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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
In mathematics, regular surface may refer to: Regular surface (differential geometry) Non-singular algebraic variety of dimension two This disambiguation
Regular_surface
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
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
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)
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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)
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
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
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)
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)
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
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
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
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
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
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
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)
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
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
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)
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
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
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
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
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
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
Classical modular curve Bolza surface Macbeath surface Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone
List_of_mathematical_shapes
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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 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
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
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
Projection on sole of shoe
exist for different surfaces: replaceable aluminum cleats which are worn in wet dirt, firm plastic cleats which are for regular surfaces, and short, plastic
Cleat_(shoe)
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
Large body of salt water
water. The salinity of water bodies varies widely, being lower near the surface and the mouths of large rivers and higher in the depths of the ocean; however
Sea
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
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
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
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
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
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
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
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
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
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
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
linguistics, a surface filter is a type of sound change that operates not at a particular point in time but over a longer period. Surface filters normally
Surface_filter
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
REGULAR SURFACE
REGULAR SURFACE
Male
German
A derivative of German Reginar, RAINER means "wise warrior."
Girl/Female
Muslim/Islamic
One who remembers Allah regularly
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bowen, with the addition of the regular English patronymic suffix -s.Altered spelling of Dutch Bouwens, a variant of Bauwens.
Girl/Female
Muslim
One who remembers Allah regularly
Girl/Female
Indian
One who remembers Allah regularly
Boy/Male
Indian, Sanskrit
Connector; Regulator
Surname or Lastname
North German
North German : variant of Asch.English : variant spelling of Ash (asche was the regular Middle English spelling of this word).
Male
Spanish
Spanish form of Roman Latin Regulus, RÉGULO means "ruler."
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' Edward Poins, an irregular humorist.
Girl/Female
Hebrew
Precious.
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bevan, with the addition of the regular English patronymic suffix -s.
Male
Italian
Italian form of German Reginar, RANIERO means "wise warrior."
Surname or Lastname
English (Devon)
English (Devon) : unexplained. Possibly an irregular variant of Birchall.
Surname or Lastname
English
English : nickname probably for a tenant whose feudal obligations included a regular payment in cash or kind (for example bread or salt) of a halfpenny.
Boy/Male
Hindu, Indian, Traditional
Conduct; Regular Performance of Worship
Girl/Female
Arabic, Muslim
Pilgrimage to Makkah Other than Regular Hajj Days
Boy/Male
Gujarati, Haryanvi, Hindu, Indian, Kannada, Marathi, Telugu
Regular; Ethical; Good in Nature
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' An irregular humorist.
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Male
Scandinavian
Scandinavian form of German Reginar, RAGNAR means "wise warrior."
REGULAR SURFACE
REGULAR SURFACE
Surname or Lastname
English
English : variant of Maggard.
Boy/Male
Indian, Punjabi, Sikh
Firm and Brave
Female
Dutch
, a young woman whose beauty ensnares men.
Boy/Male
Assamese, Gujarati, Hindu, Indian, Malayalam, Mythological, Punjabi, Sanskrit, Sikh, Tamil, Traditional
The Great God Indra; The God of the Sky; The Great God Indra (the God of the Sky); God of the Sky
Boy/Male
Hindu, Indian, Traditional
Triumph of God
Boy/Male
Hindu, Indian
Clever; Deep Mind
Female
Bulgarian
, flowers.
Female
African
born on Sunday.
Girl/Female
Scottish American French
Scottish version of the Old French Jehane, a feminine form of John: God is gracious.
Female
English
Feminine form of English Nolan, NOLENE means "little champion" or "little chariot fighter."
REGULAR SURFACE
REGULAR SURFACE
REGULAR SURFACE
REGULAR SURFACE
REGULAR SURFACE
a.
Of or pertaining to the jugular vein; as, the jugular foramen.
a.
Irregular in position; having no regular order; as, scattered leaves.
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
a.
Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.
v. t.
To cause to become regular; to regulate.
a.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
pl.
of Regulus
a.
Thorough; complete; unmitigated; as, a regular humbug.
adv.
In a regular manner; in uniform order; methodically; in due order or time.
n. pl.
A division of Echini which includes the circular, or regular, sea urchins.
a.
Not regular; not bound by monastic vows or rules; not confined to a monastery, or subject to the rules of a religious community; as, a secular priest.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
a.
Measured by an angle; as, angular distance.
pl.
of Tegula
a.
Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.
n.
One who is not regular; especially, a soldier not in regular service.
n.
A secular ecclesiastic, or one not bound by monastic rules.
a.
Of or pertaining to a tile; resembling a tile, or arranged like tiles; consisting of tiles; as, a tegular pavement.
a.
Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.
a.
Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no straight; not uniform; as, an irregular line; an irregular figure; an irregular verse; an irregular physician; an irregular proceeding; irregular motion; irregular conduct, etc. Cf. Regular.