Mathematics in nature: modeling patterns in the natural world
"Illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in na...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton University Press
2003
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Zusammenfassung: | "Illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks." "Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure."--BOOK JACKET. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXII, 360 S. Ill., graph. Darst. |
| ISBN: | 0691114293 |
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| 500 | |a Includes bibliographical references and index | ||
| 520 | 1 | |a "Illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks." "Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure."--BOOK JACKET. | |
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Datensatz im Suchindex
| _version_ | 1815786057378037760 |
|---|---|
| adam_text |
MATHEMATICS IN NATURE CONTENTS PREFACE THE MOTIVATION FOR THE BOOK;
ACKNOWLEDGMENTS; CREDITS XIII PROLOGUE WHY I MIGHT NEVER HAVE WRITTEN
THIS BOOK XXI CHAPTER ONE THE CONFLUENCE OF NATURE AND MATHEMATICAL
MODELING CONFLUENCE: EXAMPLES AND QUALITATIVE DISCUSSION OF PATTERNS IN
NATURE; ORGANIZATION OF THE BOOK. MODELING: PHILOSOPHY AND METHODOLOGY
OF MODELING, APPENDIX: A MATHEMATICAL MODEL OF SNOWBALL MELTING. CHAPTER
TWO ESTIMATION: THE POWER OF ARITHMETIC IN SOLVING FERMI PROBLEMS 17
VARIOUS AND SUNDRY EXAMPLES: GOLFBALLS, POPCORN, SOCCER BALLS, CELLS,
SAND GRAINS, HUMAN BLOOD, LOCH NESS, DENTAL FLOSS, PIANO TUNERS, HUMAN
HAIR, THE "DINOSAUR" ASTEROID, OIL, LEAVES, GRASS, HUMAN POPULATION,
SURFACE AREA, VOLUME, AND GROWTH, NEWSPAPER N, THE ATMOSPHERE, EARTH
TUNNEL, "BAND" TECTONICS, MOUNTAINS, CLOUD DROPLETS, THE "BLACK CLOUD."
CHAPTER THREE SHAPE, SIZE, AND SIMILARITY: THE PROBLEM OF SCALE 31
DIMENSIONAL ANALYSIS I * WHAT HAPPENS AS THINGS GET BIGGER? SURFACE
AREA/VOLUME AND STRENGTH/WEIGHT RATIOS AND THEIR IMPLICATIONS FOR THE
LIVING KINGDOM; GEOMETRIC SIMILARITY, ITS USEFULNESS AND ITS
LIMITATIONS; FALLING, DIVING, JUMPING, FLYING, POWER OUTPUT, RUNNING,
WALKING, FLYING AGAIN, RELATIVE STRENGTH, CELL VIABILITY. THE SPHERICITY
INDEX, BRAIN POWER, VISION AND HEARING. DIMETRODON. DIMENSIONAL ANALYSIS
II * THE BUCKINGHAM N THEOREM; VARIOUS EXAMPLES. APPENDIX: MODELS BASED
ON ELASTIC SIMILARITY. VIA CONTENTS CHAPTER FOUR METEOROLOGICAL OPTICS
I: SHADOWS, CREPUSCULAR RAYS, AND RELATED OPTICAL PHENOMENA 57 APPARENT
SIZE OF THE SUN AND MOON; CONTRAIL SHADOWS; TREE PINHOLE CAMERAS; LENGTH
OF THE EARTH'S SHADOW (AND THE MOON'S); ECLIPSES; REFLECTIONS FROM A
SLIGHTLY RIPPLED SURFACE * GLITTER PATHS AND LIQUID GOLD; HOW THICK IS
THE ATMOSPHERE? CREPUSCULAR RAYS AND CLOUD DISTANCES; TWILIGHT GLOW; THE
DISTANCE TO THE HORIZON; HOW FAR DOES THE MOON FALL EACH SECOND? THE
APPARENT SHAPE OF THE SETTING SUN. WHY IS THE SKY BLUE? RAYLEIGH
SCATTERING * A DIMENSIONAL ANALYSIS ARGUMENT, APPENDIX: A WORD ABOUT
SOLID ANGLES. CHAPTER FIVE METEOROLOGICAL OPTICS II: A "CALCULUS I"
APPROACH TO RAINBOWS, HALOS, AND GLORIES 80 PHYSICAL DESCRIPTION AND
EXPLANATION OF RAINBOWS AND SUPERNUMERARY BOWS. DERIVATION OF SNELL'S
LAW OF REFRACTION. THE PRIMARY BOW; THE SECONDARY BOW; A LITTLE ABOUT
AIRY'S THEORY. HALOS * ICE CRYSTAL FORMATION AND REFRACTION BY ICE
PRISMS; COMMON HALO PHENOMENA (AND SOME RARER FORMS); THE
CIRCUMHORIZONTAL ARC; THE GLORY; HISTORICAL DETAILS; WHY SOME TEXTBOOKS
ARE WRONG; SNOWFLAKES AND THE FAMOUS UNIQUENESS QUESTION; MIRAGES,
INFERIOR AND SUPERIOR; "CROCKER LAND" AND THE "FATA MORGANA"; THE
EQUATIONS OF RAY PATHS; IRIDESCENCE: BIRDS, BEETLES AND OTHER BUGS;
INTERFERENCE OF LIGHT IN SOAP FILMS AND OIL SLICKS. CHAPTER SIX CLOUDS,
SAND DUNES, AND HURRICANES 118 BASIC DESCRIPTIONS AND BASIC CLOUD
SCIENCE; COMMON CLOUD PATTERNS * A DESCRIPTIVE ACCOUNT OF CLOUD STREETS,
BILLOWS, LEE WAVES, AND GRAVITY WAVES; SIZE AND WEIGHT OF A CLOUD; WHY
CAN WE SEE FURTHER IN RAIN THAN IN FOG? SAND DUNES, THEIR FORMATION AND
THEIR POSSIBLE RELATIONSHIP WITH CLOUD STREETS; BOOMING DUNES AND
SQUEAKING SAND; MAYO'S HURRICANE MODEL; MORE BASIC SCIENCE AND THE
CORRESPONDING EQUATIONS; SOME NUMBERS; THE KINETIC ENERGY OF THE STORM.
CONTENTS IX CHAPTER SEVEN (LINEAR) WAVES OF ALL KINDS 139 DESCRIPTIVE
AND INTRODUCTORY THEORETICAL ASPECTS; THE "WAVE EQUATION";
GRAVITY-CAPILLARITY WAVES; DEEP WATER WAVES; SHALLOW WATER WAVES; PLANE
WAVE SOLUTIONS AND DISPERSION RELATIONS; ACOUSTIC-GRAVITY WAVES; THE
INFLUENCE OF WIND; PLANETARY WAVES (ROSSBY WAVES); WAVE SPEED AND GROUP
SPEED; AN INTERESTING OBSERVATION ABOUT PUDDLES; APPLICATIONS TO WATER
STRIDERS; EDGE WAVES AND CUSPS, SHIP WAVES AND WAKES IN DEEP AND SHALLOW
WATER, APPENDIX: MORE MATHEMATICS OF SHIP WAVES. CHAPTER EIGHT STABILITY
173 KELVIN-HELMHOLTZ (SHEAR) INSTABILITY; INTERNAL GRAVITY WAVES AND
WAVE ENERGY; BILLOW CLOUDS AGAIN; CONVECTION AND ITS CLOUDS; EFFECTS OF
THE EARTH'S ROTATION; THE TAYLOR PROBLEM; SPIDER WEBS AND THE STABILITY
OF THIN CYLINDRICAL FILMS. CHAPTER NINE BORES AND NONLINEAR WAVES 194
EXAMPLES; BASIC MECHANISMS; MATHEMATICS OF BORES; HYDRAULIC JUMPS;
NONLINEAR WAVE EQUATIONS: BURGER'S EQUATION; KORTEWEG-DE VRIES EQUATION;
BASIC WAVELIKE SOLUTIONS; SOLITARY WAVES; SCOTT RUSSELL'S "GREAT WAVE OF
TRANSLATION"; TIDES: DIFFERENTIAL GRAVITATIONAL FORCES; THE POWER OF
"TIDE": THE SLOWING POWER OF TIDAL FRICTION; TIDES, ECLIPSES AND THE
SUN/MOON DENSITY RATIO. CHAPTER TEN THE FIBONACCI SEQUENCE AND THE
GOLDEN RATIO (R) 213 PHYLLOTAXIS; THE GOLDEN ANGLE; REGULAR PENTAGONS
AND THE GOLDEN RATIO; SOME THEOREMS ON Z; RATIONAL APPROXIMATIONS TO
IRRATIONAL NUMBERS; CONTINUED FRACTION REPRESENTATION OF R; CONVERGENTS;
MISCONCEPTIONS ABOUT T. X CONTENTS CHAPTER ELEVEN BEES, HONEYCOMBS,
BUBBLES, AND MUD CRACKS 231 THE HONEYCOMB CELL AND ITS GEOMETRY;
DERIVATION OF ITS SURFACE AREA AND CONSEQUENT MINIMIZATION; COLLECTING
NECTAR: OPTIMIZING VISITS TO FLOWERS. SOAP BUBBLES AND MINIMAL SURFACES.
PLATEAU'S RULES; THE AVERAGE GEOMETRIC PROPERTIES OF FOAM; THE
ISOPERIMETRIC PROPERTY OF THE CIRCLE AND THE SAME-AREA THEOREM; PRINCESS
DIDO AND HER ISOPERIMETRIC PROBLEM; MUD CRACKS AND RELATED GEOMETRIC
THEOREMS. APPENDIX: THE ISOPERIMETRIC PROPERTY OF THE CIRCLE. CHAPTER
TWELVE RIVER MEANDERS, BRANCHING PATTERNS, AND TREES 254 BASIC
DESCRIPTION; A BESSEL FUNCTION MODEL; ANALOGY OF MEANDERS WITH STRESSES
IN ELASTIC WIRES; BRIEF ACCOUNT OF BRANCHING SYSTEMS IN RIVERS AND
TREES; RIVER DRAINAGE PATTERNS AND THE FIBONACCI SEQUENCE AGAIN. TREES;
BIOMIMETICS; THE GEOMETRIC PROPORTIONS OF TREES AND BUCKLING; SHAKING OF
TREES; GEOMETRIC-, ELASTIC-, AND STATIC STRESS SIMILARITY MODELS; HOW
HIGH CAN TREES GROW? * A BESSEL FUNCTION MODEL; THE INTERCEPTION OF
LIGHT BY LEAVES; AEOLIAN TONES; THE WHISPERS OF THE FOREST, APPENDIX:
THE STATICS AND BENDING OF A SIMPLE BEAM: BASIC EQUATIONS. CHAPTER
THIRTEEN BIRD FLIGHT 295 WING LOADING; FLAPPING FLIGHT; SOARING FLIGHT;
FORMATION FLIGHT; DRAG AND LIFT; SINKING AND GLIDING SPEEDS; HOVERING;
HELICOPTERS AND HUMMINGBIRDS. LIFT AND BERNOULLI * SOME MISCONCEPTIONS
ABOUT LIFT; REYNOLDS' NUMBER AGAIN. THE SHAPE OF WATER FROM A TAP.
CHAPTER FOURTEEN HOW DID THE LEOPARD GET ITS SPOTS? 309 RANDOM WALKS AND
DIFFUSION; A SIMPLE DERIVATION OF THE DIFFUSION EQUATION; ANIMAL AND
INSECT MARKINGS; MORPHOGENESIS: THE DEVELOPMENT OF PATTERNS; PATTERN
CONTENTS XI FORMATION BY ACTIVATOR AND INHIBITOR MECHANISMS; SEASHELLS;
MECHANISMS OF ACTIVATION AND INHIBITION; REACTION-DIFFUSION EQUATIONS *
A LINEAR MODEL; BUTTERFLY WING SPOTS: A SIMPLISTIC BUT INFORMATIVE
MATHEMATICAL MODEL. OTHER APPLICATIONS OF DIFFUSION MODELS: THE SIZE OF
PLANKTON BLOOMS; EARTH(L)Y APPLICATIONS OF HISTORICAL INTEREST: THE
DIURNAL AND ANNUAL TEMPERATURE VARIATIONS BELOW THE SURFACE; THE "AGE"
OF THE EARTH, APPENDIX: THE ANALOGY WITH THE NORMAL MODES OF RECTANGULAR
AND CIRCULAR MEMBRANES. APPENDIX FRACTALS: AN APPETITE WHETTER. 336
BIBLIOGRAPHY 341 INDEX 357 |
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| institution | BVB |
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| spelling | Adam, John A. 1949- Verfasser (DE-588)114937478 aut Mathematics in nature modeling patterns in the natural world John A. Adam Princeton [u.a.] Princeton University Press 2003 XXII, 360 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "Illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks." "Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure."--BOOK JACKET. Natuur gtt Wiskundige modellen gtt Mathematisches Modell Mathematical models Natur (DE-588)4041358-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf Natur (DE-588)4041358-5 s Naturwissenschaften (DE-588)4041421-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 http://www.loc.gov/catdir/description/prin031/2003055616.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Adam, John A. 1949- Mathematics in nature modeling patterns in the natural world Natuur gtt Wiskundige modellen gtt Mathematisches Modell Mathematical models Natur (DE-588)4041358-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Naturwissenschaften (DE-588)4041421-8 gnd |
| subject_GND | (DE-588)4041358-5 (DE-588)4114528-8 (DE-588)4041421-8 |
| title | Mathematics in nature modeling patterns in the natural world |
| title_auth | Mathematics in nature modeling patterns in the natural world |
| title_exact_search | Mathematics in nature modeling patterns in the natural world |
| title_full | Mathematics in nature modeling patterns in the natural world John A. Adam |
| title_fullStr | Mathematics in nature modeling patterns in the natural world John A. Adam |
| title_full_unstemmed | Mathematics in nature modeling patterns in the natural world John A. Adam |
| title_short | Mathematics in nature |
| title_sort | mathematics in nature modeling patterns in the natural world |
| title_sub | modeling patterns in the natural world |
| topic | Natuur gtt Wiskundige modellen gtt Mathematisches Modell Mathematical models Natur (DE-588)4041358-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Naturwissenschaften (DE-588)4041421-8 gnd |
| topic_facet | Natuur Wiskundige modellen Mathematisches Modell Mathematical models Natur Naturwissenschaften |
| url | http://www.loc.gov/catdir/description/prin031/2003055616.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT adamjohna mathematicsinnaturemodelingpatternsinthenaturalworld |