Brioschi Formula
For a curve with Metric
 | (1) |
, 
, and 
is the first Fundamental Form, the Gaussian Curvature is | (2) |
 |  |  | |
| (3) | |||
 | |  |
which can also be written
 |  |  | |
| (4) | |||
|  | (5) |
See also Fundamental Forms, Gaussian Curvature
References
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 392-393, 1993.
- Sphere-Sphere Intersection
- Sphere with Tunnel
- Spherical Bessel Differential Equation
- Spherical Bessel Function
- Spherical Bessel Function of the First Kind
- Spherical Bessel Function of the Second Kind
- Spherical Bessel Function of the Third Kind
- Spherical Cap
- Spherical Coordinates
- Spherical Design
- Spherical Excess
- Spherical Frustum
- Spherical Geometry
- Spherical Hankel Function of the First Kind
- Spherical Hankel Function of the Second Kind
- Spherical Harmonic
- Spherical Harmonic Addition Theorem
- Spherical Harmonic Closure Relations
- Spherical Harmonic Tensor
- Spherical Helix
- Spherical Point System
- Spherical Polygon
- Spherical Ring
- Spherical Sector
- Spherical Segment