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What (who) is Gaussian curvature - definition
PRODUCT OF THE PRINCIPAL CURVATURES OF A SURFACE
Gauss curvature; Liebmann's theorem; Convex curvature; Concave curvature; Gaussian radius of curvature; Brioschi formula
![[[Saddle surface]] with normal planes in directions of principal curvatures](https://commons.wikimedia.org/wiki/Special:FilePath/Minimal surface curvature planes-en.svg?width=200 "[[Saddle surface]] with normal planes in directions of principal curvatures")
Gaussian function
![The [[discrete Gaussian kernel]] (solid), compared with the [[sampled Gaussian kernel]] (dashed) for scales <math>t = 0.5,1,2,4.</math>](https://commons.wikimedia.org/wiki/Special:FilePath/Discrete Gaussian kernel.svg?width=200 "The [[discrete Gaussian kernel]] (solid), compared with the [[sampled Gaussian kernel]] (dashed) for scales <math>t = 0.5,1,2,4.</math>")
MATHEMATICAL FUNCTION
Gaussian curve; Gaussian kernel; Gauss kernel; Error Curve; Error curve; Area under Gaussian curve; Area under the bell curve; Area under gaussian curve; Gauss curve; Integral of a Gaussian function; Integral of a Gaussian Function; Gauss bell
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
Gaussian blur
![A [[halftone]] print rendered smooth through Gaussian blur](https://commons.wikimedia.org/wiki/Special:FilePath/Halftone, Gaussian Blur.jpg?width=200 "A [[halftone]] print rendered smooth through Gaussian blur")
VISUAL EFFECT
Gaussian Blur; Gaussian interpolation; Gaussian smoothing; BLURRING FILTERS; Blurring technology
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss).
Gaussian orbital
Gaussian orbitals; Gaussian-type orbital; Molecular integrals
In computational chemistry and molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the LCAO method for the representation of electron orbitals in molecules and numerous properties that depend on these.
Wikipedia
Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point:
The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.Gaussian curvature is an intrinsic measure of curvature, depending only on distances that are measured “within” or along the surface, not on the way it is isometrically embedded in Euclidean space. This is the content of the Theorema egregium.
Gaussian curvature is named after Carl Friedrich Gauss, who published the Theorema egregium in 1827.
