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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)
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
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)
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
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
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
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)
Solid with four equal triangular faces
between two triangular faces) of a regular tetrahedron is arccos(1/3)=arctan(22)≈70.529∘. The surface area of a regular tetrahedron is four times area of
Regular_tetrahedron
Solid with 12 equal pentagonal faces
the regular dodecahedron's metric properties, as well as to construct the regular dodecahedron. The surface area A and the volume V of a regular dodecahedron
Regular_dodecahedron
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)
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
Eleventh generation of Microsoft Surface Pro
The Surface Pro 11th Edition is a 2-in-1 detachable tablet computer developed by Microsoft to supersede the Surface Pro 9 and Surface Pro X. It was released
Surface_Pro_11th_Edition
Non-orientable surface with one edge
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a
Möbius_strip
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)
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
Classical modular curve Bolza surface Macbeath surface Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve (aka Lissajous
List_of_mathematical_shapes
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
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)
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
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
2024 laptop by Microsoft
The Surface Laptop 7th Edition is a laptop computer developed by Microsoft. It is the seventh generation of Surface Laptop, and was unveiled alongside
Surface_Laptop_7th_Edition
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
translation surface is obtained by gluing the opposite sides of a parallelogram. It is a flat torus with no singularities. If P is a regular 4g-gon then
Translation_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)
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)
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
Coating that prevents sticking
A non-stick surface is engineered to reduce the ability of other materials to stick to it. Non-sticking cookware is a common application, where the non-stick
Non-stick_surface
Global climate phenomenon
manifests as fluctuations in sea surface temperatures over the tropical Pacific Ocean. The warming phase of the sea surface temperature is known as "El Niño"
El_Niño–Southern_Oscillation
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
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
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
Natural satellite orbiting Earth
as the largest and most massive in relation to its parent planet. Its surface gravity is about one-sixth of Earth's, about half that of Mars, and the
Moon
Regular-season tournament of the National Basketball Association
National Basketball Association (NBA) tournament that occurs during the regular season. The tournament was officially announced on July 8, 2023, and it
NBA_Cup
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)
Underwater diving breathing gas supplied from the surface
for scuba with most of the advantages and disadvantages of a regular compressor fed surface air supply. The assembled combination of equipment is called
Surface-supplied_diving
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
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
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
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
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
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
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
Measure in 3-dimensional geometry
rays from the apex would cover a number of steradians equal to the total surface area of the unit sphere, 4π. Solid angles can also be measured in squares
Solid_angle
Non-orientable mathematical surface
bottle (/ˈklaɪn/) is an example of a surface with no distinct inside or outside. In other words, it is a one-sided surface which, if traveled upon, could be
Klein_bottle
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
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
Kepler–Poinsot polyhedron
onto a regular dodecahedron's faces. Suppose the pentagrammic faces are considered as five triangular faces. In that case, it shares the same surface topology
Small_stellated_dodecahedron
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
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
First crewed Moon landing (1969)
orbit. After a three-day transit, Armstrong and Aldrin descended to the surface aboard the LM Eagle, landing in the Sea of Tranquility (Mare Tranquillitatis)
Apollo_11
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
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
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
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
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
Polyhedron with eight triangular faces
octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four
Octahedron
Tablet computer by Microsoft
The Surface Pro 4 is the fourth-generation Surface-series 2-in-1 detachable, designed, developed, and marketed by Microsoft. The Surface Pro 4 was announced
Surface_Pro_4
travel, tourism, insurance
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