On a surface in Euclidean three-space, straightest paths, those of locally-shortest length, are called "geodesics." Kuen's surface has "Gaussian curvature" equal to -1 (away from curves where the surface pinches to a sharp edge). Concretely, for every geodesic triangle on the surface, the sum of the interior angles (in radians) is equal to pi minus the area of the triangle.
