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# A Mathematical Nature Walk

**John A. Adam **

- Hardcover2009Hardcover27.9522.95ISBN9780691128955280 pp.6 x 9 1/417 color illus. 22 halftones. 97 line illus.Live
- Paperback2011Paperback21.9517.95ISBN9780691152653264 pp.6 x 9 1/417 color illus. 22 halftones. 97 line illus.Live

- E-bookISBN9781400832903

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 Walk* will 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.

*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 of

*Mathematics in Nature*(both Princeton).

## Reviews

**--Laurence A. Marschall,**

*Natural History***--Dominic Lenton,**

*Engineering & Technology***--**

*Conservation Magazine***--David S. Mazel,**

*MAA Reviews***--**

*Mathematics Teacher***--**

*Physics World**Mathematics in Nature*to make them accessible to a larger audience. Beyond insights into specific questions about nature, the general reader will find here a remarkably lucid explanation of how mathematicians create a formulaic model that mimics the key features of some natural phenomenon. Adam particularly highlights the importance in this process of solving inverse problems. Ordinary math becomes adventure."

**--**

*Booklist***--**

*Natural History**A Mathematical Nature Walk*by John Adam, which considers some of the natural phenomena that might be encountered on a walk in the countryside (or even just a wander around one's own garden)."

**--Sarah Shepherd,**

*iSquared***--**

*Good Book Guide***--Philip McIntosh,**

*Suite101.com*## Endorsements

**--Peter Pesic, author of**

*Sky in a Bottle***--Hans Christian von Baeyer, author of**

*Information: The New Language of Science***--Neil Downie, author of**

*Vacuum Bazookas, Electric Rainbow Jelly, and 27 Other Saturday Science Projects***--Alfred S. Posamentier, coauthor of**

*The Fabulous Fibonacci Numbers**A Mathematical Nature Walk*is a true gem of popular scientific writing. He adroitly does what all good science writers should do: he inspires readers first to observe and then to analyze the world outside their windows."

**--Raymond Lee, author of**

*The Rainbow Bridge***--Kenneth G. Libbrecht, author of**

*The Snowflake: Winter's Secret Beauty***--Will Wilson, Duke University**

*A Mathematical Nature Walk*, John Adam encourages readers to explore everyday observations of the natural world from a mathematical point of view. The problems are presented in an engaging style and most of the mathematics is well within the grasp of beginning college students."

**--Brian Sleeman, University of Leeds**

## Table of Contents

Acknowledgments xix

Introduction 1

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.11: 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

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.40: How far away is that cloud? 66

Q.41: 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

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 is 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? 111

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 cause

## Other Books Written by this Author(s)

- John A. Adam

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