Kuen's Surface

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Introduction:

Kuen's surface has the same constant negative Gaussian curvature as the sphere and pseudosphere. It is quite complicated, as a front-back coloring reveals:

Definition:

Properties:

Infinitesimal Area: The infinitesimal area of a patch on the surface is given by

Gaussian Curvature: Gaussian curvature of the surface. Surface colored by Gaussian curvature.

Mean Curvature: Mean curvature of the surface. Surface colored by Mean curvature.