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The intriguing mechanics of a tractrix of cards

Published online by Cambridge University Press:  22 June 2022

Subhranil De
Subhranil De*
Affiliation:
School of Natural Sciences, Indiana University Southeast, New Albany, IN 47150, USA e-mail: subde@ius.edu
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Extract

Figure 1 shows the photograph of a tractrix made of cards. This is a simple yet captivating way to make a tractrix — an arrangement that has recently appeared in some engaging pedagogical resources and literature [1, 2]. When closely spaced cards lean like this, one after another, over a horizontal plane, the contour created is a tractrix — a curve of significance in mathematics, since its revolution around its asymptote produces a pseudosphere: a curved surface with constant negative Gaussian curvature [3, 4].

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 566 , July 2022 , pp. 281 - 290
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Copyright
© The Authors, 2022 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Polster, B., TracTricks Math Horizons, 21(4) (April 2014) pp. 18–19.Google Scholar
Walsh, Daniel, Sudo make me a pseudosphere, accessed December 2021 at https://danielwalsh.tumblr.com/post/2173134224/sudo-make-me-a-pseudosphere Google Scholar
Wolfram Math World, Tractrix, accessed December 2021 at https://mathworld.wolfram.com/Tractrix.html Google Scholar
Wolfram Math World, Pseudosphere, accessed December 2021 at https://mathworld.wolfram.com/Pseudosphere.html Google Scholar