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A mathematical nature walk /
John A. Adam.
imprint
Princeton : Princeton University Press, c2009.
description
xx, 248 p.
ISBN
0691128952 (hardcover : alk. paper), 9780691128955 (hardcover : alk. paper)
format(s)
Book
Holdings
More Details
author
imprint
Princeton : Princeton University Press, c2009.
isbn
0691128952 (hardcover : alk. paper)
9780691128955 (hardcover : alk. paper)
catalogue key
6828171
 
Includes bibliographical references and index.
A Look Inside
Excerpts
Flap Copy
"Finally a book that shows the general reader how mathematics can explain the natural phenomena that we continuously encounter but rarely understand. John Adam answers questions about nature's secrets--many of which we haven't even thought to ask. This is a delightful book."--Alfred S. Posamentier, coauthor ofThe Fabulous Fibonacci Numbers"John Adam'sA Mathematical Nature Walkis 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 ofThe Rainbow Bridge"With a mathematician's eye and a playful wit, John Adam takes a walk through the woods and returns with stories aplenty! His narratives are about nature and how things work, about looking analytically at the world around us, and about the art of creating mathematical models. For anyone with a mathematical bent who has ever asked 'what is that?,' this book will provide an interesting read and a valuable resource."--Kenneth G. Libbrecht, author ofThe Snowflake: Winter's Secret Beauty"Do not miss this memorable walk with John Adam, filled with delightful surprises that bring together nature, mathematics, and the infectious pleasure of thought, culminating in a special kind of wonder."--Peter Pesic, author ofSky in a Bottle"For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature."--Hans Christian von Baeyer, author ofInformation: The New Language of Science"John Adam presents a wonderful set of mathematical inquiries into a broad range of natural phenomena. This rich book will be interesting to mathematically minded readers who are inspired by nature."--Will Wilson, Duke University"InA 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
Flap Copy
"Finally a book that shows the general reader how mathematics can explain the natural phenomena that we continuously encounter but rarely understand. John Adam answers questions about nature's secrets--many of which we haven't even thought to ask. This is a delightful book."--Alfred S. Posamentier, coauthor of The Fabulous Fibonacci Numbers "John Adam's 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 "With a mathematician's eye and a playful wit, John Adam takes a walk through the woods and returns with stories aplenty! His narratives are about nature and how things work, about looking analytically at the world around us, and about the art of creating mathematical models. For anyone with a mathematical bent who has ever asked 'what is that?,' this book will provide an interesting read and a valuable resource."--Kenneth G. Libbrecht, author of The Snowflake: Winter's Secret Beauty "Do not miss this memorable walk with John Adam, filled with delightful surprises that bring together nature, mathematics, and the infectious pleasure of thought, culminating in a special kind of wonder."--Peter Pesic, author of Sky in a Bottle "For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature."--Hans Christian von Baeyer, author of Information: The New Language of Science "When you see a spider's web bedecked with morning dew like strings of pearls or the lazy bends in a distant river valley, you are seeing mathematics as well as beauty. You will find equations in A Mathematical Nature Walk for the evanescent colors of the sky--as well as for why you can't fly over a rainbow. John Adam can help you see a world of algebra in a drop of water, and a Fibonacci sequence in a wild flower."--Neil Downie, author of Vacuum Bazookas, Electric Rainbow Jelly, and 27 Other Saturday Science Projects "John Adam presents a wonderful set of mathematical inquiries into a broad range of natural phenomena. This rich book will be interesting to mathematically minded readers who are inspired by nature."--Will Wilson, Duke University "In 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
Flap Copy
"Finally a book that shows the general reader how mathematics can explain the natural phenomena that we continuously encounter but rarely understand. John Adam answers questions about nature's secrets--many of which we haven't even thought to ask. This is a delightful book."--Alfred S. Posamentier, coauthor ofThe Fabulous Fibonacci Numbers"John Adam'sA Mathematical Nature Walkis 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 ofThe Rainbow Bridge"With a mathematician's eye and a playful wit, John Adam takes a walk through the woods and returns with stories aplenty! His narratives are about nature and how things work, about looking analytically at the world around us, and about the art of creating mathematical models. For anyone with a mathematical bent who has ever asked 'what is that?,' this book will provide an interesting read and a valuable resource."--Kenneth G. Libbrecht, author ofThe Snowflake: Winter's Secret Beauty"Do not miss this memorable walk with John Adam, filled with delightful surprises that bring together nature, mathematics, and the infectious pleasure of thought, culminating in a special kind of wonder."--Peter Pesic, author ofSky in a Bottle"For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature."--Hans Christian von Baeyer, author ofInformation: The New Language of Science"When you see a spider's web bedecked with morning dew like strings of pearls or the lazy bends in a distant river valley, you are seeing mathematics as well as beauty. You will find equations in A Mathematical Nature Walk for the evanescent colors of the sky--as well as for why you can't fly over a rainbow. John Adam can help you see a world of algebra in a drop of water, and a Fibonacci sequence in a wild flower."--Neil Downie, author ofVacuum Bazookas, Electric Rainbow Jelly, and 27 Other Saturday Science Projects"John Adam presents a wonderful set of mathematical inquiries into a broad range of natural phenomena. This rich book will be interesting to mathematically minded readers who are inspired by nature."--Will Wilson, Duke University"InA 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
Flap Copy
"Finally a book that shows the general reader how mathematics can explain the natural phenomena that we continuously encounter but rarely understand. John Adam answers questions about natures secrets--many of which we havent even thought to ask. This is a delightful book."-- Alfred S. Posamentier, coauthor of The Fabulous Fibonacci Numbers "John Adams 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 "With a mathematicians eye and a playful wit, John Adam takes a walk through the woods and returns with stories aplenty! His narratives are about nature and how things work, about looking analytically at the world around us, and about the art of creating mathematical models. For anyone with a mathematical bent who has ever asked what is that?, this book will provide an interesting read and a valuable resource."-- Kenneth G. Libbrecht, author of The Snowflake: Winters Secret Beauty "Do not miss this memorable walk with John Adam, filled with delightful surprises that bring together nature, mathematics, and the infectious pleasure of thought, culminating in a special kind of wonder."-- Peter Pesic, author of Sky in a Bottle "For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature."-- Hans Christian von Baeyer, author of Information: The New Language of Science "When you see a spiders web bedecked with morning dew like strings of pearls or the lazy bends in a distant river valley, you are seeing mathematics as well as beauty. You will find equations in A Mathematical Nature Walk for the evanescent colors of the sky--as well as for why you cant fly over a rainbow. John Adam can help you see a world of algebra in a drop of water, and a Fibonacci sequence in a wild flower."-- Neil Downie, author of Vacuum Bazookas, Electric Rainbow Jelly, and 27 Other Saturday Science Projects "John Adam presents a wonderful set of mathematical inquiries into a broad range of natural phenomena. This rich book will be interesting to mathematically minded readers who are inspired by nature."-- Will Wilson, Duke University "In 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
Full Text Reviews
Appeared in Choice on 2009-11-01:
This work discusses questions about common occurrences in nature and how to solve them using various mathematics. Adams (Old Dominion Univ.; coauthor, Guesstimation, CH, Nov'08, 46-1541; Mathematics in Nature, CH, Jul'04, 41-6484) writes: "The book is written for anyone interested in nature, and who has willingness to think, question, and encounter a modicum of mathematics along the way." The work takes the form of 96 questions. Though it is not a textbook on modeling, the structure lends itself to using the questions to supplement perhaps a more traditional modeling book. The mathematics involved varies with the questions. For example, one question is "The Grand Canyon--How Long to Fill It with Sand?" The solution uses arithmetic. On the other hand, the question "What Causes That Ring around the Sun?" involves more sophisticated mathematics such as trigonometry and physics. This volume can suit a wide range of audiences. An advanced undergraduate may find it interesting to look at all the "mathematics" in nature, while a faculty member may want to use some of the questions in courses such as algebra, modeling, calculus, or differential equations to supplement the material. Summing Up: Recommended. Lower- and upper-division undergraduates, researchers/faculty, and general readers. S. L. Sullivan Catawba College
Reviews
Review Quotes
A catalogue of playful inquiries and their mathematical solutions.
"A catalogue of playful inquiries and their mathematical solutions."-- Conservation Magazine
A catalogue of playful inquiries and their mathematical solutions. -- Conservation Magazine
Adam has written a terrific book that takes his earlier work a step further. . . . [T]his is a well written guide not only to seeing our world with simplified and useful models and mathematics, but to asking good questions of what we see and then answering those questions on our own. I found the book delightful, engaging, and interesting. It's written for anyone with a calculus background, and that's all one needs. If you're looking for a fun book with a touch of complexity, this is a good one.
"Adam has written a terrific book that takes his earlier work a step further. . . . [T]his is a well written guide not only to seeing our world with simplified and useful models and mathematics, but to asking good questions of what we see and then answering those questions on our own. I found the book delightful, engaging, and interesting. It's written for anyone with a calculus background, and that's all one needs. If you're looking for a fun book with a touch of complexity, this is a good one."-- David S. Mazel, MAA Reviews
Adam has written a terrific book that takes his earlier work a step further. . . . [T]his is a well written guide not only to seeing our world with simplified and useful models and mathematics, but to asking good questions of what we see and then answering those questions on our own. I found the book delightful, engaging, and interesting. It's written for anyone with a calculus background, and that's all one needs. If you're looking for a fun book with a touch of complexity, this is a good one. -- David S. Mazel, MAA Reviews
[A]dam's love of both nature and mathematics is obvious, and his chatty style and sense of humour--look out for the question about spontaneously combusting haystacks--enliven a book that will get readers thinking as well as itching for a pleasant stroll.
"[A]dam's love of both nature and mathematics is obvious, and his chatty style and sense of humour--look out for the question about spontaneously combusting haystacks--enliven a book that will get readers thinking as well as itching for a pleasant stroll."-- Physics World
[A]dam's love of both nature and mathematics is obvious, and his chatty style and sense of humour--look out for the question about spontaneously combusting haystacks--enliven a book that will get readers thinking as well as itching for a pleasant stroll. -- Physics World
[A] snappy guide to the mathematics of the outdoors. . . . A sharp eye and an ingenious mind are at work on every page. . . . Read this book with pencil and paper in hand. Then go forth, enjoy the view, and impress your friends.
"[A] snappy guide to the mathematics of the outdoors. . . . A sharp eye and an ingenious mind are at work on every page. . . . Read this book with pencil and paper in hand. Then go forth, enjoy the view, and impress your friends."-- Laurence A. Marschall, Natural History
[A] snappy guide to the mathematics of the outdoors. . . . A sharp eye and an ingenious mind are at work on every page. . . . Read this book with pencil and paper in hand. Then go forth, enjoy the view, and impress your friends. -- Laurence A. Marschall, Natural History
For teachers who are interested in seeing how what they teach might be used or for students or parents who might be interested in seeing how mathematics might be used, this is an intriguing book.
"For teachers who are interested in seeing how what they teach might be used or for students or parents who might be interested in seeing how mathematics might be used, this is an intriguing book."-- Mathematics Teacher
For teachers who are interested in seeing how what they teach might be used or for students or parents who might be interested in seeing how mathematics might be used, this is an intriguing book. -- Mathematics Teacher
If you are a walker, as I am, your daypack probably contains sunscreen, a poncho, a floppy hat, and a pair of binoculars. After reading this snappy guide to the mathematics of the outdoors, by John Adam, a professor of mathematics at Old Dominion University in Virginia, you might consider tossing in a programmable calculator. . . . A sharp eye and an ingenious mind are at work on every page. . . . Read this book with pencil and paper in hand. Then go forth, enjoy the view, and impress your friends.
"If you are a walker, as I am, your daypack probably contains sunscreen, a poncho, a floppy hat, and a pair of binoculars. After reading this snappy guide to the mathematics of the outdoors, by John Adam, a professor of mathematics at Old Dominion University in Virginia, you might consider tossing in a programmable calculator. . . . A sharp eye and an ingenious mind are at work on every page. . . . Read this book with pencil and paper in hand. Then go forth, enjoy the view, and impress your friends."-- Natural History
If you are a walker, as I am, your daypack probably contains sunscreen, a poncho, a floppy hat, and a pair of binoculars. After reading this snappy guide to the mathematics of the outdoors, by John Adam, a professor of mathematics at Old Dominion University in Virginia, you might consider tossing in a programmable calculator. . . . A sharp eye and an ingenious mind are at work on every page. . . . Read this book with pencil and paper in hand. Then go forth, enjoy the view, and impress your friends. -- Natural History
Indeed, Adam has deliberately reworked topics treated in 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.
Indeed, Adam has deliberately reworked topics treated inMathematics in Natureto 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.
"Indeed, Adam has deliberately reworked topics treated in 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
Indeed, Adam has deliberately reworked topics treated in 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
Indeed, Adam has deliberately reworked topics treated inMathematics in Natureto 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
Mathematics professor John Adam has come up with a novel combination. This book will provide anyone with a solid grounding in mathematics with enough conversation starters to keep fellow walkers' brains working as hard as their legs.
"Mathematics professor John Adam has come up with a novel combination. This book will provide anyone with a solid grounding in mathematics with enough conversation starters to keep fellow walkers' brains working as hard as their legs."-- Dominic Lenton, Engineering & Technology
Mathematics professor John Adam has come up with a novel combination. This book will provide anyone with a solid grounding in mathematics with enough conversation starters to keep fellow walkers' brains working as hard as their legs. -- Dominic Lenton, Engineering & Technology
[S]urprising and entertaining. . . . Adam's book is lucidly written, making it suitable for people of all ages.
"[S]urprising and entertaining. . . . Adam's book is lucidly written, making it suitable for people of all ages."-- Good Book Guide
[S]urprising and entertaining. . . . Adam's book is lucidly written, making it suitable for people of all ages. -- Good Book Guide
The dedicated reader stands a lot to gain from delving into the text and thinking hard about the problems posed. As the saying goes, 'mathematics is not a spectator sport,' so if this book is read with pencil and paper at hand, to scribble along and confirm understanding of the mathematical trains of thought--all the better.
"The dedicated reader stands a lot to gain from delving into the text and thinking hard about the problems posed. As the saying goes, 'mathematics is not a spectator sport,' so if this book is read with pencil and paper at hand, to scribble along and confirm understanding of the mathematical trains of thought--all the better."-- Philip McIntosh, Suite101.com
The dedicated reader stands a lot to gain from delving into the text and thinking hard about the problems posed. As the saying goes, 'mathematics is not a spectator sport,' so if this book is read with pencil and paper at hand, to scribble along and confirm understanding of the mathematical trains of thought--all the better. -- Philip McIntosh, Suite101.com
There are now few (if any) areas of science where mathematics does not play a role and, by extension, many of the sights and sounds of nature can be studied using mathematics. This is the motivation behind 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).
There are now few (if any) areas of science where mathematics does not play a role and, by extension, many of the sights and sounds of nature can be studied using mathematics. This is the motivation behindA Mathematical Nature Walkby 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).
"There are now few (if any) areas of science where mathematics does not play a role and, by extension, many of the sights and sounds of nature can be studied using mathematics. This is the motivation behind 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
There are now few (if any) areas of science where mathematics does not play a role and, by extension, many of the sights and sounds of nature can be studied using mathematics. This is the motivation behind 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
There are now few (if any) areas of science where mathematics does not play a role and, by extension, many of the sights and sounds of nature can be studied using mathematics. This is the motivation behindA Mathematical Nature Walkby 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
Do not miss this memorable walk with John Adam, filled with delightful surprises that bring together nature, mathematics, and the infectious pleasure of thought, culminating in a special kind of wonder.
Finally a book that shows the general reader how mathematics can explain the natural phenomena that we continuously encounter but rarely understand. John Adam answers questions about nature's secrets--many of which we haven't even thought to ask. This is a delightful book.
For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature.
InA 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.
John Adam presents a wonderful set of mathematical inquiries into a broad range of natural phenomena. This rich book will be interesting to mathematically minded readers who are inspired by nature.
John Adam'sA Mathematical Nature Walkis 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.
When you see a spider's web bedecked with morning dew like strings of pearls or the lazy bends in a distant river valley, you are seeing mathematics as well as beauty. You will find equations in A Mathematical Nature Walk for the evanescent colors of the sky--as well as for why you can't fly over a rainbow. John Adam can help you see a world of algebra in a drop of water, and a Fibonacci sequence in a wild flower.
With a mathematician's eye and a playful wit, John Adam takes a walk through the woods and returns with stories aplenty! His narratives are about nature and how things work, about looking analytically at the world around us, and about the art of creating mathematical models. For anyone with a mathematical bent who has ever asked 'what is that?,' this book will provide an interesting read and a valuable resource.
This item was reviewed in:
Booklist, May 2009
Choice, November 2009
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Bowker Data Service Summary
How tall is that tree? How far away is that cloud, and how heavy is it? 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.
Main 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 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.
Main Description
How tall is that tree? How far away is that cloud, and how heavy is it? 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.
Main Description
How tall is that tree? How far away is that cloud, and how heavy is it? 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.
Main Description
How tall is that tree? How far away is that cloud, and how heavy is it? 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 questions 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 only, 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.
Table of Contents
Prefacep. xv
Acknowledgmentsp. xix
Introductionp. 1
At the beginning ... (General questions to challenge our powers of observation, estimation, and physical intuition)p. 11
Rainbowsp. 11
Shadowsp. 11
Clouds and cloud dropletsp. 12
Lightp. 12
Soundp. 12
The rotation of the Earthp. 12
The horizonp. 12
The appearance of distant hillsp. 12
In the "playground" (just to get our feet wet...)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 gardenp. 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 neighborhoodp. 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 shadowsp. 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 skyp. 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 nestp. 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 waterp. 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 forestp. 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 "tumors"?p. 179
In the national parkp. 183
What shapes are river meanders?p. 183
Why are mountain shadows triangular?p. 183
Why does Zion Arch appear circular?p. 191
In the night skyp. 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...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 functionsp. 231
Answers to questions 1-15p. 234
Newton's law of coolingp. 238
More mathematical patterns in naturep. 240
Referencesp. 243
Indexp. 247
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