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The Mathematics Of Patterns Symmetries And Beauties In Nature
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Book Synopsis The Mathematics of Patterns, Symmetries, and Beauties in Nature by : Bourama Toni
Download or read book The Mathematics of Patterns, Symmetries, and Beauties in Nature written by Bourama Toni and published by Springer Nature. This book was released on 2021-12-06 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas – from model systems, differential equations, statistics, and probability – all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling; thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios to the evolution dynamics of the coronavirus in some given tropical country to the spatiotemporal modeling of the progression of the pandemic. Given its scope and approach, the book will benefit researchers and students of mathematics, the sciences and engineering, and everyone else with an appreciation for the beauty of nature. The outcome is a mathematical enrichment of nature’s beauty in its various manifestations. This volume honors Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in the fields of mathematical modeling and applied mathematics. Dr. Adam has published over 110 papers and authored several books.
Book Synopsis Mathematics in Nature by : John A. Adam
Download or read book Mathematics in Nature written by John A. Adam and published by Princeton University Press. This book was released on 2011-10-02 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Symmetry written by Marcus Du Sautoy and published by Harper Collins. This book was released on 2009-10-13 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematician takes us on “a pilgrimage through the uncanny world of symmetry [in] a dramatically presented and polished treasure of theories” (Kirkus Reviews). Symmetry is all around us. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy—a writer “able to engage general readers in the cerebral dramas of pure mathematics” (Booklist)—takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry’s elusive qualities. “The author takes readers gently by the hand and leads them elegantly through some steep and rocky terrain as he explains the various kinds of symmetry and the objects they swirl around. Du Sautoy explains how this twirling world of geometric figures has strange but marvelous connections to number theory, and how the ultimate symmetrical object, nicknamed the Monster, is related to string theory. This book is also a memoir in which du Sautoy describes a mathematician’s life and how one makes a discovery in these strange lands. He also blends in minibiographies of famous figures like Galois, who played significant roles in this field.” —Publishers Weekly “Fascinating and absorbing.” —The Economist “Impressively, he conveys the thrill of grasping the mathematics that lurk in the tile work of the Alhambra, or in palindromes, or in French mathematician Évariste Galois’s discovery of the interactions between the symmetries in a group.” —Kirkus Reviews
Download or read book Patterns in Nature written by Philip Ball and published by University of Chicago Press. This book was released on 2016-04-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The acclaimed science writer “curates a visually striking, riotously colorful photographic display…of physical patterns in the natural world” (Publishers Weekly, starred review). Though at first glance the natural world may appear overwhelming in its diversity and complexity, there are regularities running through it, from the hexagons of a honeycomb to the spirals of a seashell and the branching veins of a leaf. Revealing the order at the foundation of the seemingly chaotic natural world, Patterns in Nature explores not only the math and science but also the beauty and artistry behind nature’s awe-inspiring designs. Unlike the patterns we create, natural patterns are formed spontaneously from the forces that act in the physical world. Very often the same types of pattern and form—such as spirals, stripes, branches, and fractals—recur in places that seem to have nothing in common, as when the markings of a zebra mimic the ripples in windblown sand. But many of these patterns can be described using the same mathematical and physical principles, giving a surprising unity to the kaleidoscope of the natural world. Richly illustrated with 250 color photographs and anchored by accessible and insightful chapters by esteemed science writer Philip Ball, Patterns in Nature reveals the organization at work in vast and ancient forests, powerful rivers, massing clouds, and coastlines carved out by the sea. By exploring similarities such as the branches of a tree and those of a river network, this spectacular visual tour conveys the wonder, beauty, and richness of natural pattern formation.
Book Synopsis The Beauty of Numbers in Nature by : Ian Stewart
Download or read book The Beauty of Numbers in Nature written by Ian Stewart and published by . This book was released on 2017-03-29 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Creating Symmetry by : Frank A. Farris
Download or read book Creating Symmetry written by Frank A. Farris and published by Princeton University Press. This book was released on 2015-06-02 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step illustrated introduction to the astounding mathematics of symmetry This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
Book Synopsis The Beauty of Numbers in Nature by : Ian Stewart
Download or read book The Beauty of Numbers in Nature written by Ian Stewart and published by National Geographic Books. This book was released on 2017-09-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Pattern Book: Fractals, Art And Nature by : Clifford A Pickover
Download or read book The Pattern Book: Fractals, Art And Nature written by Clifford A Pickover and published by World Scientific. This book was released on 1995-06-09 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout.Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.)
Download or read book Beautiful Symmetry written by Alex Berke and published by MIT Press. This book was released on 2020-02-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.
Book Synopsis Symmetry in Chaos by : Michael Field
Download or read book Symmetry in Chaos written by Michael Field and published by SIAM. This book was released on 2009-06-04 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: A striking full-colour book which explores how combining symmetry and chaos can lead to the construction of remarkable images. This book is an engaging look at the interplay of art and mathematics, and between symmetry and chaos. The underlying mathematics involved in the generation of the images is described.
Download or read book Symmetry written by Kristopher Tapp and published by Springer Nature. This book was released on 2021-08-28 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.
Book Synopsis The Pattern Book by : Clifford A. Pickover
Download or read book The Pattern Book written by Clifford A. Pickover and published by World Scientific. This book was released on 1995 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the patterns are computer-generated, the book is informal and emphasis is on the fun that the true pattern lover finds in doing rather than in reading about the doing.
Book Synopsis Beauty in Mathematics: Symmetry and Fractality by : Vladimir A. Testov
Download or read book Beauty in Mathematics: Symmetry and Fractality written by Vladimir A. Testov and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most important concepts underlying beauty are the concepts of symmetry and fractality, but the relationship of these concepts has not yet remained clear. For centuries, beauty was understood only as a stable order and symmetry. Synergetic worldview allows us to give a new assessment: beauty can be seen as an attractor, the result of self-organization of nature, or the flight of human thought. On the one hand, fractality can be considered one of the manifestations of symmetry in an expansive sense.
Download or read book Fearless Symmetry written by Avner Ash and published by Princeton University Press. This book was released on 2008-08-24 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.
Book Synopsis Creating Symmetry by : Frank A. Farris
Download or read book Creating Symmetry written by Frank A. Farris and published by Princeton University Press. This book was released on 2015-06-02 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step illustrated introduction to the astounding mathematics of symmetry This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
Book Synopsis The Symmetries of Things by : John H. Conway
Download or read book The Symmetries of Things written by John H. Conway and published by CRC Press. This book was released on 2016-04-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.
Download or read book Patterns in Nature written by Philip Ball and published by University of Chicago Press. This book was released on 2016-04-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the natural world is often described as organic, it is in fact structured to the very molecule, replete with patterned order that can be decoded with basic mathematical algorithms and principles. In a nautilus shell one can see logarithmic spirals, and the Golden Ratio can be seen in the seed head of the sunflower plant. These patterns and shapes have inspired artists, writers, designers, and musicians for thousands of years. "Patterns in Nature: Why the Natural World Looks the Way It Does" illuminates the amazing diversity of pattern in the natural world and takes readers on a visual tour of some of the world s most incredible natural wonders. Featuring awe-inspiring galleries of nature s most ingenious designs, "Patterns in Nature" is a synergy of art and science that will fascinate artists, nature lovers, and mathematicians alike."
