Fractals Graphics And Mathematics Education

Author : Michael Frame,Benoit Mandelbrot
Publisher : Cambridge University Press
Page : 232 pages
File Size : 50,9 Mb
Release : 2002-06-20
Category : Computers
ISBN : 0883851695

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Fractals, Graphics, and Mathematics Education by Michael Frame,Benoit Mandelbrot Pdf

Fractal Geometry is a recent edition to the collection of mathematical tools for describing nature, and is the first to focus on roughness. Fractal geometry also appears in art, music and literature, most often without being consciously included by the artist. Consequently, through this we may uncover connections between the arts and sciences, uncommon for students to see in maths and science classes. This book will appeal to teachers who have wanted to include fractals in their mathematics and science classes, to scientists familiar with fractal geometry who want to teach a course on fractals, and to anyone who thinks general scientific literacy is an issue important enough to warrant new approaches.

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 49,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475721720

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Fractals for the Classroom by Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Pdf

Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244066

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Fractals for the Classroom by Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Pdf

Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.

Author : Clifford A Pickover
Publisher : World Scientific
Page : 466 pages
File Size : 40,6 Mb
Release : 1995-06-09
Category : Mathematics
ISBN : 9789814504034

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The Pattern Book: Fractals, Art And Nature by Clifford A Pickover Pdf

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.)

Author : Robert L. Devaney,Kathleen T. Alligood
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 55,8 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821801376

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Chaos and Fractals: The Mathematics Behind the Computer Graphics by Robert L. Devaney,Kathleen T. Alligood Pdf

"Robert Devaney communicates his deep understanding as well as his enthusiasm for chaos, fractals, and dynamical systems. Starting at a level suitable for well-prepared high school students, he tells the mathematical story behind these fascinating topics. Equations and graphs are clearly shown with computer-generated characters, and Devaney's explanations are lucid and instructive. Illustrating the mathematics are forays into the colorful, unpredictable world of fractals and Julia sets. Devaney explains how the computer is used to generate the pictures and shows how the various colors are chosen for graphical representations ... Though the mathematical background required is elementary, those at the collegiate level and beyond will appreciate ... the clarity of exposition and the sheer beauty of the graphics."--Container.

Author : Nigel Lesmoir-Gordon,Will Rood
Publisher : Icon Books Ltd
Page : 429 pages
File Size : 42,9 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9781848317833

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Introducing Fractals by Nigel Lesmoir-Gordon,Will Rood Pdf

Fractals are the geometry of the natural world. They're about the broken, wrinkled, wiggly world- the uneven shapes of nature, unlike the idealised forms of Euclidean geometry. We see fractals everywhere; indeed, we are fractals ourselves. Fractal geometry is an extension of classical geometry which can make precise models of physical structures, from ferns to galaxies. It can describe the shape of a cloud as precisely as an architect can describe a house. Introducing Fractals traces the historical development of this mathematical discipline, explores its descriptive powers in the natural world, and then looks at the applications and the implications of the discoveries it has made. As John Archibald Wheeler, protégé of Niels Bohr, friend of Albert Einstein and mentor of Richard Feynman has said, 'No one will be considered scientifically literate tomorrow, who is not familiar with fractals.'

Author : Heinz-Otto Peitgen,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461237846

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The Science of Fractal Images by Heinz-Otto Peitgen,Dietmar Saupe Pdf

This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.

Author : C.A. Pickover
Publisher : Elsevier
Page : 452 pages
File Size : 43,8 Mb
Release : 1998-08-03
Category : Computers
ISBN : 0080528864

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Chaos and Fractals by C.A. Pickover Pdf

These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe,Evan Maletsky,Terry Perciante,Lee Yunker
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 41,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475752762

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Fractals for the Classroom: Strategic Activities Volume Two by Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe,Evan Maletsky,Terry Perciante,Lee Yunker Pdf

The same factors that motivated the writing of our first volume of strategic activities on fractals continued to encourage the assembly of additional activities for this second volume. Fractals provide a setting wherein students can enjoy hands-on experiences that involve important mathematical content connected to a wide range of physical and social phenomena. The striking graphic images, unexpected geometric properties, and fascinating numerical processes offer unparalleled opportunity for enthusiastic student inquiry. Students sense the vigor present in the growing and highly integrative discipline of fractal geom etry as they are introduced to mathematical developments that have occurred during the last half of the twentieth century. Few branches of mathematics and computer science offer such a contem porary portrayal of the wonderment available in careful analysis, in the amazing dialogue between numeric and geometric processes, and in the energetic interaction between mathematics and other disciplines. Fractals continue to supply an uncommon setting for animated teaching and learn ing activities that focus upon fundamental mathematical concepts, connections, problem-solving techniques, and many other major topics of elementary and advanced mathematics. It remains our hope that, through this second volume of strategic activities, readers will find their enjoyment of mathematics heightened and their appreciation for the dynamics of the world in creased. We want experiences with fractals to enliven curiosity and to stretch the imagination.

Author : Philippe R. Richard ,Steven Van Vaerenbergh ,M. Pilar Vélez
Publisher : Ed. Universidad de Cantabria
Page : 58 pages
File Size : 45,5 Mb
Release : 2020-10-29
Category : Mathematics
ISBN : 8210379456XXX

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First Symposium on Artificial Intelligence for Mathematics Education. Book of Abstracts (AI4ME 2020) by Philippe R. Richard ,Steven Van Vaerenbergh ,M. Pilar Vélez Pdf

The digital revolution that we have experienced since the last quarter of the twentieth century has had some influence, yet to be analysed and extended, on the way mathematics is made, taught and learned. While the rate of innovation in these technologies is growing exponentially, the potential impact of most information technologies on mathematical education remains to be fully exploited. In particular, several authoritative voices point out that the technology that will most likely transform education in the coming years is artificial intelligence (AI). Interestingly, today AI is mainly associated with technologies to automate tasks and lower costs, thus serving primarily the interests of the political-administrative, industrial and commercial world. In this scenario, the world of education and, more specifically, didactics, appears at best as a mere user of AI techniques developed in other fields, forgetting that AI should play a much more relevant role here, serving the human being who is doing his work as a mathematician or who is learning mathematics. The AI4ME symposium at the International Centre for Mathematical Meetings (CIEM) in Castro Urdiales is a space for research and reflection to better understand the interconnected challenges of instrumental learning of mathematics and instrumental mathematics, taking advantage of the achievements and opportunities of Artificial Intelligence for Mathematical Education. This book of abstracts gathers the summaries of the talks presented at the symposium, as well as the conclusions of each of the four thematic groups.

Author : Manfred Schroeder
Publisher : Courier Corporation
Page : 450 pages
File Size : 50,7 Mb
Release : 2009-08-21
Category : Science
ISBN : 9780486472041

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Fractals, Chaos, Power Laws by Manfred Schroeder Pdf

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer
Page : 450 pages
File Size : 46,7 Mb
Release : 1991-10-22
Category : Mathematics
ISBN : 038797041X

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Fractals for the Classroom by Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Pdf

Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.

Author : Jose L. Encarnacao,Heinz-Otto Peitgen,Georgios Sakas,Gabriele Englert
Publisher : Springer
Page : 257 pages
File Size : 40,5 Mb
Release : 2012-04-04
Category : Mathematics
ISBN : 3642956793

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Fractal Geometry and Computer Graphics by Jose L. Encarnacao,Heinz-Otto Peitgen,Georgios Sakas,Gabriele Englert Pdf

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with actual trends and topics of future research, are reported in the last section. The topics of the book are divides into four sections: Fundamentals, Computer Graphics and Optical Simulation, Simulation of Natural Phenomena, Image Processing and Image Analysis.

Author : Benoit Mandelbrot
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 51,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475740172

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Fractals and Chaos by Benoit Mandelbrot Pdf

Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.

Author : Heinz-Otto Peitgen
Publisher : Unknown
Page : 450 pages
File Size : 46,5 Mb
Release : 1992
Category : Electronic
ISBN : OCLC:716346306

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Fractals for the Classroom by Heinz-Otto Peitgen Pdf