RE: Science Porn
February 17, 2015 at 6:30 am
(This post was last modified: February 17, 2015 at 6:34 am by Alex K.)
LOL from the Wiki article on T. Egregium
The gaussian curvature is the ordinary curvature in one direction times the ordinary curvature in the other. For an intrinsically flat object, that product must be zero, i.e. if you bent it in one direction, the curvature in the other must vanish.
Quote:An application of the Theorema Egregium is seen in a common pizza-eating strategy: A slice of pizza can be seen as a surface with constant Gaussian curvature 0. Gently bending a slice must then roughly maintain this curvature (assuming the bend is roughly a local isometry). If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero. This creates rigidity in the direction perpendicular to the fold, an attribute desirable when eating pizza, as it holds its shape long enough to be consumed without a mess.
The gaussian curvature is the ordinary curvature in one direction times the ordinary curvature in the other. For an intrinsically flat object, that product must be zero, i.e. if you bent it in one direction, the curvature in the other must vanish.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition