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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
with an irregular surface. Synthetic fibers with a more regular surface seem brighter than natural fibers with an irregular surface, with the exception
Luster_(textiles)
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
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
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
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)
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
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)
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
Concept in differential equation mathematics
Riemann surface of some punctured disc around a. This presents no difficulty for a an ordinary point (Lazarus Fuchs 1866). When a is a regular singular
Regular_singular_point
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
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)
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
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
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
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
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
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
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 and the arithmetic genus of more complicated surfaces. Surfaces are sometimes called regular or irregular depending on whether or not the irregularity
Irregularity_of_a_surface
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
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
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
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 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
Genus of viruses
single-stranded RNA, around 4-5.4kb in length. These virions have a regular surface structure and are composed of 17% nucleic acid. Viral replication is
Tombusvirus
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
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
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
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
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
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
Graph property
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at
Distance-regular_graph
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)
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
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
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
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
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
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
2000 video game
Battleship: Surface Thunder (also known as Battleship 2: Surface Thunder) is a PC video game developed by Meyer/Glass Interactive and published by Hasbro
Battleship:_Surface_Thunder
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)
aside in city streets exclusively for bikes Class III: Bike route - a regular surface street that is designated as being safe or attractive to bicyclists
Transportation_in_California
In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another. The homotopy
Regular_homotopy
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)
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
Military operations involving the use of surface warships
Surface warfare is naval warfare involving surface ships. It is one of the four operational areas of naval warfare, the others being underwater warfare
Surface_warfare
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
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
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
Classical modular curve Bolza surface Macbeath surface Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone
List_of_mathematical_shapes
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
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
Surface of revolution with a hole in the middle
toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example
Toroid
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
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
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
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)
In mathematics, a planar Riemann surface (or schlichtartig Riemann surface) is a Riemann surface sharing the topological properties of a connected open
Planar_Riemann_surface
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)
regular 1. A regular surface is one whose irregularity is zero. 2. Having no singularities; see regular local ring. 3. Symmetrical, as in regular polygon
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
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
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
Planet outside of the Solar System
the Russian astronomers unusual result: regular splashes were found out.<...> Though stains on a star surface also can cause similar changes of shine
Exoplanet
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
North American professional baseball league
introduction of free agency in baseball. Modern stadiums with artificial turf surfaces began to change the game in the 1970s and 1980s. Home runs began to dominate
Major_League_Baseball
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
Species of fungus
quickly turns red with injury. Microscopically, its spores have more regular surface ridges and a more widely meshed reticulum. Lactarius fuliginosus is
Lactarius_fuliginosus
Dianalytic manifold of complex dimension 1
a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein surfaces generalize
Klein_surface
Any kind of device or material used on a road surface to convey official information
Road surface marking is any kind of device or material that is used on a road surface in order to convey official information; they are commonly placed
Road_surface_marking
American surface-to-air missile system since 1981
The MIM-104 Patriot is a mobile interceptor missile surface-to-air missile (SAM) system, the primary such system used by the United States Army and several
MIM-104_Patriot
U.S. anti-ship missile
Land Attack Missile – Expanded Response) are cruise missile variants. The regular Harpoon uses active radar homing and flies just above the water to evade
Harpoon_(missile)
Theorem in algebraic geometry
surface a Hurwitz surface. Because compact Riemann surfaces are synonymous with non-singular complex projective algebraic curves, a Hurwitz surface can
Hurwitz's automorphisms theorem
Hurwitz's_automorphisms_theorem
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