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Closed surface in three-dimensional space
A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field
Gaussian_surface
Product of the principal curvatures of a surface
differential geometry, the Gaussian curvature or Gauss curvature (symbol Κ, named after Carl Friedrich Gauss) of a smooth surface in three-dimensional space
Gaussian_curvature
Filter in electronics and signal processing
processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would
Gaussian_filter
Volume rendering technique
Gaussian splatting is a volume rendering technique that deals with the direct rendering of volume data without converting the data into surface or line
Gaussian_splatting
Measure of the electric polarizability of a dielectric material
on the surface, and d A {\displaystyle \mathrm {d} \mathbf {A} } is a differential area vector on the Gaussian surface. If the Gaussian surface uniformly
Permittivity
Mathematics of smooth surfaces
distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied
Differential geometry of surfaces
Differential_geometry_of_surfaces
Whitney umbrella Boy's surface Breather surface Cantor tree surface Channel surface Clebsch surface Gaussian curvature Gaussian surface Generalized helicoid
List_of_surfaces
Restatement of Newton's law of universal gravitation
article Gaussian surface for more details on how these derivations are done. Three such applications are as follows: We can conclude (by using a "Gaussian pillbox")
Gauss's_law_for_gravity
Study of the deformation of solids that touch each other
others. It has been repeatedly observed that engineering surfaces do not demonstrate Gaussian surface height distributions e.g. Peklenik. Leighton et al. presented
Contact_mechanics
Foundational law of electromagnetism relating electric field and charge distributions
closed surface is equal to 1/ε0 times the net electric charge enclosed within that closed surface. The closed surface is also referred to as Gaussian surface
Gauss's_law
Equations describing classical electromagnetism
opposite "magnetic charges". Precisely, the total magnetic flux through a Gaussian surface is zero, and the magnetic field is a solenoidal vector field. The Maxwell–Faraday
Maxwell's_equations
Study of still or slow electric charges
the surface." Many numerical problems can be solved by considering a Gaussian surface around a body. Mathematically, Gauss's law takes the form of an integral
Electrostatics
Type of image blur produced by a Gaussian function
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
Gaussian_blur
Gaussian noise Gaussian beam Gaussian blur, a technique in image processing Gaussian fixed point Gaussian random field Gaussian free field Gaussian integral
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
Scientific subjects
randomness and disorder. However, chaos theory posits that beneath the surface of apparent randomness in chaotic complex systems lie underlying patterns
Branches_of_physics
Set of points equidistant from a center
the surface is embedded in space. Hence, bending a surface will not alter the Gaussian curvature, and other surfaces with constant positive Gaussian curvature
Sphere
Result of differential geometry proved by Gauss
surfaces. The theorem says that Gaussian curvature can be determined entirely by measuring angles, distances and their rates of change on a surface,
Theorema_Egregium
Foundational law of classical magnetism
differential forms. Magnetic moment Vector calculus Integral Flux Gaussian surface Faraday's law of induction Ampère's circuital law Lorenz gauge condition
Gauss's_law_for_magnetism
Physical field surrounding an electric charge
slower than that of light, which makes it impossible to construct a Gaussian surface in this region that violates Gauss's law. Another technical difficulty
Electric_field
Electric charges present on the surface of a solid
(2010). "Gaussian surfaces". Georgia State University. Retrieved 27 April 2011. Kosmulski, Marek (2001), Chemical properties of material surfaces, Marcel
Surface_charge
Measure of electric field through surface
infinitesimal area on the surface with an outward facing surface normal defining its direction. For a closed Gaussian surface, electric flux is given by:
Electric_flux
Negatively-curved minimal surface
a Nadirashvili surface is an immersed complete bounded minimal surface in R 3 {\displaystyle \mathbb {R} ^{3}} with negative Gaussian curvature. The first
Nadirashvili_surface
Variant of the centimetre–gram–second unit system
Gaussian units is one of systems of units of measurement, and also one of what are considered the metric system (a set of globally accepted systems of
Gaussian_units
Calculation technique for classical electrostatics
)=(R/r)\rho (R^{2}/r,\theta ,\phi )} . Physics portal Flux Gaussian surface Image antenna Surface equivalence principle Schottky effect Griffiths, David J
Method_of_image_charges
Type of non-Euclidean geometry
geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some
Hyperbolic_geometry
Study of Boolean functions via discrete Fourier analysis
influence or average sensitivity for the indicator function of a set is Gaussian surface area, which is the Minkowski content of the boundary of the set. The
Analysis_of_Boolean_functions
Geometric surface
\mathbb {R} ^{3}} with constant negative Gaussian curvature. A "pseudospherical surface of radius R" is a surface in R 3 {\displaystyle \mathbb {R} ^{3}}
Pseudosphere
Surface specified with parameters
of curves on the surface, surface area, differential geometric invariants such as the first and second fundamental forms, Gaussian, mean, and principal
Parametric_surface
Mathematical measure of how much a curve or surface deviates from flatness
around P. If the surface were flat, the ant would find C(r) = 2πr. On curved surfaces, the formula for C(r) will be different, and the Gaussian curvature K
Curvature
Electrostatics experiment
in an electrically conducting body, the charge resides entirely on the surface. It also demonstrates the principles behind electromagnetic shielding such
Faraday's_ice_pail_experiment
Overview of and topical guide to physics
electromagnetic field, electromagnetic induction, electromagnetic radiation, Gaussian surface, magnetic field, magnetic flux, magnetic monopole, magnetic permeability
Outline_of_physics
K} is the Gaussian curvature, and dA is the area form of S. For a closed surface, by the Gauss–Bonnet theorem, the integral of the Gaussian curvature
Willmore_energy
Critical point on a surface graph which is not a local extremum
shape. Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian curvature. A
Saddle_point
Elliptic partial differential equation
details of Poisson's equation, commonly expressed in SI units (as opposed to Gaussian units), describe how the distribution of free charges generates the electrostatic
Poisson's_equation
Surface with constant mean curvature
treated as special case. Note that these surfaces are generally different from constant Gaussian curvature surfaces, with the important exception of the sphere
Constant-mean-curvature surface
Constant-mean-curvature_surface
Prototype demonstrator aircraft for the US Air Force Advanced Tactical Fighter program
pronounced chine edges) and canopy with their continuously curved, Gaussian surfaces. By 1985, HSF had evolved to be recognizably similar to the eventual
Northrop_YF-23
Theorem in differential geometry
Gaussian curvature of such a closed surface is equal to 2π times the Euler characteristic of the surface. Note that for orientable compact surfaces without
Gauss–Bonnet_theorem
Study of geometric properties of sets through measure theory
{\displaystyle \mu _{K}(E):=\mu (G_{K}(E))} for any Borel set. This is the Gaussian curvature measure associated with K {\displaystyle K} . It is a Borel measure
Geometric_measure_theory
Non-orientable surface with one edge
the open Möbius strip into a (geodesically) complete flat surface (i.e., having zero Gaussian curvature everywhere). This is the unique metric on the Möbius
Möbius_strip
Mathematical idealization of the surface of a body
distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied
Surface_(mathematics)
Technique in geometric optics
Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems using the paraxial approximation, in
Gaussian_optics
looking surfaces. Efficient generation of fractional Brownian surfaces poses significant challenges. Since the Brownian surface represents a Gaussian process
Brownian_surface
Surface area of a biomolecule accessible to a solvent
The accessible surface area (ASA) or solvent-accessible surface area (SASA) is the surface area of a biomolecule that is accessible to a solvent. Measurement
Accessible_surface_area
Concept in statistical mechanics
and statistical mechanics, the Gaussian free field (GFF) is a Gaussian random field, a central model of random surfaces (random height functions). The
Gaussian_free_field
Two-dimensional manifold
the surface. However, the famous Gauss–Bonnet theorem for closed surfaces states that the integral of the Gaussian curvature K over the entire surface S
Surface_(topology)
Surface able to be flattened without distortion
mathematics, a developable surface (historically called a torse) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened
Developable_surface
Statistical distribution for dependence between random variables
applying the Gaussian copula to credit derivatives to be one of the causes of the 2008 financial crisis; see David X. Li § CDOs and Gaussian copula. Despite
Copula_(statistics)
Differential geometry topic
locally (i.e. on a small piece of the surface). The Jacobian determinant of the Gauss map is equal to Gaussian curvature, and the differential of the
Gauss_map
Distance from the Earth surface to a point near its center
(global) mean curvature, obtained by averaging the Gaussian curvature, K {\displaystyle K} , over the surface of the ellipsoid. Using the Gauss–Bonnet theorem
Earth_radius
Infinitely connected triply periodic minimal surface
periodic minimal surface discovered by Alan Schoen in 1970. It arises naturally in polymer science and biology, as an interface with high surface area. The gyroid
Gyroid
Lens with a thickness that is negligible
s_{o}}+{1 \over s_{i}}={1 \over f}} which is known as the Gaussian thin-lens equation. The Gaussian thin-lens equation has a sign convention described as
Thin_lens
Unit of magnetic induction
known as magnetic induction or magnetic field). The unit is part of the Gaussian system of units, which inherited it from the older centimetre–gram–second
Gauss_(unit)
Unit of the auxiliary magnetic field H in the CGS system of units
magnetic field H in the CGS-EMU and Gaussian systems of units. It is equivalent to 1 dyne per maxwell. In the Gaussian system, the unit of the H-field is
Oersted
Mathematical shape
mean curvature (zero since the helicoid is a minimal surface) and the product gives the Gaussian curvature. The helicoid is homeomorphic to the plane
Helicoid
Concept in differential geometry
the plane tangent to the surface is an osculating plane of the curve. Asymptotic directions can only occur when the Gaussian curvature is negative (or
Asymptotic_curve
Outline of metrology and measurement ISO 25178: areal surface texture standard Surface roughness Gaussian filter "ISO 16610-21:2025 Geometrical product specifications
ISO_16610
Maximal and minimal curvature at a point of a surface
zero at every point, then the Gaussian curvature will be 0 and the surface is a developable surface. For a minimal surface, the mean curvature is zero at
Principal_curvature
Function used in signal processing
10^{-3}\\\hline \end{array}}} The Fourier transform of a Gaussian is also a Gaussian. Since the support of a Gaussian function extends to infinity, it must either
Window_function
Inner product of a surface in 3D, induced by the dot product
du\,dv=2\pi {\Big [}{-\cos v}{\Big ]}_{0}^{\pi }=4\pi } The Gaussian curvature of a surface is given by K = det I I p det I p = L N − M 2 E G − F 2 , {\displaystyle
First_fundamental_form
Operation in calculus
extrapolate to T(0). Gaussian quadrature evaluates the function at the roots of a set of orthogonal polynomials. An n-point Gaussian method is exact for
Integral
Envelope of light rays reflected or refracted by a curved surface/object
several micro-surfaces which are assumed smooth, i.e. the light reflected/refracted by each micro-surface forms a Gaussian caustic. Gaussian caustic means
Caustic_(optics)
Algebraic surface defined by a cubic polynomial
for X is sampled at random from the Gaussian ensemble induced by the Bombieri inner product. Two smooth cubic surfaces are isomorphic as algebraic varieties
Cubic_surface
Doughnut-shaped surface of revolution
4-space or higher dimensions. Its surface has zero Gaussian curvature everywhere. It is flat in the same sense that the surface of a cylinder is flat. In 3
Torus
Probability theory concept
the increments of fBm need not be independent. fBm is a continuous-time Gaussian process B H ( t ) {\textstyle B_{H}(t)} on [ 0 , T ] {\textstyle [0,T]}
Fractional_Brownian_motion
Electromagnetic waves that travel along an interface
Surface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or
Surface_plasmon_polariton
curve and the geodesic disk is not necessarily a planar surface. They can be used to define Gaussian curvature. Whittemore, J. K. (1901). "A Note on Geodesic
Geodesic_circle
Minimal surface
^{4}d^{2})+36(ab^{2}d^{3}-ac^{2}d^{3})=0.\end{aligned}}} The Jacobian, Gaussian curvature and mean curvature are J = 1 81 ( 1 + u 2 + v 2 ) 4 , K = − 4
Enneper_surface
On curvature of surfaces
the principal curvatures of surfaces. It may be used to prove Liebmann's theorem that a compact surface with constant Gaussian curvature must be a sphere
Hilbert's_lemma
Surface containing a line through every point
\mathbf {\dot {r}} (u_{0}),\mathbf {r} (u_{0}))=0.} A smooth surface with zero Gaussian curvature is called developable into a plane, or just developable
Ruled_surface
Optical property
criterion called Gaussian pilot beam allowing to define far- and near-field conditions consists in measuring the actual wavefront surface curvature for an
Fresnel_number
Locus of the zeros of a polynomial of degree two
respectively. These are singly ruled surfaces of zero Gaussian curvature. We see that projective transformations don't mix Gaussian curvatures of different sign
Quadric
Unbounded quadric surface
positive Gaussian curvature at every point. The surface is convex in the sense that the tangent plane at every point intersects the surface only in this
Hyperboloid
Generalization of the concept of parallel lines
{n}})={\vec {n}}} (this parameterization by normal exists for surfaces whose Gaussian curvature is strictly positive, and thus convex, smooth, and not
Parallel_curve
Nonlinear optical process
The SHG radiation pattern generated by an exciting Gaussian beam also has a (homogeneous) 2D Gaussian profile if the nonlinear medium being excited is homogeneous
Second-harmonic_generation
Optical filter
A frequency-selective surface (FSS) is a thin, repetitive surface (such as the screen on a microwave oven) designed to reflect, transmit or absorb electromagnetic
Frequency_selective_surface
Method of interpolation
Kriging (/ˈkriːɡɪŋ/), also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances
Kriging
Measurement of small-scale features on surfaces
Surface metrology is the measurement and characterization of surface topography, and is a branch of metrology. Surface primary form, surface fractality
Surface_metrology
Smoothing filler for images
bilateral filter in its surface blur tool. GIMP implements a bilateral filter in its Filters → Blur tools; and it is called Selective Gaussian Blur. The free G'MIC
Bilateral_filter
Attempt to find a consistent theory of quantum gravity
is applicable only in the vicinity of a Gaussian fixed point. In this regard asymptotic safety at the Gaussian fixed point is equivalent to perturbative
Asymptotic_safety
Intrinsic geometric structures in mathematics
transport in the frame bundle can be used to show that the Gaussian curvature of a surface M measures the amount of rotation obtained by translating vectors
Riemannian connection on a surface
Riemannian_connection_on_a_surface
orbital Gaussian polar coordinates Gaussian q-distribution Gaussian quantum Monte Carlo Gaussian surface Gaussian units Gauss–Codazzi equations (relativity)
Index_of_physics_articles_(G)
Relates the integral of Gaussian curvature of surfaces to the Euler characteristic
integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact surface. A divergent
Cohn-Vossen's_inequality
In mathematics, Gaussian brackets are a special notation invented by Carl Friedrich Gauss to represent the convergents of a simple continued fraction in
Gaussian_brackets
Geometric shape
the term "football" is more commonly used to refer to a surface of revolution whose Gaussian curvature is positive and constant, formed from a more complicated
Lemon_(geometry)
Dynamic disturbance in a medium or field
have a Gaussian shape and is called a Gaussian wave packet. Gaussian wave packets also are used to analyze water waves. For example, a Gaussian wavefunction
Wave
Matrix-valued random variable
components per matrix element. The Gaussian unitary ensemble GUE ( n ) {\displaystyle {\text{GUE}}(n)} is described by the Gaussian measure with density 1 Z GUE
Random_matrix
CGS unit of energy and mechanical work
General Conference of Weights and Measures. It is the unit of energy in Gaussian units, which are widely used in astrophysics[better source needed], applications
Erg
Type of image noise
to formation of ropes in optical speckle. Diffusing-wave spectroscopy Gaussian noise Laser speckle contrast imaging Salt and pepper noise Dainty, C.,
Speckle_(interference)
Mechanism of light transport
wavelength dependent nature of diffusion, the samples used during the (Gaussian) blur can be weighted by channel. This is somewhat of an artistic process
Subsurface_scattering
Mirror with a curved reflecting surface
curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved mirrors have surfaces that are shaped
Curved_mirror
No complete regular surface of constant negative gaussian curvature immerses in R3
states that there exists no complete regular surface S {\displaystyle S} of constant negative gaussian curvature K {\displaystyle K} immersed in R 3
Hilbert's theorem (differential geometry)
Hilbert's_theorem_(differential_geometry)
Trace radiation from the early universe
such as very large scale anisotropies, anomalous alignments, and non-Gaussian distributions. The most longstanding of these is the low-ℓ multipole controversy
Cosmic_microwave_background
Mathematical surface of constant unit negative Gaussian curvature
The Kuen surface is a mathematical surface of constant negative unit Gaussian curvature, making it an example of a pseudospherical surface. It can be
Kuen_surface
Method of spatial measurement using laser
Scientists analysed the waveform signal for extracting peak returns using Gaussian decomposition. Zhuang et al, 2017 used this approach for estimating aboveground
Lidar
German polymath and scholar (1777–1855)
established a property of the notion of Gaussian curvature. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring
Carl_Friedrich_Gauss
Method for characterising the local shape of a surface
surface with this plane. The shape of the intersection is related to the Gaussian curvature. The Dupin indicatrix is the result of the limiting process as
Dupin_indicatrix
Geometric plane containing the normal vector of a given surface
the Gaussian curvature of the surface (negative for saddle shaped surfaces). The mean of the principal curvatures is the mean curvature of the surface; if
Normal_plane_(geometry)
Tensor field in Riemannian geometry
functionally independent component. The Gaussian curvature coincides with the sectional curvature of the surface. It is also exactly half the scalar curvature
Riemann_curvature_tensor
Column of one fluid moving through another
contaminant released into a river. Gaussian distributions are established by Fickian diffusion, and follow a Gaussian, or bell-shaped, distribution. For
Plume_(fluid_dynamics)
Manifold or algebraic variety of dimension n in a space of dimension n+1
has no rational point, but has many points that are rational over the Gaussian rationals. A projective (algebraic) hypersurface of dimension n – 1 in
Hypersurface
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