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Greeting cards and fractals

Published online by Cambridge University Press:  01 August 2016

Peter Hilton
Affiliation:
Department of Mathematical Sciences, SUNY at Binghamton, Binghamton, New York 13902-6000 and Department of Mathematics, University of Central Florida, Orlando, FL 32816
Jean Pedersen
Affiliation:
Department of Mathematics, Santa Clara University, Santa Clara, CA 95053 e-mail: [email protected]
Hans Walser
Affiliation:
Mathematik-Departement, ETH Zürich, 8092 Zürich, Switzerland, and Department of Mathematics, Santa Clara University, Santa Clara, CA 95053

Extract

We will discuss in this article a fractal-like structure made from a flat piece of paper. What will motivate most people to want to make the structure is that it is pretty. In fact, the exercise has two rather obvious uses. First, greeting card companies may want to use the idea to manufacture interesting 3-dimensional cards which fit conveniently into envelopes; and, second, teachers may wish to teach students how to make it (and this process will also involve teaching them some beautiful mathematics). The structure itself is a model for a stage in a self-similarity process leading to a fractal. Building the model involves scoring a flat piece of paper in a prescribed manner, cutting along some of the score lines, and then folding some lines as ‘mountain’ folds and others as ‘valley’ folds.

Type
Articles
Copyright
Copyright © The Mathematical Association 1997

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References

1. Hilton, Peter, Holton, Derek and Pedersen, Jean, Mathematical reflections – in a room with many mirrors, Springer-Verlag, New York (1997).Google Scholar
2. Mandelbrot, Benoit B., The fractal geometry of nature, Freeman, New York (1977).Google Scholar