A mathematical nature walk:
Presents ninety-six questions about many common natural phenomena and then shows how to answer them using mostly basic mathematics and precalculus.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a.]
Princeton University Press
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Presents ninety-six questions about many common natural phenomena and then shows how to answer them using mostly basic mathematics and precalculus. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XX, 248 S. Ill., graph. Darst. |
| ISBN: | 9780691128955 |
Internformat
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| 245 | 1 | 0 | |a A mathematical nature walk |c John A. Adam |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton University Press |c 2009 | |
| 300 | |a XX, 248 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 8 | |a Presents ninety-six questions about many common natural phenomena and then shows how to answer them using mostly basic mathematics and precalculus. | |
| 650 | 7 | |a Natuurverschijnselen |2 gtt | |
| 650 | 7 | |a Wiskunde |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics in nature |v Miscellanea | |
| 650 | 4 | |a Mathematical analysis |v Miscellanea | |
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Datensatz im Suchindex
| _version_ | 1815786057382232064 |
|---|---|
| adam_text |
Contents
Preface
ху
Acknowledgments
xix
Introduction
ι
At the beginning
. 11
(General questions to challenge our powers of observation,
estimation, and physical intuition)
Q.1-Q.6: Rainbows
11
Q.7: Shadows
11
Q.8-9: Clouds and cloud droplets
12
Q.10: Light
12
Q.ll: Sound
12
Q.12-13: The rotation of the Earth
12
Q.14: The horizon
12
Q.15: The appearance of distant hills
12
In the "playground"
13
(just to get our feet wet.
. .)
Q.16: Loch Ness
—
how long to empty it?
13
Q.17: The Grand Canyon—how long to fill it with sand?
14
Q.18: Just how large an area is a million acres?
15
Q.19: Twenty-five billion hamburgers
—
how many have
you eaten?
16
Q.20: How many head of cattle would be required to
satisfy the
(1978)
daily demand for meat in the
United States?
16
Q.21: Why could King Kong never exist?
17
Contents
Q.22:
Why do small bugs dislike taking showers?
18
Q.23: How fast is that raindrop falling?
18
Q.24: Why can haystacks explode if they're too big?
20
In the garden
24
Q.25: Why can I see the "whole universe" in my garden
globe?
24
Q.26: How long is that bee going to collect nectar?
25
Q.27: Why are those drops on the spider's web so
evenly spaced?
27
Q.28: What is the Fibonacci sequence?
31
Q.29: So what is the "golden angle"?
35
Q.30: Why are the angles between leaves "just so"?
36
In the neighborhood
43
Q.31: Can you infer fencepost (or bridge) "shapes"
just by walking past them?
43
Q.32: Can you weigh a pumpkin just by carefully
looking at it?
48
Q.33: Can you determine the paths of low-flying ducks?
53
In the shadows
58
Q.34: How high is that tree? (An estimate using elliptical
light patches)
58
Q.35: Does my shadow accelerate?
59
Q.36: How long is the Earth's shadow?
61
Q.37: And Jupiter's? And Neptune's?
63
Q.38: How wide is the Moon's shadow?
63
In the sky
64
Q.39: How far away is the horizon (neglecting refraction)?
64
Q.4O: How far away is that cloud?
66
Q.4i: How well is starlight reflected from a calm body
of water?
67
Q.42: How heavy is that cloud?
71
Q.43: Why can we see farther in rain than in fog?
72
Contents
Q.44:
How far away does that "road puddle" mirage
appear to be?
73
Q.45: Why is the sky blue?
77
Q.46: So how much more /s violet light scattered than red?
79
Q.47: What causes variation in colors of butterfly wings,
bird plumage, and oil slicks?
80
Q.48: What causes the metallic colors in that cloud?
84
Q.49: How do rainbows form? And what are those fringes
underneath the primary bow?
85
Q.50: What about the secondary rainbow?
92
Q.51: Are there higher-order rainbows?
93
Q.52: So what is that triple rainbow?
95
Q.53: Is there a "zeroth"-order rainbow?
98
Q.54: Can bubbles produce "rainbows"?
99
Q.55: What would "diamondbows" look like?
100
Q.56: What causes that ring around the Sun?
101
Q.57: What is that shaft of light above the setting Sun?
109
Q.58: What is that colored splotch of light beside the Sun?
1
1
1
Q.59: What's that "smiley face" in the sky?
113
Q.60: What are those colored rings around the shadow
of my plane?
. 116
Q.61: Why does geometrical optics imply infinite intensity
at the rainbow angle?
118
In the nest
122
Q.62: How can you model the shape of birds' eggs?
122
Q.63: What is the sphericity index?
123
Q.64: Can the shape of an egg be modeled trigonometrically?
124
Q.65: Can the shape of an egg be modeled algebraically?
127
Q.66: Can the shape of an egg be modeled using calculus?
130
Q.67: Can the shape of an egg be modeled geometrically?
134
In (or on) the water
137
Q.68: What causes a glitter path?
137
Q.69: What is the path of wave intersections?
140
Q.70: How fast do waves move on the surface of water?
141
Q.71: How do moving ships produce that wave pattern?
148
Q.72: How do rocks in a flowing stream produce
different patterns?
152
xii Contents
Q.
73:
Can waves be stopped by opposing streams?
154
Q.74: How far away is the storm?
157
Q.75: How fast is the cairn region
ofthat
"puddle wave"
expanding?
158
Q.76: How much energy do ocean waves have?
160
Q.77: Does a wave raise the average depth of the water?
162
Q.78: How can ship wakes prove the Earth is "round"?
164
ІП
the forest
168
Q.79: How high can trees grow?
168
Q.80: How much shade does a layer of leaves provide
for the layer below?
172
Q.81: What is the "murmur of the forest"?
174
Q.82: How opaque is a wood or forest?
176
Q.83: Why do some trees have "tumors"?
179
In the national park
183
Q.84: What shapes are river meanders?
183
Q.85: Why are mountain shadows triangular?
189
Q.86: Why does Zion Arch appear circular?
191
In the night sky
194
Q.87: How are star magnitudes measured?
194
Q.88: How can I stargaze with a flashlight?
196
Q.89: How can you model a star?
197
Q.90: How long would it take the Sun to collapse?
205
Q.91: What are those small rings around the Moon?
207
Q.92: How can you model an eclipse of the Sun?
210
At the end
. 217
Q.93: How can you model walking?
217
Q.94: How "long" is that tree?
221
Q.95: What are those "rays" I sometimes see at or
after sunset?
224
Q.96: How can twilight help determine the height of
the atmosphere?
228
Contents
xü¡
Appendix 1:
A very short glossary of mathematical terms
and functions
231
Appendix
2:
Answers to questions
1-15 234
Appendix
3:
Newton's law of cooling
238
Appendix
4:
More mathematical patterns in nature
240
References
243
Index
247 |
| any_adam_object | 1 |
| author | Adam, John A. 1949- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV036079220 |
| illustrated | Illustrated |
| indexdate | 2024-11-15T11:02:06Z |
| institution | BVB |
| isbn | 9780691128955 |
| language | English |
| lccn | 2008044828 |
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| physical | XX, 248 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton University Press |
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| spelling | Adam, John A. 1949- Verfasser (DE-588)114937478 aut A mathematical nature walk John A. Adam Princeton, NJ [u.a.] Princeton University Press 2009 XX, 248 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Presents ninety-six questions about many common natural phenomena and then shows how to answer them using mostly basic mathematics and precalculus. Natuurverschijnselen gtt Wiskunde gtt Mathematik Mathematics in nature Miscellanea Mathematical analysis Miscellanea Natur (DE-588)4041358-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Natur (DE-588)4041358-5 s Mathematisches Modell (DE-588)4114528-8 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018970321&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Adam, John A. 1949- A mathematical nature walk Natuurverschijnselen gtt Wiskunde gtt Mathematik Mathematics in nature Miscellanea Mathematical analysis Miscellanea Natur (DE-588)4041358-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4041358-5 (DE-588)4114528-8 (DE-588)7651795-0 |
| title | A mathematical nature walk |
| title_auth | A mathematical nature walk |
| title_exact_search | A mathematical nature walk |
| title_full | A mathematical nature walk John A. Adam |
| title_fullStr | A mathematical nature walk John A. Adam |
| title_full_unstemmed | A mathematical nature walk John A. Adam |
| title_short | A mathematical nature walk |
| title_sort | a mathematical nature walk |
| topic | Natuurverschijnselen gtt Wiskunde gtt Mathematik Mathematics in nature Miscellanea Mathematical analysis Miscellanea Natur (DE-588)4041358-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Natuurverschijnselen Wiskunde Mathematik Mathematics in nature Miscellanea Mathematical analysis Miscellanea Natur Mathematisches Modell Mathematische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018970321&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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