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A Mathematical Nature Walk
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 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.
280 pages, Hardcover
First published March 14, 2008
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Displaying 1 - 8 of 8 reviews
May 31, 2021
I enjoyed this book, but it was not what I was expecting. From its title I thought it would be a more or less conventional natural history book, describing the plants, animals, and scenery of forest paths and seashore strolls, with the added interest of some math and physics to give greater insight into the surroundings. Instead, it consists of ninety-six extended word problems framed around natural phenomena, some silly and trivial, such as how long it would take to fill the Grand Canyon with sand, and some much more involved, such as employing optical physics to describe atmospheric phenomena, or the amount of fusion-generated outward force necessary for the sun to counteract its own gravity. There is a lot of calculus in this book, as well as algebra, geometry, trigonometry and even a bit of differential equations.
The format initially took me aback, but as I worked my way through the questions I found myself appreciating the elegance of the algorithms, as each step proceeded logically to an answer. Although I haven’t used calculus in a long long time, I was pleased with how much I was able to dredge up from my college memories. Considering how hard I worked to pass those classes, I was happy to know that some of it stuck around in the dim recesses of my brain. There were times when I needed to consult the internet to refresh my memory about certain functions, but the book was a rewarding experience. I particularly enjoyed the section on calculating eclipses, and found myself saying, “So that’s how it’s done.”
Even some things that many people already know are explained in a clear way that can add to one’s understanding. For instance, to the age-old question “Why is the sky blue?” here is a well written answer:
There were also explanations of things that I had never thought about, the kind of things that make you go, “Hmm,” as in the description of river meanders.
So, what other of questions does the book tackle? Here is a selection:
- Why could King Kong never exist?
- How fast is that raindrop falling?
- Why can haystacks spontaneously combust if they’re too big?
- Why are the drops on the spider’s web so evenly spaced?
- What is the Fibonacci Sequence and how is it used?
- Can the shape of a bird’s egg be modeled using trigonometry? Algebraically? With calculus? Geometrically?
- How fast do waves move on the surface of water?
- How can ships’ wakes prove the Earth is round?
- How are star magnitudes measured?
I did have some problems with the book, although they had nothing to do with the author or his explanations. I got the book from my local library via the Hoopla app, which is not my favorite e-book format. Illustrations of the more complex steps in the problems, such as those using integrals or Greek letters, are rendered as graphics. Even on a ten inch tablet they were smaller than was comfortable, and were invariably fuzzy, making them even harder to read. Hoopla does not support the fingertip pinch-and-spread technique of most Apple apps, so reading the equations was harder than it need have been. Hoopla also allows searches on only single words, so if, for example, you wanted to find a phrase with the word “oscillate” in it, you get a list of every instance of that word in the entire book, and have to scroll through them to find the one you want; trying to search on more than one word crashes the app. Finally, the page numbering system did not work at all; sometimes page numbers even went backwards, and once I hit page 48 it stayed at that number for the remainder of the book. Clearly Hoopla needs work.
With those reservations aside, I enjoyed this book. The step by step solutions to the problems were well presented. The author teaches math, and has clearly developed a feel for how to provide just the right amount of information to lead students to the correct answers. The book also has an excellent bibliography, and I added several additional titles to my to-read list.
The format initially took me aback, but as I worked my way through the questions I found myself appreciating the elegance of the algorithms, as each step proceeded logically to an answer. Although I haven’t used calculus in a long long time, I was pleased with how much I was able to dredge up from my college memories. Considering how hard I worked to pass those classes, I was happy to know that some of it stuck around in the dim recesses of my brain. There were times when I needed to consult the internet to refresh my memory about certain functions, but the book was a rewarding experience. I particularly enjoyed the section on calculating eclipses, and found myself saying, “So that’s how it’s done.”
Even some things that many people already know are explained in a clear way that can add to one’s understanding. For instance, to the age-old question “Why is the sky blue?” here is a well written answer:
The electric field of the incident sunlight causes electrons in the molecules to oscillate, and re-radiate the light; this is what is meant here by the word ‘scattering.’ The degree of scattering is inversely proportional to the fourth power of the wavelength of the light; blue light being of shorter wavelength than red, it is scattered the most. Consequently, we see blue sky except when we look in the direction of the sun at sunrise or sunset, where the long path through which the light passes depletes the blue light, leaving a predominately longer wavelength red light.
There were also explanations of things that I had never thought about, the kind of things that make you go, “Hmm,” as in the description of river meanders.
let’s start with some observational details, obtained from a study of more than fifty rivers by Luna Leopold and coworkers. They are of interest in connection with the apparent regular ‘sinuosity’ of rivers the world over. From their study of more than 50 rivers, the following statements can be made:
(i) No river, regardless of size, runs straight for more than 10 times its width.
(ii) The radius of a bend is nearly always 2-3 times the width of the river at that point.
(iii) The wavelength (distance between analogous points of analogous bends) is 7-10 times the (average) width.”
So, what other of questions does the book tackle? Here is a selection:
- Why could King Kong never exist?
- How fast is that raindrop falling?
- Why can haystacks spontaneously combust if they’re too big?
- Why are the drops on the spider’s web so evenly spaced?
- What is the Fibonacci Sequence and how is it used?
- Can the shape of a bird’s egg be modeled using trigonometry? Algebraically? With calculus? Geometrically?
- How fast do waves move on the surface of water?
- How can ships’ wakes prove the Earth is round?
- How are star magnitudes measured?
I did have some problems with the book, although they had nothing to do with the author or his explanations. I got the book from my local library via the Hoopla app, which is not my favorite e-book format. Illustrations of the more complex steps in the problems, such as those using integrals or Greek letters, are rendered as graphics. Even on a ten inch tablet they were smaller than was comfortable, and were invariably fuzzy, making them even harder to read. Hoopla does not support the fingertip pinch-and-spread technique of most Apple apps, so reading the equations was harder than it need have been. Hoopla also allows searches on only single words, so if, for example, you wanted to find a phrase with the word “oscillate” in it, you get a list of every instance of that word in the entire book, and have to scroll through them to find the one you want; trying to search on more than one word crashes the app. Finally, the page numbering system did not work at all; sometimes page numbers even went backwards, and once I hit page 48 it stayed at that number for the remainder of the book. Clearly Hoopla needs work.
With those reservations aside, I enjoyed this book. The step by step solutions to the problems were well presented. The author teaches math, and has clearly developed a feel for how to provide just the right amount of information to lead students to the correct answers. The book also has an excellent bibliography, and I added several additional titles to my to-read list.
April 27, 2021
I really liked this one, despite having difficulties understanding most of it (i’ve never been good with math). But! it woke an interest in me, and some sort of fascination, and it made me think and reflect (in the capacity I’m able lol)
January 11, 2015
Many people have pointed out that mathematics is surprisingly effective at describing, modeling and explaining natural phenomena. This book is one of the best demonstrations of that awesome fact. Adam uses his powers of observation, occasionally a camera and his knowledge of mathematics to encounter and then mathematically describe ninety-six ordinary natural phenomena.
Some of the questions answered are:
*) Can you see farther in the rain or in fog?
*) Why can haystacks explode if they are too large?
*) What causes rings around the sun?
*) What is the murmur of the forest?
*) How long is the Earth's shadow?
While the questions are interesting, the true significance of the book is the quality of the answers. Adam does a superb job in explaining why things appear the way they do. No corners are cut in the mathematics, when calculus is needed to explain something it is used to the extent necessary.
This book would be an excellent textbook for courses in applied physics or mathematics where the research component is simply walking around outside, looking at things and then asking the simple but important question, "Why is that?"
Published in Journal of Recreational Mathematics, reprinted with permission
Some of the questions answered are:
*) Can you see farther in the rain or in fog?
*) Why can haystacks explode if they are too large?
*) What causes rings around the sun?
*) What is the murmur of the forest?
*) How long is the Earth's shadow?
While the questions are interesting, the true significance of the book is the quality of the answers. Adam does a superb job in explaining why things appear the way they do. No corners are cut in the mathematics, when calculus is needed to explain something it is used to the extent necessary.
This book would be an excellent textbook for courses in applied physics or mathematics where the research component is simply walking around outside, looking at things and then asking the simple but important question, "Why is that?"
Published in Journal of Recreational Mathematics, reprinted with permission
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December 29, 2025Wonderful Math and Physics of Nature Book Using Real Approximations
If you are looking for a book that gives you real mathematics modeling for phenomena in nature, this is perfect. Yes, you will need some math sophistication to get the most out of this book, but it offers a great ratio of understanding to math equations used. This is a rare book because it caters more to the math part of math in nature.
If you are looking for a book that gives you real mathematics modeling for phenomena in nature, this is perfect. Yes, you will need some math sophistication to get the most out of this book, but it offers a great ratio of understanding to math equations used. This is a rare book because it caters more to the math part of math in nature.
September 16, 2017
An eclectic book in selection of material and variation of mathematical depth, but still got me thinking about the world. A good holiday read.
Did Not Finish
June 24, 2026I started this on my Kindle and got to about page 25, but doubt that I'll continue. I think the math is over my head—but that impression might be affected by how hard the equations are to read in my Kindle. Very poor display! I just opened this in the Kindle app on my iPad, and the equations are easier to read. But I still wasn't able to find the color plates, supposedly grouped in a special section in the middle of the book. I'd be happy to see them in grayscale in my Kindle or in color on my iPad, but they just aren't there.
March 14, 2012
A Mathematical Nature Walk is a collection of problems that highlight the use of mathematical modeling to explain and predict phenomena in nature. The math required in most of the problems requires at least high school math and some college level Calculus. All of the problems (even the simplest) require some deep thinking about the mathematics involved.
As a book, I much prefer to dip in and of this work like a collection of poetry. There is something to be found in each question, but it is difficult to gather in one sustained reading cover to cover.
As a book, I much prefer to dip in and of this work like a collection of poetry. There is something to be found in each question, but it is difficult to gather in one sustained reading cover to cover.
May 25, 2010
I'm grateful for his creativity and interest. He has corrolated mathematics to the real world and shown why it matters and how it can be fun. It does not dumb us down. The copy I checked out of the library, however, had handwritten corrections or questions about his mathematical assertions on pp 145,146,147, and I've spoken with an electrical engineer who quit reading at about that point for the same reasons.
Displaying 1 - 8 of 8 reviews