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Cycloids, Billiards, Lissajou: Using the Computer to Visualize Irrational Numbers, and What Can This Be Good For

Cycloids, Billiards, Lissajou: Using the Computer to Visualize Irrational Numbers, and What Can... COMPUTER MATH SNAPSHOTS CYCLOIDS, BILLIARDS, LISSAJOU: USING THE COMPUTER TO VISUALIZE IRRATIONAL NUMBERS, AND WHAT CAN THIS BE GOOD FOR MARITA BARABASH Achva Academic College for Education Beer Tovia Reg. Council Shikmim M.P. 79800, Israel E-mail: marita@macam.ac.il In this snapshot the author contrasts the differential behavior of three familiar parameterized curves for rational and irrational values of the para- meter. Students can explore a rich diversity of curves through investigating the parameter space. Through visualizing the difference between curves of rational and irrational parameters, students can better appreciate the distinction and come to gain more sophisticated intuitions about functions. Computer Math Snapshots Editor: Uri Wilensky Center for Connected Learning and Computer-Based Modeling Northwestern University, U.S.A. e-mail: uri@northwestern.edu We discuss here three families of curves that all possess the same property: each of them has a closed bounded symmetric form at rational values of a ratio of some principal parameters of the system from which they originate, and is an infinite bounded curve that never follows any finite segment of itself, if this ratio is irrational. For each of these three families, this mathematical fact is easily proven, and provides a creative possibility for visualizing the difference between rational and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

Cycloids, Billiards, Lissajou: Using the Computer to Visualize Irrational Numbers, and What Can This Be Good For

"Technology, Knowledge and Learning" , Volume 8 (3) – Oct 11, 2004

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Education; Learning and Instruction; Mathematics Education; Educational Technology; Science Education; Creativity and Arts Education
ISSN
2211-1662
eISSN
1573-1766
DOI
10.1023/B:IJCO.0000021933.32305.f2
Publisher site
See Article on Publisher Site

Abstract

COMPUTER MATH SNAPSHOTS CYCLOIDS, BILLIARDS, LISSAJOU: USING THE COMPUTER TO VISUALIZE IRRATIONAL NUMBERS, AND WHAT CAN THIS BE GOOD FOR MARITA BARABASH Achva Academic College for Education Beer Tovia Reg. Council Shikmim M.P. 79800, Israel E-mail: marita@macam.ac.il In this snapshot the author contrasts the differential behavior of three familiar parameterized curves for rational and irrational values of the para- meter. Students can explore a rich diversity of curves through investigating the parameter space. Through visualizing the difference between curves of rational and irrational parameters, students can better appreciate the distinction and come to gain more sophisticated intuitions about functions. Computer Math Snapshots Editor: Uri Wilensky Center for Connected Learning and Computer-Based Modeling Northwestern University, U.S.A. e-mail: uri@northwestern.edu We discuss here three families of curves that all possess the same property: each of them has a closed bounded symmetric form at rational values of a ratio of some principal parameters of the system from which they originate, and is an infinite bounded curve that never follows any finite segment of itself, if this ratio is irrational. For each of these three families, this mathematical fact is easily proven, and provides a creative possibility for visualizing the difference between rational and

Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Oct 11, 2004

References