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## Serendipity with Cut Paper

The word "serendipity" is a good description for my experiences with web-browsing. For example, on an afternoon browse, I first came across a site that carried examples of "cut paper art". I have mentioned this topic previously, but new examples always amaze me....what a creative person can do with a single sheet of paper, some cuts, and some clever folds. My mind wanders...and wonders: what could a creative student using the idea of cut paper art to represent 3-dimensional functions.

This web site led me to the Plus Magazine web site (which has been recommended previously) and a further connection between mathematics and art. Though I had explored this site before, I somehow missed seeing this article on "Maths and Art: The Whistlestop Tour" . by Lewis Dartnell. He does a great job of overviewing some neat connections involving geometric patterns, the golden ratio, geometric abstractionism, tesselations, origami, anamorphic art, fractals, and minimal energy surfaces. Whew!

But, via the "art" of googling, Dartnell's article led to an even better article, "Imaging Maths - Unfolding Polyhedra" by Konrad Polthier. It incluses some great animations for paper-folding specific to polyhedra and objects such as the Clifford Torus, the Császár torus, the Boy Surface, and the cantenoid. For example, the object shown to the right is a paper model of the Boy Surface, which has "the least number of vertices among all polyhedral realizations consisting of triangle"...and you can see it unfold!

PLUS (pardon the pun), the article includes a link to the Unfolder module, a piece of of Java software (written by Klaus Hildebrandt)that allows you to unfold and build your own paper models. And if you have time, explore the linked articles in the reference list...if fact, I suggest you make the time. Both you and your students will enjoy these "cut paper" explorations!