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| Preface | |
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| Acknowledgements | |
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| Introduction | |
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| At the beginning: (General questions to challenge our powers of observation, estimation, and physical intuition)� | |
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| Rainbows | |
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| Shadows | |
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| Clouds and cloud droplets | |
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| Light | |
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| Sound | |
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| The rotation of the Earth | |
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| The horizon | |
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| The appearance of distant hills | |
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| In the "playground": (just to get our feet wet�) | |
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| Loch Ness-how long to empty it? | |
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| The grand Canyon-how long to fill it with sand? | |
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| Just how large an area is a million acres? | |
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| Twenty-five billion hamburgers-how many have you eaten? | |
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| How many head of cattle would be required to satisfy the (1978) daily demand for meat in the United States> | |
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| Why could King Kong never exist? | |
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| Why do small bugs dislike taking showers? | |
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| How fast is that raindrop falling? | |
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| Why can haystacks explode if they're too big? | |
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| In the garden | |
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| Why can I see the "whole universe" in my garden globe? | |
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| How long is that bee going to collect nectar? | |
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| Why are those drops on the spider's web so evenly spaced? | |
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| What is the Fibonacci sequence? | |
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| So what is the "golden angle"? | |
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| Why are the angles between leaves "just so"? | |
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| In the neighborhood | |
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| Can you infer fencepost (or bridge) "shapes" just by walking past them? | |
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| Can you weigh a pumpkin just by carefully looking at it? | |
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| Can you determine the paths of low-flying ducks? | |
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| In the shadows | |
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| How high is that tree? (An estimate using elliptical light patches) | |
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| Does my shadow accelerate? | |
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| How long is the Earth's shadow? | |
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| And Jupiter's? And Neptune's? | |
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| How wide is the Moon's shadow? | |
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| In the sky | |
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| How far away is the horizon (neglecting refraction)? | |
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| How far away is that cloud? | |
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| How well is starlight reflected from a calm body of water? | |
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| How heavy is that cloud? | |
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| Why can we see farther in rain than in fog? | |
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| How far away does that 'road puddle" mirage appear to be? | |
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| Why is the sky blue? | |
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| So how much more is violet light scattered than red? | |
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| What causes variation in colors of butterfly wings, bird plumage, and oil slicks? | |
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| What causes the metallic colors in that cloud? | |
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| How do rainbows form? And what are those fringes underneath the primary bow? | |
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| What about the secondary rainbow? | |
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| Are there higher-order rainbows? | |
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| So what is that triple rainbow? | |
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| Is there a "zeroth"-order rainbow? | |
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| Can bubbles produce "rainbows"? | |
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| What would "diamondbows" look like? | |
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| What causes that ring around the Sun? | |
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| What is that shaft of light above the setting Sun? | |
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| What is that colored splotch of light beside the Sun? | |
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| What's that "smiley face" in the sky? | |
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| What are those colored rings around the shadow of my plane? | |
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| Why does geometrical optics imply infinite intensity at the rainbow angle? | |
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| In the nest | |
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| How can you model the shape of birds' eggs? | |
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| What is the sphericity index? | |
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| Can the shape of an egg be modeled trigonometrically? | |
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| Can the shape of an egg be modeled algebraically? | |
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| Can the shape of an egg be modeled using calculus? | |
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| Can the shape of an egg be modeled geometrically? | |
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| In (or on) the water | |
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| What causes a glitter path? | |
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| What is the path of wave intersections? | |
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| How fast do waves move on the surface of water? | |
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| How do moving ships produce that wave pattern? | |
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| How do rocks in a flowing stream produce different patterns? | |
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| Can waves be stopped by opposing streams? | |
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| How far away is the storm? | |
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| How fast is the calm region of that 'puddle wave" expanding? | |
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| How much energy do ocean waves have? | |
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| Does a wave raise the average depth of the water? | |
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| How can ship wakes prove the Earth is "round"? | |
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| In the forest | |
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| How high can trees grow? | |
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| How much shade does a layer of leaves provide for the layer below? | |
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| What is the "murmur of the forest"? | |
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| How opaque is a wood or forest? | |
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| Why do some trees have "turmors"? | |
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| In the national park | |
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| What shapes are river meanders? | |
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| Why are mountain shadows triangular? | |
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| Why does Zion Arch appear circular? | |
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| In the night sky | |
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| How are star magnitudes measured? | |
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| How can I stargaze with a flashlight? | |
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| How can you model a star? | |
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| How long would it take the Sun to collapse? | |
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| What are those small rings around the Moon? | |
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| How can you model an eclipse of the Sun? | |
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| At the end � | |
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| How can you model walking? | |
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| How "long" is that tree? | |
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| What are those "rays" I sometimes see at or after sunset? | |
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| How can twilight help determine the height of the atmosphere? | |
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| A very short glossary of mathematical terms and functions | |
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| Answers to questions 1-15 | |
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| Newton's law of cooling | |
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| More mathematical patterns in nature | |
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| References | |
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| Index | |