Mathematical Nature Walk

ISBN-10: 0691152659

ISBN-13: 9780691152653

Edition: 2012

Authors: John A. Adam

List price: $17.95 Buy it from $14.19
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Description:

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.
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Book details

List price: $17.95
Copyright year: 2012
Publisher: Princeton University Press
Publication date: 10/2/2011
Binding: Paperback
Pages: 264
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.056
Language: English

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

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