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The Beauty of Numbers in Nature by Ian Stewart Pdf
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.
"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.
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.
Mathematicians with special interest in biology, physics, geography, astronomy, architecture, design, etc., and being prepared to take pictures at any time, might try to answer unusual questions like the followings: What do a zebra, a tiger shark, and a hard coral have in common? How is this with drying mud, wings of dragon flies, and the structures of leaves? What is the “snail king” and is there also a “worm king”? Which curves stay of the same type after being photographed? Do fishes see like we do if we look through a fisheye lens? Which geometric properties of an object have physical consequences? Which kinds of geometric patterns appear when waves are interfering? In this book you can find 180 double pages with at least as many questions of this kind. The principle to attack a problem is often similar: It starts with a photo that is for some reasons remarkable. In a short description an explanation is offered, including relevant Internet links. Additionally one can frequently find computer simulations in order to illustrate and confirm.
Uncertainty is everywhere. It lurks in every consideration of the future - the weather, the economy, the sex of an unborn child - even quantities we think that we know such as populations or the transit of the planets contain the possibility of error. It's no wonder that, throughout that history, we have attempted to produce rigidly defined areas of uncertainty - we prefer the surprise party to the surprise asteroid. We began our quest to make certain an uncertain world by reading omens in livers, tea leaves, and the stars. However, over the centuries, driven by curiosity, competition, and a desire be better gamblers, pioneering mathematicians and scientists began to reduce wild uncertainties to tame distributions of probability and statistical inferences. But, even as unknown unknowns became known unknowns, our pessimism made us believe that some problems were unsolvable and our intuition misled us. Worse, as we realized how omnipresent and varied uncertainty is, we encountered chaos, quantum mechanics, and the limitations of our predictive power. Bestselling author Professor Ian Stewart explores the history and mathematics of uncertainty. Touching on gambling, probability, statistics, financial and weather forecasts, censuses, medical studies, chaos, quantum physics, and climate, he makes one thing clear: a reasonable probability is the only certainty.
Math Wonders to Inspire Teachers and Students by Alfred Posamentier Pdf
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.
An enlightening vision of how the laws of mathematics find organic expression in the beauty and patterns of nature, written by an acclaimed mathematician and science writer.
The constants of nature are the numbers that define the essence of the Universe. They tell us how strong its forces are, and what its fundamental laws can do: the strength of gravity, of magnetism, the speed of light, and the masses of the smallest particles of matter. They encode the deepest secrets of the Universe and express at once our greatest knowledge and our greatest ignorance about the cosmos. Their existence has taught us the profound truth that Nature abounds with unseen regularities. Yet, while we have become skilled at measuring the values of these constants, our frustrating inability to explain or predict their values shows how much we still have to learn about the inner workings of the Universe. What is the ultimate status of these constants of Nature? Are they truly constant? Could life have evolved and persisted if they were even slightly different? And are there other Universes where they are different? These are some of the issues that this book grapples with. It looks back to the discoveries of the first constants of Nature and the impact they had on scientists like Einstein. This book also tells the story of a tantalising new development in astronomy. For the first time astronomical observations are suggesting that some of the constants of Nature were different when the Universe was younger. So are our laws of Nature slowly changing? Is anything about our Universe immune from the ravages of time? Are there any constants of Nature at all?
Topics in Mathematical Modeling is an introductory textbook on mathematical modeling. The book teaches how simple mathematics can help formulate and solve real problems of current research interest in a wide range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. Yet the prerequisites are minimal: calculus and elementary differential equations. Among the many topics addressed are HIV; plant phyllotaxis; global warming; the World Wide Web; plant and animal vascular networks; social networks; chaos and fractals; marriage and divorce; and El Niño. Traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition are also included. Most chapters begin with the history of a problem, follow with a demonstration of how it can be modeled using various mathematical tools, and close with a discussion of its remaining unsolved aspects. Designed for a one-semester course, the book progresses from problems that can be solved with relatively simple mathematics to ones that require more sophisticated methods. The math techniques are taught as needed to solve the problem being addressed, and each chapter is designed to be largely independent to give teachers flexibility. The book, which can be used as an overview and introduction to applied mathematics, is particularly suitable for sophomore, junior, and senior students in math, science, and engineering.
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.
Invites young readers to learn the numbers one to twenty using simple text and illustrations of various things in nature, including plants, animals, and shells.
Fibonacci Numbers by Nikolai Nikolaevich Vorob'ev Pdf
An engaging treatment of an 800-year-old problem explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. Its entertaining style will appeal to recreational readers and students alike.
A mathematical sightseeing tour of the natural world from the author of THE MAGICAL MAZE Why do many flowers have five or eight petals, but very few six or seven? Why do snowflakes have sixfold symmetry? Why do tigers have stripes but leopards have spots? Mathematics is to nature as Sherlock Holmes is to evidence. Mathematics can look at a single snowflake and deduce the atomic geometry of its crystals; it can start with a violin string and uncover the existence of radio waves. And mathematics still has the power to open our eyes to new and unsuspected regularities - the secret structure of a cloud or the hidden rhythms of the weather. There are patterns in the world we are now seeing for the first time - patterns at the frontier of science, yet patterns so simple that anybody can see them once they know where to look.
Fibonacci Sequence and Golden Ratio by Leong Ying Pdf
Euler's formula is used to derive a number theory that groups natural numbers into four distinct sets obeying twenty new arithmetic rules of addition and multiplication.All possible natural number sequences are calculated from seed values defined by the four group sets. Positive odd number bases are the roots to the Fibonacci sequence, and the only unique group function that can generate even and odd natural numbers. The remaining three groups generate only even numbers or unnatural ratios.The inter and intra ratios of the four group elements are evaluated. The inter-values determine that the Fibonacci sequence is the only function generating the full sets of natural numbers. The intra-ratio of all four groups asymptotically approaches the Golden ratio.From these deterministic evaluations of the natural number groups, it can be concluded that nature's natural tendency is to adopt the Fibonacci sequence as its preferred numbered building blocks, and that the ratio of its structures will naturally approach the Golden ratio.
