Turtle Geometry

The Computer as a Medium for Exploring Mathematics
Author: Harold Abelson,Andrea A. DiSessa
Publisher: MIT Press
ISBN: 9780262510370
Category: Computers
Page: 477
View: 1992

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Turtle Geometry presents an innovative program of mathematical discovery thatdemonstrates how the effective use of personal computers can profoundly change the nature of astudent's contact with mathematics. Using this book and a few simple computer programs, students canexplore the properties of space by following an imaginary turtle across the screen.The concept ofturtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms,this group has done extensive work with preschool children, high school students and universityundergraduates. Harold Abelson is an associate professor in the Department of Electrical Engineeringand Computer Science at MIT. Andrea diSessa is an associate professor in the Graduate School ofEducation, University of California, Berkeley.

Geometry Turned On

Dynamic Software in Learning, Teaching, and Research
Author: James King,Doris Schattschneider
Publisher: Cambridge University Press
ISBN: 9780883850992
Category: Mathematics
Page: 206
View: 9568

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Articles about the uses of active, exploratory geometry carried out with interactive computer software.

An Integrated Introduction to Computer Graphics and Geometric Modeling


Author: Ronald Goldman
Publisher: CRC Press
ISBN: 1439803358
Category: Computers
Page: 574
View: 8123

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Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

Logo

A Retrospective
Author: D Lamont Johnson,Cleborne D Maddux
Publisher: CRC Press
ISBN: 9780789003744
Category: Computers
Page: 212
View: 1549

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In Logo: A Retrospective, you?ll look back and see why attempts to teach Logo in American schools failed the first time it was introduced, and you?ll learn what you can do so educators don?t make the same mistake again. You?ll explore how teachers can sidestep the all-too-familiar cycle of zealous overselling, eventual disappointment, backlash, and abandonment that undermined Logo?s first appearance in American school curricula. Of particular interest to teachers, parents, computer programmers, and members of the general public, Logo: A Retrospective, thoroughly and more accurately outlines Logo?s philosophical and theoretical framework and shows you how you can play a part in the current Logo renaissance already thriving in Australia, Latin America, and Europe. Specifically, this book contains: a decade?s worth of scholarly research on Logo information concerning Logo?s future and evolution strategies for handling student autonomy and teacher intervention recent software design data and feedback for learning Logo new research on computer programming?s effects on children?s cognitive development Without a doubt, computers and other electronic media will be a vital source of learning in the classrooms of the future. The development of powerful new versions of the Logo language, such as MicroWorlds, is welcome evidence that Logo?s popularity is on the rise. So put the past behind you. Read Logo: A Retrospective, and see what?s presently giving schoolchildren all over the world a fresh headstart at their classroom computer terminals.

Turtles, Termites, and Traffic Jams

Explorations in Massively Parallel Microworlds
Author: Mitchel Resnick
Publisher: MIT Press
ISBN: 9780262680936
Category: Computers
Page: 163
View: 1795

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"A Bradford book." Includes bibliographical references (p. [157]-163).

Windows on Mathematical Meanings

Learning Cultures and Computers
Author: Richard Noss,Celia Hoyles
Publisher: Springer Science & Business Media
ISBN: 9400916965
Category: Education
Page: 278
View: 7448

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This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

Perspectives on the Teaching of Geometry for the 21st Century

An ICMI Study
Author: Carmelo Mammana,V. Villani
Publisher: Springer Science & Business Media
ISBN: 9401152268
Category: Education
Page: 353
View: 8752

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In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.

The Algorithmic Beauty of Plants


Author: Przemyslaw Prusinkiewicz,Aristid Lindenmayer
Publisher: Springer Science & Business Media
ISBN: 1461384761
Category: Computers
Page: 228
View: 8654

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Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.

Computers and mathematics

the use of computers in undergraduate instruction : a project of the Committee on Computers in Mathematics Education of the Mathematical Association of America
Author: David Alexander Smith,Mathematical Association of America. Committee on Computers in Mathematics Education
Publisher: Mathematical Assn of Amer
ISBN: 9780883850596
Category: Mathematics
Page: 147
View: 7939

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App Inventor 2

Create Your Own Android Apps
Author: David Wolber,Hal Abelson,Ellen Spertus,Liz Looney
Publisher: "O'Reilly Media, Inc."
ISBN: 1491907231
Category: Computers
Page: 360
View: 7116

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Yes, you can create your own apps for Android devices—and it’s easy to do. This extraordinary book introduces you to App Inventor 2, a powerful visual tool that lets anyone build apps. Learn App Inventor basics hands-on with step-by-step instructions for building more than a dozen fun projects, including a text answering machine app, a quiz app, and an app for finding your parked car! The second half of the book features an Inventor’s Manual to help you understand the fundamentals of app building and computer science. App Inventor 2 makes an excellent textbook for beginners and experienced developers alike. Use programming blocks to build apps—like working on a puzzle Create custom multi-media quizzes and study guides Design games and other apps with 2D graphics and animation Make a custom tour of your city, school, or workplace Control a LEGO® MINDSTORMS® NXT robot with your phone Build location-aware apps by working with your phone’s sensors Explore apps that incorporate information from the Web

A Beginner's Guide to Constructing the Universe

The Mathematical Archetypes of Nature, Art, and Science
Author: Michael S. Schneider
Publisher: Harper Collins
ISBN: 0062043161
Category: Science
Page: 384
View: 8630

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The Universe May Be a Mystery, But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round. Why one and two weren't considered numbers by the ancient Greeks. Why squares show up so often in goddess art and board games. What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster and a cathedral. And much more.

MAA Notes


Author: N.A
Publisher: The Mathematical Association of America
ISBN: N.A
Category: Education
Page: N.A
View: 4920

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