Japanese artist Hiroshi Sugimoto is best known for his photography, especially his gloriously simple compositions of seascapes and lightning. But my favorites are his sculptures based on mathematical models. According to Art News, “Drawn to the objects’ purity of form and also inspired by Man Ray’s interest in photographing mathematical models, Sugimoto first photographed nineteenth-century plaster examples for his Conceptual Forms series. During the process, he was struck by the softness and fragility of the vintage models – many had lost pieces or no longer possessed the sharpness that they were meant to represent. Sugimoto sought to extend the limits of these mathematical models using cutting-edge technology, searching out the highest-level precision metalworking team in Japan. For Conceptual Form 009, a model of the equation for a surface containing a single point extended to infinity, Sugimoto succeeded in creating an infinity point with a mere one millimeter diameter, the minimum width before the material itself becomes structurally unstable.”
I can’t even begin to understand the math behind it, but as a visual representation of an “infinity point” it’s hard to top that. If you live in LA, don’t miss the chance to see an exhibition of Sugimoto’s work at the Getty Museum from February 4-June 8 . If you don’t, see lots more of his work at his website.
The Finch and Pea 
Thanks for posting, this is beautiful. Mathematically, this is (one half of) a pseudosphere. You can read more about that figure here: http://mathworld.wolfram.com/Pseudosphere.html or here: http://en.wikipedia.org/wiki/Pseudosphere