extreme waarden gtt Mathématiques - Histoire Mathématiques - Histoire ram Maximums et minimums Optimisation mathématique ram Wiskunde gtt calcul infinitésimal inriac dérivation inriac historique mathématique inriac maximisation inriac minimisation inriac optimisation mathématique inriac Geschichte Mathematik Mathematics History Maxima and minima Extremwert (DE-588)4137272-4 gnd rswk-swf Extremwert (DE-588)4137272-4 s Geschichte z DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010479274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nahin, Paul J. 1940- When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible Calcul infinitésimal ram Extreme waarden gtt Mathématiques - Histoire Mathématiques - Histoire ram Maximums et minimums Optimisation mathématique ram Wiskunde gtt calcul infinitésimal inriac dérivation inriac historique mathématique inriac maximisation inriac minimisation inriac optimisation mathématique inriac Geschichte Mathematik Mathematics History Maxima and minima Extremwert (DE-588)4137272-4 gnd |
| subject_GND | (DE-588)4137272-4 |
| title | When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible |
| title_auth | When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible |
| title_exact_search | When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible |
| title_full | When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible Paul J. Nahin |
| title_fullStr | When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible Paul J. Nahin |
| title_full_unstemmed | When least is best how mathematicians discovered many clever ways to make things as small (or as large) as possible Paul J. Nahin |
| title_short | When least is best |
| title_sort | when least is best how mathematicians discovered many clever ways to make things as small or as large as possible |
| title_sub | how mathematicians discovered many clever ways to make things as small (or as large) as possible |
| topic | Calcul infinitésimal ram Extreme waarden gtt Mathématiques - Histoire Mathématiques - Histoire ram Maximums et minimums Optimisation mathématique ram Wiskunde gtt calcul infinitésimal inriac dérivation inriac historique mathématique inriac maximisation inriac minimisation inriac optimisation mathématique inriac Geschichte Mathematik Mathematics History Maxima and minima Extremwert (DE-588)4137272-4 gnd |
| topic_facet | Calcul infinitésimal Extreme waarden Mathématiques - Histoire Maximums et minimums Optimisation mathématique Wiskunde calcul infinitésimal dérivation historique mathématique maximisation minimisation optimisation mathématique Geschichte Mathematik Mathematics History Maxima and minima Extremwert |
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