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Underwater E-Cones

Cut out a paper disk, place it over a coffee cup, and use a pen tip to press down on the disk's center. The result: the paper curls up and forms both a conical point and a cone-shaped fold. Oddly, this is connected to marine algae...another application triump for the mathematical sciences!

Researchers at the Ecole normale supérieure studied how these conical points generated "e-cones." That is, if you first remove a wedge from a circular disk, the pushed pen tip forms a regular cone without a fold. But, if you add a wedge larger than the removed wedge, the result is an E-cone with a fold (the E stands for excess).

The scientists showed that E-cones can assume an infinite number of shapes, without the intervention of any external force. By modeling these E-cones as an attempt to predict their shape and the elastic stresses generated, they concluded that the bi-fold symmetrical shape is the one with the lowest energy. And, this same shape is found in certain marine algae, spontaneously assuming it during growth.

Another win for mathematics...so keep playing with your papers!

Source: ScienceDaily, October 30, 2008