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Getting Euler's Line to Relax

Getting Euler's Line to Relax COMPUTER MATH SNAPSHOTS E. PAUL GOLDENBERG Education Development Center, Inc. 55 Chapel Street Newton, MA 02458-1060 USA Computer Math Snapshots Editor: Uri Wilensky Center for Connected Learning and Computer-Based Modeling Northwestern University, U.S.A. e-mail: uriw@media.mit.edu This column will publish short (from just a few lines to a couple of pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathem- atics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computational theory. Snapshots are subject to peer review. In this issues snapshot, Goldenberg takes us on a Lakatosian journey – relaxing more and more hypothesis of an elementary Euclidean geometry theorem to arrive at its topological heart. School mathematics typically expects students to accept the “givens” as given, and asks them, at most, to understand (e.g., prove) the consequences. By contrast, mathematicians often pursue the hypothesis of a theorem as vigorously as the conclusion – to decide, for example, whether all the givens are necessary, or how the theorem generalizes when the conditions are relaxed. This snapshot charts the zany course of one such investigation accessible to high http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

Getting Euler's Line to Relax

"Technology, Knowledge and Learning" , Volume 6 (2) – Oct 5, 2004

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Publisher
Springer Journals
Copyright
Copyright © 2001 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/A:1017907209271
Publisher site
See Article on Publisher Site

Abstract

COMPUTER MATH SNAPSHOTS E. PAUL GOLDENBERG Education Development Center, Inc. 55 Chapel Street Newton, MA 02458-1060 USA Computer Math Snapshots Editor: Uri Wilensky Center for Connected Learning and Computer-Based Modeling Northwestern University, U.S.A. e-mail: uriw@media.mit.edu This column will publish short (from just a few lines to a couple of pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathem- atics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computational theory. Snapshots are subject to peer review. In this issues snapshot, Goldenberg takes us on a Lakatosian journey – relaxing more and more hypothesis of an elementary Euclidean geometry theorem to arrive at its topological heart. School mathematics typically expects students to accept the “givens” as given, and asks them, at most, to understand (e.g., prove) the consequences. By contrast, mathematicians often pursue the hypothesis of a theorem as vigorously as the conclusion – to decide, for example, whether all the givens are necessary, or how the theorem generalizes when the conditions are relaxed. This snapshot charts the zany course of one such investigation accessible to high

Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Oct 5, 2004

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