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Folding a triangle

Published online by Cambridge University Press:  23 January 2015

Andrew Jobbings
Andrew Jobbings*
Affiliation:
4 West Avenue, Baildon, Shipley BD17 5HA
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Extract

The Original problem

Take a right-angled triangle ABC, where ∠C = 90°, and fold along UV so that C lies on AB, as shown in Figure 1, where C' is the new position of C.

Problem: Where should one fold in order to minimise the area of the folded triangld CUV?

This problem was discussed by Hirschhom in [1], where he gives its origins and provides a solution, describing the answer as ‘quite remarkable’. However, he does not relate the answer to the geometry of the configuration. We adopt a more geometrical approach and use some simple folding ideas—there is a close relationship between paper folding and geometry which deserves to be more widely known (see [2] for example).

Type
Articles
Information
The Mathematical Gazette , Volume 97 , Issue 539 , July 2013 , pp. 210 - 217
Copyright
Copyright © The Mathematical Association 2013

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References

1. Hirschhorn, Michael D., A triangle-folding problem, Math. Gaz. 95 (November 2011) pp. 514–517.Google Scholar
2. Geretschlliger, Robert, Geometric origami, Arbelos (2008).Google Scholar
3. Loy, Jim, Trisection of an angle. url: http://www.jimloy.com/geometry/trisect.htm Google Scholar
4. Verrill, Helena, Origami trisection of an angle. url: http://www. math.lsu.edu/~verrill/origami/trisect/ Google Scholar