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Topics referred to by the same term
Look up planar in Wiktionary, the free dictionary. Planar is an adjective meaning "relating to a plane (geometry)". Planar may also refer to: Planar (computer
Planar
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Type of SMPS transformer
Planar transformers are high frequency transformers used in isolated switchmode power supplies operating at high frequency. As opposed to conventional
Planar_transformer
Puzzle computer game involving planar graphs
Planarity is a 2005 puzzle computer game by John Tantalo, based on a concept by Mary Radcliffe at Western Michigan University. The name comes from the
Planarity
Photographic lens designed by Paul Rudolph
The Zeiss Planar is a photographic lens designed by Paul Rudolph at Carl Zeiss in 1896. Rudolph's original was a six-element symmetrical double Gauss lens
Zeiss_Planar
American digital display manufacturer
Planar Systems, Inc. is an American digital display manufacturing corporation with a facility in Hillsboro, Oregon. Founded in 1983 as a spin-off from
Planar_Systems
German optics company
(9×12 cm fmt) Planar lenses (5 elements in 4 groups) Planar 80mm ƒ/2.8 (6×7 cm fmt) Planar 100mm ƒ/2.8 (6.5×9 cm fmt) Planar 135mm ƒ/3.5 Planar 135mm ƒ/3
Zeiss_(company)
Process used to make microchips
The planar process is a manufacturing process used in the semiconductor industry to build individual components of a transistor, and in turn, connect those
Planar_process
Molecular geometry of symmetry D_3h
In chemistry, trigonal planar is a molecular geometry model with one atom at the center and three atoms at the corners of an equilateral triangle, called
Trigonal planar molecular geometry
Trigonal_planar_molecular_geometry
alternating planar algebras first appeared in the work of Hernando Burgos-Soto on the Jones polynomial of alternating tangles. Alternating planar algebras
Alternating_planar_algebra
Algorithmic problem of finding non-crossing drawings
In graph theory, the planarity testing problem is the algorithmic problem of testing whether a given graph is a planar graph (that is, whether it can
Planarity_testing
In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor. They also provide an appropriate
Planar_algebra
Molecular geometry of five coplanar atoms
In chemistry, the square planar molecular geometry describes the stereochemistry (spatial arrangement of atoms) that is adopted by certain chemical compounds
Square planar molecular geometry
Square_planar_molecular_geometry
Planar chirality, also known as 2D chirality, is the special case of chirality for two dimensions. Most fundamentally, planar chirality is a mathematical
Planar_chirality
Outcrop of rock in the sea formed by the growth and deposit of stony coral skeletons
A coral reef is an underwater ecosystem characterized by reef-building corals. Reefs are formed of colonies of coral polyps held together by calcium carbonate
Coral_reef
Audiophile turntable by Rega Research
The Rega Planar 3, together with its successors, the P3 and RP3, is a well-known budget audiophile turntable by British hi-fi manufacturer, Rega Research
Rega_Planar_3
Graph theory concept
In graph theory, a planar cover of a finite graph G is a finite covering graph of G that is itself a planar graph. Every graph that can be embedded into
Planar_cover
Fracture or discontinuity in displaced rock
In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant displacement as a result of rock-mass
Fault_(geology)
Graph representing faces of another graph
In the mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has
Dual_graph
Graph with at most one crossing per edge
In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing
1-planar_graph
Mathematical model of a thin, flat object
In mathematics, a planar lamina (or plane lamina) is a plane figure representing a thin, usually uniform, flat layer of a solid. It serves also as an idealized
Planar_lamina
Method of arranging pixel data
In computer graphics, planar is the method of arranging pixel data into several bitplanes of RAM. Each bit in a bitplane is related to one pixel on the
Planar_(computer_graphics)
Reflex of the human foot
The plantar reflex is a superficial reflex elicited when the sole of the foot is stimulated with a blunt instrument. The reflex can take one of two forms
Plantar_reflex
Classification of a two-dimensional repetitive pattern
three-dimensional space groups. A proof that there are only 17 distinct groups of such planar symmetries was first carried out by Evgraf Fedorov in 1891 and then derived
Wallpaper_group
Graph with edges non-crossing and upward
In graph drawing, an upward planar drawing of a directed acyclic graph is an embedding of the graph into the Euclidean plane, in which the edges are represented
Upward_planar_drawing
Planar cell polarity (PCP) is a type of cell polarity in which the cells are oriented in a coordinated way across the plane of an epithelial tissue. The
Planar_cell_polarity
Transmission lines with flat ribbon-like conducting or dielectric lines
Planar transmission lines are transmission lines with conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines.
Planar_transmission_line
3D projection in which points in 3D space are linearly mapped onto a 2D plane
Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional
Planar_projection
Boolean satisfiability problem restricted to a planar incidence graph
the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence
Planar_SAT
Any planar graph can be subdivided by removing a few vertices
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into
Planar_separator_theorem
A Sawyer motor or planar motor (also called area drive) is a multi-coordinate drive that can perform several independent movements in one plane. Goods
Sawyer_motor
Construction in projective geometry
{\displaystyle T\colon R^{3}\to R\,} may be called a ternary system. A planar ternary ring (PTR) or ternary field is special type of ternary system used
Planar_ternary_ring
The planar Hall sensor is a type of magnetic sensor based on the planar Hall effect of ferromagnetic materials. It measures the change in anisotropic
Planar_Hall_sensor
On cycle bases of planar graphs
In graph theory, Mac Lane's planarity criterion is a characterisation of planar graphs in terms of their cycle spaces, named after Saunders Mac Lane who
Mac Lane's planarity criterion
Mac_Lane's_planarity_criterion
Area of discrete mathematics
planar straight-line graph. Any planar graph can be represented as a planar straight-line graph by Fáry's theorem. The planar straight-line graph is the special
Graph_theory
Characterization of planar graphs by matroids
Whitney's planarity criterion is a matroid-theoretic characterization of planar graphs, named after Hassler Whitney. It states that a graph G is planar if and
Whitney's_planarity_criterion
Natural number
{\displaystyle N-1} is a prime number. The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries)
4
Main printed circuit board used for a computing device
higher-end models in the PS/2 line, such as the Model 80, used the term planar instead. Apple commonly uses logic board in its technical documentation
Motherboard
Semiconductor foundry company
1993 200 Bulk – Planar – – – CS-24 500 1993 200 Bulk – Planar – – – 5L 500 1993 200 Bulk – Planar – – – 5S 500 1994 200 Bulk – Planar – – – SiGe 5HP 500
GlobalFoundries
The planar reentry equations are the equations of motion governing the unpowered reentry of a spacecraft, based on the assumptions of planar motion and
Planar_reentry_equations
2D surface which extends indefinitely
trigonometry, graph theory, and graphing are performed in a two-dimensional or planar space. In mathematics, a Euclidean plane is a Euclidean space of dimension
Plane_(mathematics)
Device which converts input forces and motion to output forces and motion
called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of Special Euclidean group SE, consisting of planar rotations
Mechanism_(engineering)
Cylindrical equidistant map projection
panoramic image. The forward projection transforms spherical coordinates into planar coordinates. The reverse projection transforms from the plane back onto
Equirectangular_projection
Type of loudspeaker
tweeters. Some loudspeaker designers use a planar magnetic tweeter, sometimes called a quasi-ribbon. Planar magnetic tweeters are generally less expensive
Tweeter
Topological quantum error correcting code
with open boundary conditions, the planar code. As of 2025, Google Quantum AI has implemented a distance-7 planar code on their newest generation of superconducting
Surface_code
Assembly of systems connected to manage forces and movement
the special cases, planar or spherical simple open chain, M = ∑ i = 1 j f i , {\displaystyle M=\sum _{i=1}^{j}\ f_{i},} planar or spherical simple
Linkage_(mechanical)
On forbidden subgraphs in planar graphs
forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states that a finite graph is planar if and only if it does not contain
Kuratowski's_theorem
Figure formed by two rays meeting at a common point
Krystek, Michael P. (2022), "On Angular Measures in Axiomatic Euclidean Planar Geometry", Measurement Science Review, 22 (4): 152–159, doi:10.2478/msr-2022-0019
Angle
Geometric property of objects being in the same plane
In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar
Coplanarity
Geometric graph with unit edge lengths
in which no edges cross. Every matchstick graph is a planar graph, but some otherwise-planar unit distance graphs (such as the Moser spindle) have a
Unit_distance_graph
Technique for drawing non-planar graphs
graph drawing methods from planar graphs to graphs that are not planar, by embedding the non-planar graphs within a larger planar graph. Planarization may
Planarization
Set of laboratory techniques for separation of mixtures
with DNA, the higher the salt concentration needed to elute that protein. Planar chromatography is a separation technique in which the stationary phase is
Chromatography
Planar laser-induced fluorescence (PLIF) is an optical diagnostic technique widely used for flow visualization and quantitative measurements. PLIF has
Planar laser-induced fluorescence
Planar_laser-induced_fluorescence
Superconformal Yang–Mills theory
0 (planar graph) contribution survives. Planar Feynman diagrams are graphs in which no propagator cross over another one, in contrast to non-planar Feynman
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Planar hexacoordinate carbon in chemistry describes a molecular geometry featuring a planar arrangement of carbon with six surrounding atoms. No actual
Planar_hexacoordinate_carbon
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
Planar maps require at most four colors
coloring of the planar graph of adjacencies between regions. In graph-theoretic terms, the theorem states that for a loopless planar graph G {\displaystyle
Four_color_theorem
On forbidden minors in planar graphs
forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite graph is planar if and only if its minors include neither
Wagner's_theorem
Technique used to separate non-volatile mixtures
2009.12.071) F. Geiss (1987): Fundamentals of thin layer chromatography planar chromatography, Heidelberg, Hüthig, ISBN 3-7785-0854-7 Justus G. Kirchner
Thin-layer_chromatography
Aperture lens
The Carl Zeiss Planar 50mm f/0.7 is one of the largest relative aperture (fastest) lenses in the history of photography. The lens was developed for the
Carl_Zeiss_Planar_50mm_f/0.7
The first planar monolithic integrated circuit (IC) chip was demonstrated in 1960. The idea of integrating electronic circuits into a single device was
Invention of the integrated circuit
Invention_of_the_integrated_circuit
Assignment of vector fields to manifolds
In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces
Tangent_space
Mathematical model of the physical space
book IX, proposition 20. Euclid refers to a pair of lines, or a pair of planar or solid figures, as "equal" (ἴσος) if their lengths, areas, or volumes
Euclidean_geometry
Four-dimensional algebra over the real numbers
The planar quaternions make up a four-dimensional algebra over the real numbers. Their primary application is in representing rigid body motions in 2D
Applications of dual quaternions to 2D geometry
Applications_of_dual_quaternions_to_2D_geometry
the University of Amsterdam, who in 1970 used them to characterize rigid planar structures. However, this characterization, the Geiringer–Laman theorem
Laman_graph
Flat surface
{\displaystyle \mathbb {R} ^{3}} . A plane segment or planar region (or simply "plane", in lay use) is a planar surface region; it is analogous to a line segment
Euclidean planes in three-dimensional space
Euclidean_planes_in_three-dimensional_space
Tree data structure that partitions a 2D area
quadtrees with random insertion have been studied under the name weighted planar stochastic lattices. Point quadtrees are constructed as follows. Given the
Quadtree
System to specify locations on Earth
are not Cartesian because the measurements are angles and are not on a planar surface. A full GCS specification, such as those listed in the EPSG and
Geographic_coordinate_system
Point fixed to a body undergoing planar movement
velocity center, instantaneous center, or pole of planar displacement) of a body undergoing planar movement is a point that has zero velocity at a particular
Instant_centre_of_rotation
Disruption of the periodicity of a crystal lattice
types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method
Crystallographic_defect
2015 video game
name Worlds of Magic: Planar Conquest; which has been sometimes described as an improved sequel. In 2016 Worlds of Magic: Planar Conquest was also released
Worlds_of_Magic
Mathematical invariance under transformations
In everyday life, Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') refers to a sense of harmonious
Symmetry
Vehicle wing mirror
of the world permits planar, convex, and/or aspheric mirrors on either side of the vehicle. American research suggests non-planar driver-side mirrors may
Side-view_mirror
Graph layout on multiple half-planes
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the
Book_embedding
Antenna used in wireless communication
1950s as a bent-wire antenna. However, its most widespread use is as a planar inverted-F antenna (PIFA) in mobile wireless devices for its space saving
Inverted-F_antenna
Planar fabric in rock
Cleavage, in structural geology and petrology, describes a type of planar rock feature that develops as a result of deformation and metamorphism. The degree
Cleavage_(geology)
Vehicle propelled fully or mostly by electricity
carbon-based supercapacitors. Advanced hybrid designs include all-solid-state planar micro-supercapacitors based on 2D vanadium nitride nanosheets and cobalt
Electric_vehicle
This is a list of tessellations. Tessellation Uniform tiling Convex uniform honeycombs List of k-uniform tilings List of Euclidean uniform tilings Uniform
List_of_tessellations
Mechanical linkage consisting of four links connected by joints in a loop
assembly is called a planar four-bar linkage. Spherical and spatial four-bar linkages also exist and are used in practice. Planar four-bar linkages are
Four-bar_linkage
resulted in a planar chiral DMAP, which can be used as an enantioselective catalyst. Fu, Gregory C. (2004-08-01). "Asymmetric Catalysis with "Planar-Chiral"
Fu's_Planar_DMAP
Converts an electrical audio signal into a corresponding sound
of the first kind. A planar source such as this radiates sound uniformly for wavelengths longer than the dimensions of the planar source, and as frequency
Loudspeaker
the graph is planar), χ (chromatic number) and χ' (chromatic index) are also sortable, allowing searching for a parameter. In the planarity column, T indicates
List of graphs by edges and vertices
List_of_graphs_by_edges_and_vertices
Planar Crown is a series of Blind mate electrical RF connectors manufactured by API Weinchel. It is fitted for example to the RF input connector of the
Planar_Crown_connector
In graph drawing, a clustered planar graph is a graph together with a hierarchical clustering on its vertices, such that the graph can be drawn together
Clustered_planarity
Planar graph embedding where edges map to straight-line segments
theory, a planar straight-line graph (PSLG), also called a straight-line plane graph or plane straight-line graph, is an embedding of a planar graph in
Planar_straight-line_graph
Line of twin-lens and single-lens reflex cameras by Rollei
camera than their imitators.[citation needed] The highly regarded Zeiss Planar f2.8 and Schneider Xenotar lenses, both 80mm focal length and fast in comparison
Rolleiflex
German glider, 1974
The Schleicher ASK 18 is a single-seat sailplane that was built by the German manufacturer Alexander Schleicher GmbH & Co. It was designed to be a sturdy
Schleicher_ASK_18
On tangency patterns of circles
planar. The circle packing theorem states that these are the only requirements for a graph to be a coin graph: every finite connected simple planar graph
Circle_packing_theorem
Erectile female sexual organ
description of clitoral anatomy. MRI measurements, which provide a live and multi-planar method of examination, now complement the FFWHC's, as well as O'Connell's
Clitoris
On coloring the edges of graphs
path of two adjacent edges. In Vizing's planar graph conjecture, Vizing (1965) states that all simple, planar graphs with maximum degree six or seven
Vizing's_theorem
Complexity class
and dominating set problems for planar graphs are NP-complete, but can be solved in subexponential time using the planar separator theorem. "Each instance
NP-completeness
Magic: The Gathering expansion block
expert-level block consisting of the expansion sets Time Spiral (October 6, 2006), Planar Chaos (February 2, 2007), and Future Sight (May 4, 2007). It is set on the
Time_Spiral
This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International
List of planar symmetry groups
List_of_planar_symmetry_groups
Non-crossing graph with vertices on outer face
In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar
Outerplanar_graph
other. Interferometers are typically used to accurately measure distances. Planar lightwave circuits are either optical integrated circuits (ICs) or optical
Planar lightwave circuit interferometer
Planar_lightwave_circuit_interferometer
Japanese camera brand
Planar T* f1,4 50 mm Contax 139 Quartz with Distagon T* f4,0 18 mm Contax 159MM body Contax 167MT with Distagon T* f2,8 28 mm Contax S2 with Planar T*
Contax
Two geometries based on axioms closely related to those specifying Euclidean geometry
quadratic forms are admitted, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called
Non-Euclidean_geometry
MOS field-effect transistor with more than one gate
architecture (planar vs. non-planar design) and the number of channels/gates (2, 3, or 4). A planar double-gate MOSFET (DGMOS) employs conventional planar (layer-by-layer)
Multigate_device
Programmable machine that processes data
monolithic IC was fabricated using the planar process, developed by his colleague Jean Hoerni in early 1959. In turn, the planar process was based on Carl Frosch
Computer
Degree of concentration of countable objects
The number density (symbol: n or ρN) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules,
Number_density
PLANAR
PLANAR
PLANAR
PLANAR
Boy/Male
American, Australian, British, Chinese, Christian, English, French, German, Jamaican, Teutonic
Firebrand; Son of a German; High-spirited
Surname or Lastname
English
English : variant of Fosse. There has been some confusion with northwestern English force in the sense of ‘waterfall’, it is possible that the surname may also have arisen as a topographic name for someone living by a waterfall.French : topographic name for someone who lived by a fortress or stronghold, Old French force, Late Latin fortia, a derivative of fortis ‘strong’ (see Fort). There are several places named with this word (for example in Aude, and baronial lands in the Dordogne), and it may also be a habitational name from any of these.
Surname or Lastname
English
English : habitational name from a place in Lancashire named Cocker, from the Cocker river (a Celtic name apparently derived from an element kukro ‘winding’) + Old English hÄm ‘homestead’ or hamm ‘enclosure hemmed in by water’.
Girl/Female
British, English
Female Version of Wesley
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from places called Monceaux, in Calvados and Orne, or Monchaux, in Nord and Seine-Maritime. These get their name from the plural form of Old French moncel ‘hillock’, Late Latin monticellum, a diminutive of mons. Compare Mont.
Boy/Male
Tamil
Variant of Jaydev (God has heard
Girl/Female
Latin American
True image; honest image. Biblical - from the maiden who handed Christ her handkerchief on the...
Girl/Female
Polish
Rose.
Male
French
Norman French form of Norman Germanic Hunfrid, ONFROI means "giant peace."
Surname or Lastname
English
English : status name for a servant.
PLANAR
PLANAR
PLANAR
PLANAR
PLANAR
pl.
of Planaria
pl.
of Planaria
n.
One of the Planarida, or Dendrocoela; any turbellarian worm.
n.
Any species of turbellarian worms belonging to Planaria, and many allied genera. The body is usually flat, thin, and smooth. Some species, in warm countries, are terrestrial.
n. pl.
A division of Turbellaria; the Dendrocoela.
a.
Like the planarians.
a.
Of or pertaining to a plane.
n.
Any worm belonging to the Plathelminthes; also, sometimes applied to the planarians.