What is included with this book?
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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