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Topics referred to by the same term
In mathematics, regular surface may refer to: Regular surface (differential geometry) Non-singular algebraic variety of dimension two This disambiguation
Regular_surface
Mathematics of smooth surfaces
a regular surface. Using the first fundamental form, it is possible to define new objects on a regular surface. Geodesics are curves on the surface which
Differential geometry of surfaces
Differential_geometry_of_surfaces
Topics referred to by the same term
automaton (related to the regular expression) Regular map (graph theory), a symmetric tessellation of a closed surface Regular matroid, a matroid which
Regular
Physical property of textiles
irregular surface, with the exception of silk, which has a regular surface. Luster is the degree of gloss or sheen possessed by the fiber or textile surface. Luster
Luster_(textiles)
No complete regular surface of constant negative gaussian curvature immerses in R3
geometry, Hilbert's theorem (1901) states that there exists no complete regular surface S {\displaystyle S} of constant negative gaussian curvature K {\displaystyle
Hilbert's theorem (differential geometry)
Hilbert's_theorem_(differential_geometry)
Product of the principal curvatures of a surface
covariant derivative and g is the metric tensor. At a point p on a regular surface in R3, the Gaussian curvature is also given by K ( p ) = det S ( p
Gaussian_curvature
Size and shape used to model the Earth for geodesy
on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific
Figure_of_the_Earth
Type of non-Euclidean geometry
cannot isometrically immerse a complete hyperbolic plane (a complete regular surface of constant negative Gaussian curvature) in a 3-D Euclidean space.
Hyperbolic_geometry
Solid with twenty equal triangular faces
regular icosahedron can be unfolded into 43,380 different nets. The earliest net appeared in Albrecht Dürer's Painter's Manual in 1525. The surface area
Regular_icosahedron
Convex polyhedron with regular faces
known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not a uniform polyhedron. There are 92 such solids:
Johnson_solid
literature, this is sometimes also called a "relief drainage system". The regular surface drainage systems, which start functioning as soon as there is an excess
Drainage_system_(agriculture)
Four-dimensional analogues of the regular polyhedra in three dimensions
(face-to-face) in a regular fashion, forming the surface of the 4-polytope which is a closed, curved 3-dimensional space (analogous to the way the surface of the earth
Regular_4-polytope
Area of all the sides of the object, excluding the area of its base and top
lateral surface area is the sum of the areas of all the triangular lateral faces, excluding the base. For a regular pyramid — one whose base is a regular polygon
Lateral_surface
Solid with four equal triangular faces
\left(1/3\right)=\arctan \left(2{\sqrt {2}}\right)\approx 70.529^{\circ }} . The surface area of a regular tetrahedron is four times area of an equilateral triangle: A =
Regular_tetrahedron
Official army of a state or country
A regular army is the official army of a state or country (the official armed forces), contrasting with irregular forces, such as volunteer irregular
Regular_army
Mathematical idealization of the surface of a body
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be
Surface_(mathematics)
Four-dimensional analogue of the cube
cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract
Tesseract
Surface specified with parameters
two choices of the unit normal vector to a surface at a given point, but for a regular parametrized surface, the preceding formula consistently picks one
Parametric_surface
Topics referred to by the same term
function of algebraic varieties a regular map (graph theory), a symmetric 2-cell embedding of a graph into a closed surface This disambiguation page lists
Regular_map
Any of the five regular polyhedra
geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent
Platonic_solid
Solid with eight equal triangular faces
Within this structure, the graph forms a topological surface called a Whitney triangulation. A regular octahedron is a polyhedron with eight equilateral
Regular_octahedron
Solid with 12 equal pentagonal faces
can be applied to the regular dodecahedron's metric properties, as well as to construct the regular dodecahedron. The surface area A {\displaystyle A}
Regular_dodecahedron
Root which grows above the ground
the surface of other plants – have developed cups and scales that gather rainwater or dew. The aerial roots in this case work as regular surface roots
Aerial_root
Flat-sided three-dimensional shape
M. (1939), "The regular sponges, or skew polyhedra", Scripta Mathematica, 6: 240–244 Loeb, Arthur L. (2013), "Polyhedra: Surfaces or solids?", in Senechal
Polyhedron
Topics referred to by the same term
theorem (differential geometry), stating there exists no complete regular surface of constant negative gaussian curvature immersed in R 3 {\displaystyle
Hilbert's_theorem
Soviet and Russian mathematician
on it. This means that the surface admits only trivial infinitesimal bendings. If the metric of a convex surface is regular of regularity Ск, k≥2, in a
Aleksei_Pogorelov
Polyhedron with regular congruent polygons as faces
A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron
Regular_polyhedron
Satellites that formed around their parent planet
In astronomy, a regular moon or a regular satellite is a natural satellite following a relatively close, stable, and circular orbit which is generally
Regular_moon
Negatively-curved minimal surface
V. (1963), "The impossibility in Euclidean 3-space of a complete regular surface with a negative upper bound of the Gaussian curvature", Doklady Akademii
Nadirashvili_surface
Surface in 3D space defined by an implicit function of three variables
implicit surface is a surface in Euclidean space defined by an equation F ( x , y , z ) = 0. {\displaystyle F(x,y,z)=0.} An implicit surface is the set
Implicit_surface
Mathematical concept
follows from proper base change. The surface and the base curve are assumed to be non-singular (complex manifolds or regular schemes, depending on the context)
Elliptic_surface
Laptop computer developed by Microsoft
{{cite web}}: CS1 maint: url-status (link) "Microsoft debuts major Surface overhauls that regular people can't buy". Ars Technica. 22 March 2024. v t e
Surface_Laptop_6
Algebraic surface with many double points
In algebraic geometry, a Barth surface is one of the complex nodal surfaces in 3 dimensions with large numbers of double points found by Wolf Barth (1996)
Barth_surface
Techniques for creating complex surfaces in 3D graphics software
element. Freeform surfaces do not have rigid radial dimensions, unlike regular surfaces such as planes, cylinders and conic surfaces. They are used to
Freeform_surface_modelling
Surface with constant mean curvature
geometry, constant-mean-curvature (CMC) surfaces are surfaces with constant mean curvature. This includes minimal surfaces as a subset, but typically they are
Constant-mean-curvature surface
Constant-mean-curvature_surface
2-in-1 detachable by Microsoft
Surface 3 is a 2-in-1 detachable from the Microsoft Surface series, introduced by Microsoft in 2015. Unlike its predecessor, the Surface 2, Surface 3
Surface_3
In mathematics, a Riemann surface
\Gamma } on the Poincaré disk, the fundamental domain of the Bolza surface is a regular octagon with angles π 4 {\displaystyle {\tfrac {\pi }{4}}} and corners
Bolza_surface
Type of reading disorder
(i.e. exception words). For example, a patient with surface dyslexia can correctly read regular words like "mint", but will fail when presented with
Surface_dyslexia
Microsoft hybrid notebook computer
fifth-generation Surface Pro (marketed as the Surface Pro, colloquially referred to as the Surface Pro 2017 or Surface Pro 5) is a Surface-series 2-in-1
Surface_Pro_(2017)
Geometric representation of material yield
A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of
Yield_surface
Composite building material in England
with a lime-based mixture and paint it. This produced a consistent, regular surface which could be used to build the symmetrical façades required in Georgian
Bungaroosh
1992 Cyclone-class patrol ship
Operations Command rejected them as too big for commando missions, and the regular surface Navy dismissed them as too small for any of its missions. The Navy
USS_Cyclone
Method of representing objects in 3D computer graphics
types of surfaces: Regular (or canonical) surfaces include surfaces of revolution such as cylinders, cones, spheres, and tori, and ruled surfaces (linear
Computer representation of surfaces
Computer_representation_of_surfaces
Polytope with highest degree of symmetry
presented to construct a regular polyhedron is via a fold-out net. To obtain a fold-out net of a polyhedron, one takes the surface of the polyhedron and
Regular_polytope
Surface formed from spheres centered along a curve
In geometry and topology, a channel surface or canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve
Channel_surface
Concept in integration theory
{\partial \varphi }{\partial u_{2}}}\right|^{2}=\det(J^{T}J)} For a regular surface, this determinant is non-vanishing; equivalently, the Jacobian matrix
Volume_element
Rational surface in 5-dimensional projective space
is regular – the Veronese map is biregular. More precisely, the images of open sets in the Zariski topology are again open. The Veronese surface is the
Veronese_surface
Classical modular curve Bolza surface Macbeath surface Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone
List_of_mathematical_shapes
Shape of textile fibers from cross sectional view
with a more regular surface seem brighter than natural fibers with an irregular surface, with the exception of silk, which has a regular surface. Different
Cross_section_(fiber)
Eleventh generation of Microsoft Surface Pro
supersede the Surface Pro 9 and Surface Pro X. It was released shortly after the Intel x86-based Surface Pro 10, and unveiled alongside the Surface Laptop (7th
Surface_Pro_(11th_generation)
Symmetric tessellation of a closed surface
In mathematics, a regular map is a symmetric tessellation of a closed surface. More precisely, a regular map is a decomposition of a two-dimensional manifold
Regular_map_(graph_theory)
Geometric space with four dimensions
seen in the accompanying 2D animation of one of the simplest possible regular 4D objects, the tesseract, which is analogous to the 3D cube. The idea
Four-dimensional_space
Traits of plants and animals
these traits are associated with the environment. In habitats with regular surface fires, similar species developed traits such as thick bark and self-pruning
Fire_adaptations
Measure of a two-dimensional surface
The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface
Surface_area
One of two different regular graphs with 16 vertices
faces; and in the non-orientable surface of genus 6, forming tetragonal faces. The characteristic polynomial of the 5-regular Clebsch graph is ( x + 3 ) 5
Clebsch_graph
Natural number
polygon with 20 edges. Bring's curve is a Riemann surface, whose fundamental polygon is a regular hyperbolic icosagon. The largest number of faces a
20_(number)
2024 laptop by Microsoft
The Surface Laptop of the 7th generation, also referred to as the Surface Laptop 7th Edition, is a laptop computer developed by Microsoft. It is the seventh
Surface Laptop (7th generation)
Surface_Laptop_(7th_generation)
Practice of fishing by drawing a baited line or lure behind a boat
pushing water aggressively on the surface to, most commonly, tracking along in a straight line with a regular surface pop and bubble trail. Besides the
Trolling_(fishing)
1999 Cyclone-class patrol ship
Command rejected them as too big for special operations missions and regular surface Navy dismissed them as too small for any of its missions, the Navy
USS_Tornado
Basal organ of a vascular plant
above the surface on other plants, aerial roots serve for reaching to water sources or reaching the surface, and then functioning as regular surface roots
Root
Compact Riemann surface of genus 3
Hurwitz surfaces are tiled in the same way, as quotients. This tiling is uniform but not regular (it is by scalene triangles), and often regular tilings
Klein_quartic
Mathematical technique used in environmental sciences
a regular grid of points from scattered observations such as archeological finds or soil survey results. Agterberg, Frits P. (1984), "Trend Surface Analysis"
Trend_surface_analysis
Blue area of an ice sheet
rippled surfaces have almost regular surface patterns, although wholly smooth blue-ice areas exist as well, and the terrain even of rippled surfaces features
Blue-ice_area
number field (which is the case above). An arithmetic surface is then a regular fibered surface over a Dedekind scheme of dimension one. This generalisation
Arithmetic_surface
Badge of the United States Navy
pin. Surface line personnel who are not yet qualified have the 1160 officer designator: once qualified they receive the 1110 designator for Regular Navy
Surface_warfare_insignia
Differentiable function whose derivative is everywhere injective
^{3}} by a regular homotopy of immersions f t : S 2 → R 3 . {\displaystyle f_{t}:\mathbb {S} ^{2}\to \mathbb {R} ^{3}.} Boy's surface is an immersion
Immersion_(mathematics)
Surface that locally minimizes its area
below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint
Minimal_surface
Natural satellite orbiting Earth
size, while the reflectance (albedo) of its surface is comparable to that of asphalt. About 59% of the surface of the Moon is visible from Earth owing to
Moon
translation surface is obtained by gluing the opposite sides of a parallelogram. It is a flat torus with no singularities. If P {\displaystyle P} is a regular 4
Translation_surface
Static pressure exerted by the weight of the Earth's atmosphere
on the atmospheric gases above the surface and is a function of the mass of the planet, the radius of the surface, and the amount and composition of the
Atmospheric_pressure
Size of a two-dimensional surface
region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the
Area
Result of differential geometry proved by Gauss
{S}}} be regular surfaces, and let r = r ( u , v ) {\displaystyle \mathbf {r} =\mathbf {r} (u,v)} be a parametrisation of a patch of the surface S {\displaystyle
Theorema_Egregium
Genus of viruses
viruses are about 140–170 nm wide and 220–300 nm long, and have a regular surface structure; tubules with a diameter of 10–20 nm form a criss-cross pattern
Parapoxvirus
Solid with six equal square faces
polyhedron. That is, no plane intersecting its surface only along edges, thereby cutting into two or more convex, regular-faced polyhedra. Given a cube with edge
Cube
Polyhedron with 12 faces
the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and
Dodecahedron
Skew polygon derived from a polytope
surface of a 4-polytope is a 3-dimensional space (the 3-sphere), the Petrie polygon of a regular 4-polytope is a 3-dimensional helix in this surface.
Petrie_polygon
M, Rietkerk M, Borren W, Lapshina E, Bleuten W, Wassen MJ (2008). "Regular Surface Patterning of Peatlands: Confronting Theory with Field Data". Ecosystems
Patterned_vegetation
Other commonly encountered regular-shaped surfaces are subway walls and pillars. Image Geometry Correction onto irregular surfaces is the most advanced form
Image_geometry_correction
Fantasy franchise
has a unique topology. In addition to the «regular» surface, the earth has a «reverse side». The two surfaces are connected by pathways located in several
The_Wolfhound
Species of bacterium
Stewart, Murray; Murray, Robert (6 November 1981). "Structure of the Regular Surface Layer of Aquaspirillum serpens MW5". Journal of Bacteriology. 150 (1):
Aquaspirillum_serpens
International Association for Sports Surface Sciences (ISSS) is the union of labs and experts in the field of sports surfaces. It was founded in 1985 in Switzerland
International Association for Sports Surface Sciences
International_Association_for_Sports_Surface_Sciences
Largest moon of Saturn
at 20 Saturn radii or 1.2 million km above Saturn's apparent surface. From Titan's surface, Saturn, disregarding its rings, subtends an arc of 5.09 degrees
Titan_(moon)
Polyhedra are determined by surface distance
surface has a given metric, it may also be possible for there to exist non-convex polyhedra with the same metric. An example is given by the regular icosahedron:
Alexandrov's theorem on polyhedra
Alexandrov's_theorem_on_polyhedra
Polyhedron with non-planar faces
In geometry, the regular skew polyhedra are generalizations to the set of regular polyhedra which include the possibility of nonplanar faces or vertex
Regular_skew_polyhedron
Fourth planet from the Sun
has suggested that any water on the Martian surface may have been too salty and acidic to support regular terrestrial life. The environmental conditions
Mars
tend to swim constantly north at 4-5 knots (5–9 km/h) and will have regular surface intervals. At this time the whales are utilizing the Inshore Northern
Whale_watching_in_Sydney
C(P) surface, since it is the "complement" of the Schwarz P surface. It can be extended with further handles, converging towards the expanded regular octahedron
Neovius_surface
Spherical polyhedron composed of lunes
tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices. A regular n-gonal hosohedron has Schläfli symbol
Hosohedron
Infrastructure for draining excess rain and ground water from impervious surfaces
storm drain, storm sewer (United Kingdom, U.S. and Canada), highway drain, surface water drain/sewer (United Kingdom), or stormwater drain (Australia and
Storm_drain
Set of points equidistant from a center
A sphere (from Ancient Greek σφαῖρα (sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points
Sphere
Mirror-like wave reflection
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface. The law of reflection states that a
Specular_reflection
do not cover the surface of a circle finitely many times. In addition to the planar regular polygons there are infinitely many regular skew polygons. Skew
List_of_regular_polytopes
Substance that lowers surface tension
surface tension or interfacial tension between two liquids, a liquid and a gas, or a liquid and a solid. The word surfactant is a blend of "surface-active
Surfactant
Global climate phenomenon
global climate phenomenon that emerges from variation in winds and sea surface temperatures over the tropical Pacific Ocean. Those variations have an
El_Niño–Southern_Oscillation
World Wide Web content existing on darknets
public organizations and individuals. Users of the dark web refer to the regular web as clearnet due to its unencrypted nature. The Tor dark web or onionland
Dark_web
Tablet-hybrid computer device
The Surface Pro 2 is a Surface-series 2-in-1 detachable produced by Microsoft. Unveiled at an event in New York City on September 23, 2013, and released
Surface_Pro_2
Body of salt water covering most of Earth
these processes and components together make up ocean surface ecosystems. Tides are the regular rise and fall in water level experienced by oceans, primarily
Ocean
Poset representing certain properties of a polytope
versa. For example, a traditional polytope is regular if all its facets and vertex figures are regular, but this is not necessarily so for an abstract
Abstract_polytope
Infinite polyhedron with non-planar faces
p*(q−2) in any regular generalized polyhedron. Every regular pseudopolyhedron approximates a negatively curved surface. The seven regular pseudopolyhedra
Skew_apeirohedron
In Riemann surface theory and hyperbolic geometry, the MacBeath surface, also called MacBeath curve or the Fricke–MacBeath surface curve, is the genus-7
MacBeath_surface
travel, tourism, insurance
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travel, tourism, insurance