# Computer Math Snapshots

Computer Math Snapshots 66 URI WILENSKY Figure 1. Mack (below) carries the plane on which Yertle walks. Mack’s forward move- ments shift the plane as Yertle walks upon it, but when Mack turns left or right the plane does not turn. not affect the position of Mack, the turtle under him. Each turtle maintains its own independent heading information; thus, when Mack turns right or left, he does not affect Yertle’s heading (nor, of course, does Yertle’s turning affect Mack’s). It may be helpful to elaborate on this image just a bit more. We can imagine that Mack is carrying on his back an entire plane on which Yertle is moving. Mack’s forward movements carry along the plane on his back, but Mack’s right and left turns are not conveyed to the plane on his back. Thus, Yertle’s movements effectively represent a superposition of his own personal turtle walk and the forward movements taken by Mack underneath him (see Figure 1). Starting from this image, we might now ask what would happen if (say) Mack were to walk along in a straight line, while Yertle were to walk in an approximation to a circle. Speciﬁcally, suppose that Mack is repeating forever a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

# Computer Math Snapshots

, Volume 5 (1) – Oct 5, 2004
20 pages

/lp/springer-journals/computer-math-snapshots-sq9vjoEiiw
Publisher
Springer Journals
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:1009850018153
Publisher site
See Article on Publisher Site

### Abstract

66 URI WILENSKY Figure 1. Mack (below) carries the plane on which Yertle walks. Mack’s forward move- ments shift the plane as Yertle walks upon it, but when Mack turns left or right the plane does not turn. not affect the position of Mack, the turtle under him. Each turtle maintains its own independent heading information; thus, when Mack turns right or left, he does not affect Yertle’s heading (nor, of course, does Yertle’s turning affect Mack’s). It may be helpful to elaborate on this image just a bit more. We can imagine that Mack is carrying on his back an entire plane on which Yertle is moving. Mack’s forward movements carry along the plane on his back, but Mack’s right and left turns are not conveyed to the plane on his back. Thus, Yertle’s movements effectively represent a superposition of his own personal turtle walk and the forward movements taken by Mack underneath him (see Figure 1). Starting from this image, we might now ask what would happen if (say) Mack were to walk along in a straight line, while Yertle were to walk in an approximation to a circle. Speciﬁcally, suppose that Mack is repeating forever a

### Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Oct 5, 2004

### References

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