Counterexamples in Origami | Roots of Unity, Scientific American Blog Network


how reliable is the triangulation? How accurately does it reflect the properties of the original surface? For example, as we increase the number of triangles in the approximation of the surface, will the surface area of the triangulated surface get close to the surface area of the original surface? In 1880, mathematician and righteous facial hair maintainer Hermann Schwarz answered this question in the negative by producing a counterexample, a surface and sequence of triangulated approximations for which the surface area of the triangulations gets arbitrarily large and hence doesn’t converge to the surface area of the original surface.

Counterexamples in Origami | Roots of Unity, Scientific American Blog Network Thursday, December 5, 2013 @ 11:48am | Modified

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how reliable is the triangulation? How accurately does it reflect the properties of the original surface? For example, as we increase the number of triangles in the approximation of the surface, will the surface area of the triangulated surface get close to the surface area of the original surface? Karl Hermann Amandus Schwarz, who first described the Schwarz lantern. Image: public domain, via Wikimedia Commons. In surface? In 1880, mathematician and righteous facial hair maintainer Hermann Schwarz answered this question in the negative by producing a counterexample, a surface and sequence of triangulated approximations for which the surface area of the triangulations gets arbitrarily large and hence doesn’t converge to the surface area of the original surface.
- Thursday, December 5, 2013 @ 9:39am

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