The Beauty Of Numbers In Nature

Think of a zebra's stripes, the complexities of a spider's web, the uniformity of desert dunes, or the spirals in a sunflower head ... think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth forms the principles of mathematics. Starting with the simplest patterns, each chapter looks at a different kind of patterning system and the mathematics that underlies it. In doing so the book also uncovers some universal patterns, both in nature and man-made, from the basic geometry of ancient Greece to the visually startling fractals that we are familiar with today. Elegantly illustrated, The Beauty of Numbers in Nature is an illuminating and engaging vision of how the apparently cold laws of mathematics find expression in the beauty of nature.

From a zebra's stripes to a spider's web: an engaging examination of patterns in nature and the mathematics that underlie them. From a zebra's stripes to a spider's web, from sand dunes to snowflakes, nature is full of patterns underlaid by mathematical principles. In The Beauty of Numbers in Nature, Ian Stewart shows how life forms from the principles of mathematics. Each chapter in The Beauty of Numbers in Nature explores a different kind of patterning system and its mathematical underpinnings. In doing do, the book also uncovers some universal patterns—both in nature and made by humans—from the basic geometry of ancient Greece to the complexities of fractals. Stewart draws on a wide range of sources to examine the mathematics of patterns: the Pythagoreans' obsession with numbers as the philosophical basis of the universe; a great mathematician who wondered about how a violin makes music; a clerk in a patent office who realized that space and time can get mixed together; a maverick mathematician who questioned why nature spurns such regular geometric shapes as spheres and cylinders in favor of jagged lightning bolts, asymmetrically branching trees, and the uneven terrain of mountainsides. The book begins with a simple and often-asked question about the shape and individual uniqueness of snowflakes. How can such a strange mixture of regularity and irregularity exist in a tiny bit of frozen water? By the end of the book, readers will have learned that mathematical patterns can come in many guises, some of which don't resemble patterns at all.

"It appears to us that the universe is structured in a deeply mathematical way. Falling bodies fall with predictable accelerations. Eclipses can be accurately forecast centuries in advance. Nuclear power plants generate electricity according to well-known formulas. But those examples are the tip of the iceberg. In Nature's Numbers, Ian Stewart presents many more, each charming in its own way.. Stewart admirably captures compelling and accessible mathematical ideas along with the pleasure of thinking of them. He writes with clarity and precision. Those who enjoy this sort of thing will love this book."—Los Angeles Times

ALSC Notable Children's Book A wonderful introduction to one of the most beautiful connections between mathematics and the natural world–the Fibonacci sequence–through a series of stunning nature photographs. Discover the biggest mathematical mystery in nature—Fibonacci numbers! Named after a famous mathematician, the number pattern is simple and starts with: 1, 1, 2, 3, 5, 8, 13. Each number in the sequence comes from adding the two numbers before it. What's the mystery? The pattern crops up in the most unexpected places. You'll find it in the disk of a sunflower, the skin of a pineapple, and the spiral of a nautilus shell. This book brings math alive, celebrates science, and will inspire kids to see nature through new eyes.

Are you "proud" to admit that you never liked math? Were never good in math? Are you struggling to pique your students' interest in math? Are you bored by the routine, mechanical aspects of teaching to the test in mathematics? This book offers a plethora of ideas to enrich your instruction and helps you to explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, Alfred S. Posamentier reveals the amazing symmetries, patterns, processes, paradoxes, and surprises that await students and teachers who look beyond the rote to discover wonders that have fascinated generations of great thinkers. Using the guided examples, help students explore the many marvels of math, including * The Amazing Number 1,089. Follow the instructions to reverse three-digit numbers, subtract them, and continue until everyone winds up with . . . 1,089! * The Pigeonhole Principle. All students know that guesstimating works sometimes, but now they can use this strategy to solve problems. * The Beautiful Magic Square. Challenge students to create their own magic squares and then discover the properties of Dürer's Magic Square. The author presents examples to entice students (and teachers) to study mathematics--to make mathematics a popular subject, not one to dread or avoid. Note: This product listing is for the Adobe Acrobat (PDF) version of the book.

From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Designed for ages grades K-5 and to be done at home or with small groups, this interactive multi-activity mini-course introduces children to the Fibonacci sequence and how math and art can intersect with science and nature. It takes one of the most fascinating mathematical topics, the Fibonacci sequence, and the related Golden Ratio, and shows children how math can be used to see patterns in all kinds of natural settings, such as leaf arrangement, snail shells, and hurricanes. The mini-course includes a richly illustrated story-based lesson, as well as games, activities, and projects that appeal to all types of learners. An illustrated story about Fibonacci and his imaginary bean stalk introduces children to the mathematical concepts of sequences and sets, as well as an illustration of Fibonacci's famous pattern. By creating their own Fibonacci Flower Books, children then begin to investigate some of the places the famous sequence is found in nature. Children are then encouraged to visualize the relationship between numbers and shapes as they learn how to create their own Golden Spirals from the Fibonacci sequence. What elements of nature can they see in their spirals? Next, in the Purely Numbers Game, children reinforce and expand their understanding of these mathematical concepts by making their own mathematical sets. Finally, children will have fun testing how well they know the Fibonacci sequence by playing the movement-based Walk for Fibonacci. Most materials needed to complete the mini-course can be cut from the book. The mini-course requires only a few additional common household items to complete the activities: Colored pencils, eraser, pencil, scissors, mathematical compass (optional), two dice, blank paper, tape or glue. Upon completing the mini-course, children will be provided with links to additional online resources and will earn new concept badges for their Science Tool Kit (included in the mini-course)- - including Sequence, Pattern, Phyllotaxis, Opposite Phyllotaxis, and Sum.

How our intuitive understanding of numbers is deeply rooted in our biology, traceable through both evolution and development. Humans' understanding of numbers is intuitive. Infants are able to estimate and calculate even before they learn the words for numbers. How have we come to possess this talent for numbers? In A Brain for Numbers, Andreas Nieder explains how our brains process numbers. He reports that numerical competency is deeply rooted in our biological ancestry; it can be traced through both the evolution of our species and the development of our individual minds. It is not, as it has been traditionally explained, based on our ability to use language. We owe our symbolic mathematical skills to the nonsymbolic numerical abilities that we inherited from our ancestors. The principles of mathematics, Nieder tells us, are reflections of the innate dispositions wired into the brain. Nieder explores how the workings of the brain give rise to numerical competence, tracing flair for numbers to dedicated “number neurons” in the brain. Drawing on a range of methods including brain imaging techniques, behavioral experiments, and twin studies, he outlines a new, integrated understanding of the talent for numbers. Along the way, he compares the numerical capabilities of humans and animals, and discusses the benefits animals reap from such a capability. He shows how the neurobiological roots of the brain's nonverbal quantification capacity are the evolutionary foundation of more elaborate numerical skills. He discusses how number signs and symbols are represented in the brain; calculation capability and the “neuromythology” of mathematical genius; the “start-up tools” for counting and developmental of dyscalculia (a number disorder analogous to the reading disorder dyslexia); and how the brain processes the abstract concept of zero.