A sphere is an elliptic surface with constant positive curvature. A pseudosphere is a hyperbolic surface with constant negative curvature. This pseudosphere is called a Breather. The animation shows how the surface changes from Kuen's surface into a breather with many ribs when the parameter is changed.
References:
http://www.math.ucla.edu/~bon/kuen.html
http://mathworld.wolfram.com/Pseudosphere.html
http://matematiku.wordpress.com/2011/05/18/parametric-breather-pseudospherical-surface/
Animation by Paul Nylander
Wow! That is something truly new to me, which I didn't think of before!
ReplyDeleteKiril Minanov ..should I be worried about you? =)
ReplyDeleteIf you want, here is an interactive web application that draws these type of surfaces (among many others).
ReplyDeleteIt requires Java installed on your computer:
http://3d-xplormath.org/j/applets/en/index.html
You can find the Breather in the menu on the left: Surfaces > Pseudospherical surfaces > Breather
Thanks Enrico Altavilla =)
ReplyDeleteIntelligent....Very cool
ReplyDeleteGaussian curvature is awesome in general. Gauss was also a baller.
ReplyDeleteI don't mean to geek out, but <3 Gauss-Bonnet <3 is my favorite theorem