## Surfaces of Curvature K=1 Gallery

Surfaces in this gallery have a constant Gauss curvature (K), equal to 1 at
every point on the surface. The unit sphere is the most well-known example of
such a surface (although it is not included among the exhibits in this gallery).

To define the curvature of a surface at a point on the surface, consider a plane
that is perpendicular to the surface and passes through that point. The intersection
of that plane with the surface is a curve that contains the surface point. Consider
the curvature of the curve at that point. (This curvature can be defined, for example,
as 1/r, where r is the radius of the circle that best approximates the curve at that
point, the so-called *osculating circle*.) Different planes will produce different
curvatures, but among all the curvatures, there are a maximum value and a minimum value.
The minimum and maximum values are called the *principal curvatures* of the surface
at the given point, and the Gaussian curvature at that point is defined as the
product of the two principal curvatures.

The Surfaces of Curvature K=1 gallery is one of several sub-galleries of the
Surfaces Gallery. For more information on parametric surfaces, you should
see the documentation for the Surfaces Gallery.