A Mathematical Nature Walk

by Adam, John A.

• ISBN13: 9780691152653
• ISBN10: 0691152659
• Edition: Reprint
• Format: Paperback
• Copyright: 2011-09-12
• Publisher: Princeton Univ Pr

Summary

How heavy is that cloud? Why can you see farther in rain than in fog? Why are the droplets on that spider web spaced apart so evenly? If you have ever asked questions like these while outdoors, and wondered how you might figure out the answers, this is a book for you. An entertaining and informative collection of fascinating puzzles from the natural world around us, A Mathematical Nature Walkwill delight anyone who loves nature or math or both. John Adam presents ninety-six questions about many common natural phenomena--and a few uncommon ones--and then shows how to answer them using mostly basic mathematics. Can you weigh a pumpkin just by carefully looking at it? Why can you see farther in rain than in fog? What causes the variations in the colors of butterfly wings, bird feathers, and oil slicks? And why are large haystacks prone to spontaneous combustion? These are just a few of the questions you'll find inside. Many of the problems are illustrated with photos and drawings, and the book also has answers, a glossary of terms, and a list of some of the patterns found in nature. About a quarter of the questions can be answered with arithmetic, and many of the rest require only precalculus. But regardless of math background, readers will learn from the informal descriptions of the problems and gain a new appreciation of the beauty of nature and the mathematics that lies behind it.

Author Biography

John a. Adam is professor of mathematics at Old Dominion University. He is the coauthor of Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin and the author or Mathematics in Nature (both Princeton).

Table of Contents

Preface	p. xv
Acknowledgements	p. xix
Introduction	p. 1
At the beginning: (General questions to challenge our powers of observation, estimation, and physical intuition)à	p. 11
Rainbows	p. 11
Shadows	p. 11
Clouds and cloud droplets	p. 12
Light	p. 12
Sound	p. 12
The rotation of the Earth	p. 12
The horizon	p. 12
The appearance of distant hills	p. 12
In the "playground": (just to get our feet wetà)	p. 13
Loch Ness-how long to empty it?	p. 13
The grand Canyon-how long to fill it with sand?	p. 14
Just how large an area is a million acres?	p. 15
Twenty-five billion hamburgers-how many have you eaten?	p. 16
How many head of cattle would be required to satisfy the (1978) daily demand for meat in the United States>	p. 16
Why could King Kong never exist?	p. 17
Why do small bugs dislike taking showers?	p. 18
How fast is that raindrop falling?	p. 18
Why can haystacks explode if they're too big?	p. 20
In the garden	p. 24
Why can I see the "whole universe" in my garden globe?	p. 24
How long is that bee going to collect nectar?	p. 25
Why are those drops on the spider's web so evenly spaced?	p. 27
What is the Fibonacci sequence?	p. 31
So what is the "golden angle"?	p. 35
Why are the angles between leaves "just so"?	p. 36
In the neighborhood	p. 43
Can you infer fencepost (or bridge) "shapes" just by walking past them?	p. 43
Can you weigh a pumpkin just by carefully looking at it?	p. 48
Can you determine the paths of low-flying ducks?	p. 53
In the shadows	p. 58
How high is that tree? (An estimate using elliptical light patches)	p. 58
Does my shadow accelerate?	p. 59
How long is the Earth's shadow?	p. 61
And Jupiter's? And Neptune's?	p. 63
How wide is the Moon's shadow?	p. 63
In the sky	p. 64
How far away is the horizon (neglecting refraction)?	p. 64
How far away is that cloud?	p. 66
How well is starlight reflected from a calm body of water?	p. 67
How heavy is that cloud?	p. 71
Why can we see farther in rain than in fog?	p. 72
How far away does that 'road puddle" mirage appear to be?	p. 73
Why is the sky blue?	p. 77
So how much more is violet light scattered than red?	p. 79
What causes variation in colors of butterfly wings, bird plumage, and oil slicks?	p. 80
What causes the metallic colors in that cloud?	p. 84
How do rainbows form? And what are those fringes underneath the primary bow?	p. 85
What about the secondary rainbow?	p. 92
Are there higher-order rainbows?	p. 93
So what is that triple rainbow?	p. 95
Is there a "zeroth"-order rainbow?	p. 98
Can bubbles produce "rainbows"?	p. 99
What would "diamondbows" look like?	p. 100
What causes that ring around the Sun?	p. 101
What is that shaft of light above the setting Sun?	p. 109
What is that colored splotch of light beside the Sun?	p. 111
What's that "smiley face" in the sky?	p. 113
What are those colored rings around the shadow of my plane?	p. 116
Why does geometrical optics imply infinite intensity at the rainbow angle?	p. 118
In the nest	p. 122
How can you model the shape of birds' eggs?	p. 122
What is the sphericity index?	p. 123
Can the shape of an egg be modeled trigonometrically?	p. 124
Can the shape of an egg be modeled algebraically?	p. 127
Can the shape of an egg be modeled using calculus?	p. 130
Can the shape of an egg be modeled geometrically?	p. 134
In (or on) the water	p. 137
What causes a glitter path?	p. 137
What is the path of wave intersections?	p. 140
How fast do waves move on the surface of water?	p. 141
How do moving ships produce that wave pattern?	p. 148
How do rocks in a flowing stream produce different patterns?	p. 152
Can waves be stopped by opposing streams?	p. 154
How far away is the storm?	p. 157
How fast is the calm region of that 'puddle wave" expanding?	p. 158
How much energy do ocean waves have?	p. 160
Does a wave raise the average depth of the water?	p. 162
How can ship wakes prove the Earth is "round"?	p. 164
In the forest	p. 168
How high can trees grow?	p. 168
How much shade does a layer of leaves provide for the layer below?	p. 172
What is the "murmur of the forest"?	p. 174
How opaque is a wood or forest?	p. 176
Why do some trees have "turmors"?	p. 179
In the national park	p. 183
What shapes are river meanders?	p. 183
Why are mountain shadows triangular?	p. 189
Why does Zion Arch appear circular?	p. 191
In the night sky	p. 194
How are star magnitudes measured?	p. 194
How can I stargaze with a flashlight?	p. 196
How can you model a star?	p. 197
How long would it take the Sun to collapse?	p. 205
What are those small rings around the Moon?	p. 207
How can you model an eclipse of the Sun?	p. 210
At the end à	p. 217
How can you model walking?	p. 217
How "long" is that tree?	p. 221
What are those "rays" I sometimes see at or after sunset?	p. 224
How can twilight help determine the height of the atmosphere?	p. 228
A very short glossary of mathematical terms and functions	p. 231
Answers to questions 1-15	p. 234
Newton's law of cooling	p. 238
More mathematical patterns in nature	p. 240
References	p. 243
Index	p. 247
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