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...

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...

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...

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...

Planar Systems, Inc. is an American digital display manufacturing corporation with a facility in Hillsboro, Oregon. Founded in 1983 as a spin-off from...

(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...

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...

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...

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 transformers are high frequency transformers used in isolated switchmode power supplies operating at high frequency. As opposed to conventional...

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 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...

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...

The planar process is a manufacturing process used in the semiconductor industry to build individual components of a transistor, and in turn, connect those...

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...

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...

The planar reentry equations are the equations of motion governing the unpowered reentry of a spacecraft, based on the assumptions of planar motion and...

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 chirality, also known as 2D chirality, is the special case of chirality for two dimensions. Most fundamentally, planar chirality is a mathematical...

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...

Planar hexacoordinate carbon in chemistry describes a molecular geometry featuring a planar arrangement of carbon with six surrounding atoms. No actual...

In chemistry, the square planar molecular geometry describes the stereochemistry (spatial arrangement of atoms) that is adopted by certain chemical compounds...

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 projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional...

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...

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...

{\displaystyle T\colon R^{3}\to R\,} may be called a ternary system. A planar ternary ring (PTR) or ternary field is a special type of ternary system...

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 transmission lines are transmission lines with conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines....

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...

alternating planar algebras first appeared in the work of Hernando Burgos-Soto on the Jones polynomial of alternating tangles. Alternating planar algebras...

{\displaystyle n=2} (two variables), also called the plane Jacobian conjecture or planar Jacobian conjecture, is the only case that remains unresolved in 2026. The...

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...

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...

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...

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...

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...

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...

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...

0 (planar graph) contribution survives. Planar Feynman diagrams are graphs in which no propagator cross over another one, in contrast to non-planar Feynman...

mathematics In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete...

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...

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...

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...

{\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)...

The first planar monolithic integrated circuit (IC) chip was demonstrated in 1960. The idea of integrating electronic circuits into a single device was...

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...

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...

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...

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...

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...

with a metal and added a 2-substituent to the ring. This resulted in a planar chiral set of enantioselective DMAP analogs. As of 2018,[update] at least...

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...

characteristics over time. The planar transistor was developed by Dr. Jean Hoerni at Fairchild Semiconductor in 1959. The planar process used to make these...

every planar graph have an integral Fáry embedding? More unsolved problems in mathematics In mathematics, Harborth's conjecture states that every planar graph...

{\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...

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...

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...

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...

panoramic image. The forward projection transforms spherical coordinates into planar coordinates. The reverse projection transforms from the plane back onto...

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...

coloring of the planar graph of adjacencies between regions. In graph-theoretic terms, the theorem states that for a loopless planar graph G {\displaystyle...

It has book thickness 3 and queue number 2. The graph is neither planar nor 1-planar. The Robertson graph is also a Hamiltonian graph which possesses...

the University of Amsterdam, who in 1970 used them to characterize rigid planar structures. However, this characterization, the Geiringer–Laman theorem...

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...

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...

Digital planar holography (DPH) is a method for designing and fabricating miniature components for integrated optics. It was invented by Vladimir Yankov...

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...

called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of Special Euclidean group SE, consisting of planar rotations...

The planar quaternions make up a four-dimensional algebra over the real numbers. Their primary application is in representing rigid body motions in 2D...

Planar laser-induced fluorescence (PLIF) is an optical diagnostic technique widely used for flow visualization and quantitative measurements. PLIF has...

Planar Handbook is an optional supplemental source book for the 3.5 edition of the Dungeons & Dragons fantasy roleplaying game. It contains updates for...

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...

with DNA, the higher the salt concentration needed to elute that protein. Planar chromatography is a separation technique in which the stationary phase is...

quadtrees with random insertion have been studied under the name weighted planar stochastic lattices. Point quadtrees are constructed as follows. Given the...

2009.12.071) F. Geiss (1987): Fundamentals of thin layer chromatography planar chromatography, Heidelberg, Hüthig, ISBN 3-7785-0854-7 Justus G. Kirchner...

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...

generated from two to exactly one. Mac Lane's planarity criterion, named after Saunders Mac Lane, characterizes planar graphs in terms of their cycle spaces and...

tweeters. Some loudspeaker designers use a planar magnetic tweeter, sometimes called a quasi-ribbon. Planar magnetic tweeters are generally less expensive...

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...

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...

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...

The Sony Zeiss Planar T* FE 50mm F1.4 ZA is a large-aperture, standard full-frame prime lens for the Sony E-mount. It was released by Sony in July 2016...

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...

may equivalently be defined as the planar 3-trees, the maximal planar chordal graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked...

study of planar graphs, blossom trees are trees with additional directed half edges. Each blossom tree is associated with an embedding of a planar graph...

VANGL planar cell polarity protein 2 is a protein that in humans is encoded by the VANGL2 gene. The protein encoded by the VANGL2 gene is a membrane protein...

carbon-based supercapacitors. Advanced hybrid designs include all-solid-state planar micro-supercapacitors based on 2D vanadium nitride nanosheets and cobalt...

In chemistry, the pentagonal planar molecular geometry describes the shape of compounds where five atoms, groups of atoms, or ligands are arranged around...

types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method...

four graphs is planar; however, the Erdős–Gyárfás conjecture is now known to be true for the special case of 3-connected cubic planar graphs (Heckman...

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...

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...

color theorem was found only in 1976. First of all, one associates a simple planar graph G {\displaystyle G} to the given map, namely one puts a vertex in...

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...

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...

Wiktionary, the free dictionary. Fault commonly refers to: Fault (geology), planar rock fractures showing evidence of relative movement Fault (law), blameworthiness...

other. Interferometers are typically used to accurately measure distances. Planar lightwave circuits are either optical integrated circuits (ICs) or optical...

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...

reaching sufficient pressures during such an event. Planar fractures are parallel sets of multiple planar cracks or cleavages in quartz grains; they develop...

Planar deformation features, or PDFs, are optically recognizable microscopic features in grains of silicate minerals (usually quartz or feldspar), consisting...

This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International...

In graph theory, an st-planar graph is a bipolar orientation of a plane graph for which both the source and the sink of the orientation are on the outer...

In everyday life, Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') refers to a sense of harmonious...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

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...

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...

that is nowhere zero. It is intimately connected (by duality) to coloring planar graphs. Let G = (V,E) be a digraph and let M be an abelian group. A map...

The planar hydroid (Sertularella arbuscula) is a branching colonial hydroid in the family Sertulariidae. Planar hydroids are bright yellow and branched...

planar graph has a Hamiltonian cycle. It strengthens an earlier theorem of Hassler Whitney according to which every 4-vertex-connected maximal planar...

Cambridge Research Centre in the 1950s. Stripline is the earliest form of planar transmission line. A stripline circuit uses a flat strip of metal which...

the molecule contains 2 lone pairs (6 − 4 = 2), resulting in a square planar molecular geometry. The overall geometry is further refined by distinguishing...

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...

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...

secrete oxidizable neurotransmitters by "loading" them with 5-HT or dopamine. Planar patch clamp is a novel method developed for high throughput electrophysiology...

and dominating set problems for planar graphs are NP-complete, but can be solved in subexponential time using the planar separator theorem. "Each instance...

This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight...

transistor pioneer, and a member of the "traitorous eight". He developed the planar process, an important technology for reliably fabricating and manufacturing...

The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without...

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)...

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*...

The number density (symbol: n or ρN) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules,...

This is a list of tessellations. Tessellation Uniform tiling Convex uniform honeycombs List of k-uniform tilings List of Euclidean uniform tilings Uniform...

Cleavage, in structural geology and petrology, describes a type of planar rock feature that develops as a result of deformation and metamorphism. The degree...

cosmology from that of its contemporary AD&D game, which is a more open planar system that is less regulated than that of its counterpart. The planes were...

Rolleiflex SLX system: Lens hood Rollei-HFT Planar 80 mm f/2.8 lens Film holder Camera body (with back opened) Battery Folding waist-level finder Fast...

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...

special cases become planar or spherical simple open chain, M = ∑ i = 1 j   f i , {\displaystyle M=\sum _{i=1}^{j}\ f_{i},} planar or spherical simple...

theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex...

University, Russia "For the proof of conformal invariance of percolation and the planar Ising model in statistical physics." Cédric Villani École Normale Supérieure...

that supports the sculpture from below. A plinth is defined as a flat and planar support which separates the sculpture from the environment. A pedestal,...

For 4-regular planar graphs, additional necessary conditions can be derived from Grinberg's theorem. An example of a 4-regular planar graph that does...

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...

the whole graph. Theorem—A 4-connected planar triangulation has a Hamiltonian cycle. Theorem—A 4-connected planar graph has a Hamiltonian cycle. An algebraic...

thin layer of platinum and comes in both heated and unheated forms. The planar-style sensor entered the market in 1990 and significantly reduced the mass...

formed from a set of letters (or words) in such a way that it has a non-planar spelling net. Gary S. Bloom, Allan Gewirtz, John W. Kennedy, and Peter J...

systems can produce large induced-drag reductions relative to a conventional planar wing, there is no significant aerodynamic advantage that uniquely accrues...

composite number with two prime factors. 267 is the number of planar partitions of the number 12. Planar partitions are the number of ways in which the given number...

The Vortex of Madness and Other Planar Perils is an adventure module for the 2nd edition of the Advanced Dungeons & Dragons fantasy role-playing game....

not have a five-vertex complete graph as a minor are the 3-clique-sums of planar graphs with the eight-vertex Wagner graph; this structure theorem can be...

In computational geometry, a CC system or counterclockwise system is a ternary relation pqr introduced by Donald Knuth to model the clockwise ordering...

Additionally, Abrash enabled the VGA's planar memory mode (also called "unchained mode"). Even though planar memory mode is a documented part of the...

reality. Optical waveguides can be classified according to their geometry (planar, strip, or fiber waveguides), mode structure (single-mode, multi-mode),...

measurements was made at ten frequencies (0.25 to 8-MHz). There were two planar electron traps mounted on opposite sides of the spacecraft. The trap consisted...

made of sheet metal and wire that Jane Fluegel terms a "three-dimensional planar counterpart of Cubist painting" that marks a "revolutionary departure from...

the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists a collection of k planar graphs, all having the...

symmetric and planar structure consists of four fused benzene rings. Triphenylene has delocalized 18-π-electron systems based on a planar structure, corresponding...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

can be constructed as a strong product of path graphs. Decompositions of planar graphs and related graph classes into strong products have been used as...

Contarex Contarex Special with Planar 50 mm f/2; note bayonet lugs are on the body instead of the lens The Contarex with Planar 55 mm f/1.4 From left, Sonnar...

In mathematics, a planar Riemann surface (or schlichtartig Riemann surface) is a Riemann surface sharing the topological properties of a connected open...

Planar Doppler Velocimetry (PDV), also referred to as Doppler Global Velocimetry (DGV), determines flow velocity across a plane by measuring the Doppler...

decades. Non-planar wingtips provide the wake control benefit of winglets, with less parasitic drag penalty, if designed carefully. The non-planar wing tip...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

them) either is a polygon or resembles a polygon, but is not necessarily planar, and the vertices of the two end polygons are joined by either a curve or...

Master Rules (Planar Spider),(1985), Creature Catalogue (1986), D&D Master Module M5 Talons of Night (1987), Rules Cyclopedia (Planar Spider, Rhagodessa)...

not a planar graph. Multiple proofs of this impossibility are known, and form part of the proof of Kuratowski's theorem characterizing planar graphs...

In mathematics, Sobolev spaces for planar domains are one of the principal techniques used in the theory of partial differential equations for solving...

planar Hamiltonian graph. A graph G is subhamiltonian if G is a subgraph of another graph aug(G) on the same vertex set, such that aug(G) is planar and...

A planar Fourier capture array (PFCA) is a tiny camera that requires no mirror, lens, focal length, or moving parts. It is composed of angle-sensitive...

slightly more stable than those of copper(III). For instance, the square planar periodate [Ag(IO5OH)2]5− and tellurate [Ag{TeO4(OH)2}2]5− complexes may...

a regular projection of a knot, or knot diagram is thus a quadrivalent planar graph with over/under-decorated vertices. The local modifications of this...

A plane joint (arthrodial joint, gliding joint, plane articulation) is a synovial joint which, under physiological conditions, allows only gliding movement...

equipped with the Westinghouse AN/APG-66 fire-control radar. Its slotted planar array antenna was designed to be compact to fit into the F-16's relatively...

in a graph drawing. It states that every drawing in the plane of a non-planar graph contains a pair of independent edges (not both sharing an endpoint)...

Planar reflectarray fed by a horn antenna. Structure showing unit cells. This antenna has fixed cell delays, configured by different cutout sizes in each...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

tangential to it at the equator. The cylinder is then unrolled to give the planar map.[page needed] The fraction ⁠R/a⁠ is called the representative fraction...

3-connected planar graph G {\displaystyle G} , a maximal set of laminar 3-separators can be found in linear time. This is non-trivial because some planar graphs...

wheel graphs. A maximal planar graph is a planar graph in which all faces, even the outer face, are triangles. A maximal planar graph is node-pancyclic...

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...

graph theory, Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors. According to the four-color...

IEMs exhibiting common weaknesses of planar magnetic drivers, such as their size and high price, innovations in planar magnetic drivers now allow for newer...

these joints called a mechanism. Two levers, or cranks, are combined into a planar four-bar linkage by attaching a link that connects the output of one crank...

fraction of an analyte in the mobile phase of a chromatographic system. In planar chromatography in particular, the retardation factor RF is defined as the...

projection surfaces are cylindrical (e.g., Mercator), conic (e.g., Albers), and planar (e.g., stereographic). Many mathematical projections, however, do not neatly...

lightning channel exceed 30,000 K, with sufficient pressure to produce planar deformation features in SiO2, a kind of polymorphism. This is also known...

commonly use short pieces of transmission line, usually in the form of printed planar transmission lines, arranged in certain patterns to build circuits such...

radar program. Accordingly, the N019 was originally intended to have a flat planar array antenna and full digital signal processing, for a detection and tracking...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

mathematics, the left-right planarity test or de Fraysseix–Rosenstiehl planarity criterion is a characterization of planar graphs based on the properties...

as revolutes, as is necessary for the links to be two-force members. A planar truss is one where all members and nodes lie within a two-dimensional plane...

planar graph has a Hamiltonian cycle. An analogous theorem of Thomas and Yu holds for graphs on the projective plane. For 4-vertex-connected planar and...

Grötzsch, who used it as an example in connection with his 1959 theorem that planar triangle-free graphs are 3-colorable. The Grötzsch graph is a member of...

(also Benioff–Wadati zone or Benioff zone or Benioff seismic zone) is a planar zone of seismicity corresponding with the down-going slab in a subduction...

be planar. Some graphs have both non-crossing embeddings with non-unit vertex distances and unit-distance embeddings with crossings; these are planar unit-distance...

Jansen's linkage is a planar leg mechanism designed by the kinetic sculptor Theo Jansen to generate a smooth walking motion. Jansen has used his mechanism...

rotation. This theorem in three dimensions extends a similar representation of planar isometries as rotation. Once the screw axis is selected, the screw displacement...

stereoelectronic effects. The spiro transition state is favored over the planar due to the non-bonding orbitals of the superior oxygen donating into the...

professional markets; in 1961, the retail price (including the 50 mm f/2.0 Planar lens) was $499. The camera bodies are complex; for example, the first model...

between the planar and staggered forms) may be attributed to electrostatic interactions as unfavorable O−O repulsion is maximized in the planar form. Oxalate...

of a complete graph All Hamiltonian paths Non-planarity game All edges of a complete graph All non-planar sub-graphs Arithmetic progression game The numbers...

the Su-27. In this original N011 form, it deployed a mechanically scanned planar array with 960 mm diameter, ±85 degrees scan sector. The peak output power...

In mathematics, the sumset of two subsets A and B of an (additive) abelian group is formed by adding each element of A to each element of B: A + B = {...

graph, and the connection between this decomposition and the planar embeddings of a planar graph, were first investigated by Saunders Mac Lane (1937);...

unstable, non-planar compound which is non-aromatic. The dianion, however, satisfies Hückel's rule, is thermally stable, and is planar. Benzocyclooctatetraene...

#P-complete as well. This is the counting version of Planar 3SAT. The hardness reduction from 3SAT to Planar 3SAT given by Lichtenstein has the additional property...

graph, and has order dimension at most three if and only if G is at most planar (Schnyder's theorem). However, graphs whose incidence posets have order...

Extra-planar nebulae...

In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has (4n + 2)π-electrons, where n is a non-negative...

anions [XeF5]−. The [XeF5]− ion was the first example of a pentagonal planar molecular geometry AX5E2 species. It was prepared by the reaction of [N(CH3)4]F...

An ideal solid surface is flat, rigid, perfectly smooth, and chemically homogeneous, and has zero contact angle hysteresis. Zero hysteresis implies the...

Concepts Affine transformation Back-face culling Clipping Collision detection Planar projection Reflection Rendering Beam tracing Cone tracing Checkerboard rendering...

multicoated) 503 with Zeiss Planar 2.8/80 (CF black barrel, T*) 2000FC/M with Zeiss Planar 2.8/80 (F black barrel, T*) 500C with Zeiss S-Planar 5.6/120 (C chrome...

counting version of Planar 3SAT. The hardness reduction from 3SAT to Planar 3SAT given by Lichtenstein is parsimonious. This implies that Planar #3SAT is #P-complete...

{\displaystyle O(n\log n)} time, for instance by using integer sorting algorithms, planar convex hulls can also be computed more quickly: the Graham scan algorithm...

spherical aberration, which could lower peripheral contrast. Double Gauss/Planar tweaks formed the basis for most normal and near-normal prime lens designs...

vessels. The objective of this process is to present to the observer a planar representation of the object's characteristics, most notably the illustrations...

Triax is widely used for the connection of cameras in television studios. Planar format transmission lines are flat conductors manufactured by a number of...

that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face (or region) so that no two faces that...

mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane....

brain scanning or where images are needed very rapidly, is called echo-planar imaging (EPI): In this case, each RF excitation is followed by a train of...

Kasteleyn, and Neville Temperley, counts the number of perfect matchings in a planar graph in polynomial time. This same task is #P-complete for general graphs...

(illustration, right) the central arch and side arches are raised on four massive planar piers[clarification needed]. Donato Bramante's original plan for St Peter's...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

is the Hughes AN/AWG-9 X band radar; the antenna is a 36 in (91 cm)-wide planar array, and has integrated Identification friend or foe antennas. The AWG-9...

of two co-ordinate systems, the first being planar motion and the latter being cylindrical motion. In planar motion, the velocity and acceleration components...

has a weight of 250 kg and uses a 680 mm electronically scanned slotted planar array antenna which offers a detection range of 90 km against a target with...

special cases become planar or spherical simple open chain, M = ∑ i = 1 j   f i , {\displaystyle M=\sum _{i=1}^{j}\ f_{i},} planar or spherical simple...

moving parallel to the axis; a helix. The first definition describes a planar curve, that extends in both of the perpendicular directions within its plane;...

bombs, sometimes in place of more conventional control surfaces, such as planar fins. They were developed in the 1950s by a team led by Sergey Belotserkovskiy [ru]...

Peaucellier–Lipkin inversor), invented in 1864, was the first true planar straight line mechanism – the first planar linkage capable of transforming rotary motion into...

nitric oxide have a linear molecular shape. Trigonal planar: Molecules with the trigonal planar shape are somewhat triangular and in one plane (flat)...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

version of the game took the form of a flat wooden board inscribed with a planar graph with the same combinatorial structure as the dodecahedron (a Schlegel...

\varphi ^{10}).\end{aligned}}} In the original definition of the projection, planar coordinates were lineally interpolated from a table of 19 latitudes and...

(or the mesh current method) is a circuit analysis method for planar circuits; planar circuits are circuits that can be drawn on a plane surface with...

Unsolved problem in mathematics Do planar graphs have universal point sets of subquadratic size? More unsolved problems in mathematics In graph drawing...

time. In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis. The minimum weight cycle basis of a planar graph corresponds...

Outlands (a Planescape campaign setting guide), Morte's Planar Parade (a bestiary of planar creatures), and Turn of Fortune's Wheel (an adventure module)...

sound: a construction of aural surfaces and regular surfaced planes, a planar conception, the product of a mechanistic discipline, with an emphasis upon...

In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices"...

mathematical field of graph theory, Fáry's theorem states that any simple, planar graph can be drawn without crossings so that its edges are straight line...

oscillator Inductor Relay reed relay mercury relay Other devices Hall effect sensor SQUID Spin valve Magnetic tunnel junction (MTJ) Planar Hall sensor ggNMOS...

graph-theoretic terms, the polyhedral graphs are the 3-vertex-connected, planar graphs. The analogue concept for polytopes of general dimension are the...

Property of a planar simple closed curve...

is equal to zero, which are the values 0 and −1. Cassini ovals appear as planar sections of tori, but only when the cutting plane is parallel to the axis...

group is known as the double group, D4′. With species such as the square-planar complex of the silver(II) ion [AgF4]2− the relevant double group is also...

Zeiss HFT Planar 7 6 0.45 m (1 ft 6 in) 47 mm (1.9 in) 62 mm (2.4 in) 230 g (8.1 oz) 49 mm Voigtländer Color-Ultron Identical to HFT Planar 50 f/1.8–16...

the other. Thus, every graph either has a planar drawing (in which case it belongs to the family of planar graphs) or it has a subdivision of at least...

these imposing structures have earned them the nickname "elephant cages". Planar array – a flat two-dimensional array of antennas. Since an array of omnidirectional...

embedding. If the graph isn't planar, it raises an exception. Planar embeddings exactly preserve the topology of planar networks—useful for circuit schematics...

board to form the "windings" of a planar transformer, replacing the turns of wire used to make other types. Some planar transformers are commercially sold...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

estimates as well as exact numbers for the number of rectangulations of planar point sets. That means, we fix a point set and consider the number of rectangulations...

in planar graphs. Tutte paths have been applied to solve several important problems on planar graphs: Binary spanning trees: Every 3-connected planar graph...

between two planar semi-infinite walls. This approximation is widely used to estimate forces between colloidal particles, as forces between two planar bodies...

the aim of providing a straightedge at a right angle or other particular planar angle to a baseline. The simplest form of set square is a triangular piece...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

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...

The effect seen on two co-planar polygons...

collagen-containing extracellular matrix Biological process Wnt signaling pathway, planar cell polarity pathway positive regulation of osteoblast proliferation positive...

Department of Electrical Engineering from 1978 to 1981. He initially focused on planar microwave circuit modeling, later expanding into time-domain methods for...

For planar graphs, Dunbar et al. conjectured in 1998: If G is a planar graph, then b(G) ≤ Δ(G) + 1. This conjecture has been verified for planar graphs...

conventions such as tapering provide this information more effectively. Upward planar drawing uses the convention that every edge is oriented from a lower vertex...

Hart's inversors are two planar mechanisms that provide a perfect straight line motion using only rotary joints. They were invented and published by Harry...

embedded: different planar embeddings of a single graph may lead to different dual graphs. Matroid duality is an algebraic extension of planar graph duality...

crystal classes (Hermann-Mauguin) Primitive Inverse Central Axial Planar Inverse-planar Planar-axial Triclinic None 1 1 Monoclinic 1 twofold axis of rotation...

In remote sensing, ground sample distance (GSD) in a digital photo of the ground from air or space is the distance between pixel centers measured on the...

crystal. These planes, which show up as lines under a microscope, are called planar deformation features (PDFs), or shock lamellae. Shocked quartz was discovered...

forbidden minors, in the same way that Wagner's theorem characterizes the planar graphs as being the graphs that do not have the complete graph K 5 {\displaystyle...

foliation of a rock is a planar feature that often contains a linear feature called lineation. Similarly, a fault plane is a planar feature that may contain...

processing Bare Ti ~50 - - None TiO2 TiO Ti4O7 TiO4 (Planar) ~33 2.2 700 Oxidation TiO2 TiO Ti4O7 (Planar) ~45 4 700 Oxidation TiO2 TiO Ti4O7 TiO4 (Hollow)...

minor of a graph with property P also has property P. For instance, being a planar graph is minor-closed. Every minor-closed property is monotone, but not...

planar waves instead of a ray tracing model. This reduces computation and lowers requirements for optics knowledge. The waves are considered planar between...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

contains the query point (e.g. the Voronoi diagram). In the planar case, we are given a planar subdivision S, formed by multiple polygons called faces, and...

Wetting is the ability of a liquid to maintain contact with a solid surface by displacing another substance or material – either a gas, or other liquid...

degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case...

Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to...

shutter Portrait lenses 120 f/2–16 Planar (HFT) SL66 7 5 0.4 m (14 in) 90×87 mm (3.5×3.4 in) 810 g (29 oz) 86 f/5.6–45 S-Planar (HFT) SL66 6 4 0.4 m (14 in)...

cases, as polygonal chains. Every transitively reduced st-planar graph, a directed acyclic planar graph with a single source and a single sink, both on the...

also several new categories (although the gem dragons did not return): "planar dragons" which are defined as dragons that were warped by living on a plane...

{i+j+k-1}{i+j+k-2}}=\prod _{i=1}^{r}\prod _{j=1}^{s}{\frac {i+j+t-1}{i+j-1}}.} The planar case (when t = 1) yields the binomial coefficients: B ( r , s , 1 ) = (...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes...

invented the planar integrated circuit. The industry preferred Fairchild's invention over Texas Instruments' because the transistors in planar ICs were interconnected...

from the Latin word folium, meaning "leaf", and refers to its sheet-like planar structure. It is caused by shearing forces (pressures pushing different...

family of planar graphs, so the problem of computing the coefficients of the Tutte polynomial for a given graph is #P-hard even for planar graphs. Much...

a molecule adopting a non-planar geometry to avoid the destabilization that results from antiaromaticity. If it were planar, it would have a single eight-electron...

volume V of the body. The polar moment of inertia of a body undergoing planar movement can be computed relative to any reference point S, I S = ∫ V ρ...

comes from the Greek word for ‘near’ and so periplanar means “approximately planar”. In their article “Periplanar or Coplanar?” Kane and Hersh point out that...

conventional speakers in relying not on cones mounted in an enclosure, but on a planar driver system mounted in a panel. A Magneplanar's sound reproducing mechanism...

approach to generating 3-dimensional, optimized stellarator fields using only planar coils (Thea Energy) In December 2025, Thea Energy completed a milestone...

is a red liquid with the formula CSCl2. It is a molecule with trigonal planar geometry. There are two reactive C–Cl bonds that allow it to be used in...

Concepts Affine transformation Back-face culling Clipping Collision detection Planar projection Reflection Rendering Beam tracing Cone tracing Checkerboard rendering...

(hypothetical) crystals. A planar cover of a graph is a finite covering graph that is itself a planar graph. The property of having a planar cover may be characterized...

without changing its number of crossings. In particular, every planar graph has a planar arc diagram. However, this embedding may need to use more than...

Finite-difference time-domain electromagnetic solver Open-source Momentum MoM-based planar EM simulation in Keysight ADS Commercial Numerical Electromagnetics Code...

intersection lineations, the trace of a planar feature on another planar surface). The inclination of a planar structure in geology is measured by strike...

In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object. For example, a cube has six faces in this...

however in this case the polyhedral symbol specifies that the complex is non-planar. There are two digits. The first digit is the priority number of the ligand...

between them. The design can be realised in planar format but it has a more natural implementation in coax – in planar, the two lines have to be kept apart so...

regular octahedron is a special case in which all three quadrilaterals are planar squares. Schönhardt polyhedron, a non-convex polyhedron that cannot be partitioned...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

a hydrogen (chemical formula of (CH)n). Furthermore, while graphene is planar due to its double-bonded nature, graphane is rugged, with the hexagons adopting...

Flamingo was originally identified as a Drosophila protein involved in planar cell polarity. Mammals have three flamingo homologs, CELSR1, CELSR2, CELSR3...

"awesome powers" to "plenty of horrors to encounter in space". Morte's Planar Parade was the bestiary book contained within the Planescape: Adventures...

from this technique are generally not planar. For some planar graphs, the optimal angular resolution of a planar straight-line drawing is O(1/d3), where...

that is expected to have a carbon atom in with a stable, unusual square-planar coordination rather than the usual tetrahedral geometry of a carbon atom...

Harary, who proved in 1975 that it was the smallest non-Hamiltonian maximal planar graph. The same graph had already been given as an example of a non-Hamiltonian...

undirected planar graphs of maximum degree three, directed planar graphs with indegree and outdegree at most two, bridgeless undirected planar 3-regular...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

"Every planar map is four colorable. Part I. Discharging", Illinois J. Math 21: 429–490. MR 0543795 K. Appel, W. Haken, and J. Koch (1977), "Every planar map...

which a shape is compact. The circle and the sphere are the most compact planar and solid shapes, respectively. Various compactness measures are used. However...

is special case of Liouville–Bratu–Gelfand equation in mathematics. For planar vessel, there is an exact solution. Here j = 0 {\displaystyle j=0} , then...

co-graphic is sometimes called a planar matroid (but this should not be confused with matroids of rank 3, which generalize planar point configurations); these...

C6H6. The benzene molecule is composed of six carbon atoms joined in a planar hexagonal ring with one hydrogen atom attached to each. As it contains only...

efficiently on them. The planar graphs do not have bounded treewidth, because the n × n {\displaystyle n\times n} grid graph is a planar graph with treewidth...

a wire in the shape of a spiral or helix which could be a solenoid or a planar structure. One field where these are found is nuclear magnetic resonance...

algorithm Kirkpatrick, David G.; Seidel, Raimund (1986). "The ultimate planar convex hull algorithm?". SIAM Journal on Computing. 15 (1): 287–299. doi:10...

algorithms are known that solve the problem for planar graphs in linear time. By the Euler characteristic of planar graphs, m ≤ 3n - 6 ∈ O(n), so this is in...

of the king's graph, called a kinggraph, is formed from a squaregraph (a planar graph in which each bounded face is a quadrilateral and each interior vertex...

solids that are soluble in organic solvents. Thiuram disulfides feature planar dithiocarbamate subunits, which are linked by an S−S bond of 2.00 Å. The...

smooth Riemann mapping theorem can be generalized to multiply connected planar regions with smooth boundary. The Beltrami coefficient in these cases is...

played on planar graphs. The following proof is from theorem 3 of. Since planar GG is a special case of GG, and GG is in PSPACE, so planar GG is in PSPACE...

three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in the form of a circular cone can be projected onto...

also known as stochastic Loewner evolution (SLEκ), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensional...

in biological systems. The simplest case of the instability arises at a planar interface within a porous medium or Hele-Shaw cell, and was treated by Saffman...

NAND-like) 1T-1C capacitor arrays Density High (potential Tb/mm2) Low (Mb range, planar limits) Read Non-destructive Destructive (write-after-read) Endurance 109–1012...

Reference 14 29026 All tricubes 14 All tricubes 18 68 All tree-like tetracubes 22 23 pentacubes 22 3 22 tree-like pentacubes 22 1 Non-planar pentacubes...

Minimum correct summations required = 3m2 + 4 Diagonal: Each of the 3m planar arrays must be a simple magic square. The 6 oblique squares are also simple...

are valid for most other geometries. The exception is square-planar because square-planar complexes typically abide by the 16-electron rule. Assuming ligands...

this principle is Hadamard's three-circle theorem. On simply connected planar domains, there is a close connection between harmonic measure and the theory...

In geometry, coaxial means that several three-dimensional linear or planar forms share a common axis. The two-dimensional analogue is concentric. Common...

equals are subtracted from equals, then the remainders are equal" (among planar shapes, those of the same area were called "equal"). The propositions in...

_{n}={\frac {(2n-1)\pi }{l}}.} When h / l ≪ 1 {\displaystyle h/l\ll 1} , the planar Couette flow is recovered, as shown in the figure. Taylor–Couette flow is...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of spatial reference...

NP-complete, implying that no simple characterization is likely to exist. Every planar graph is a string graph: one may form a string graph representation of an...

In the field of computer vision, any two images of the same planar surface in space are related by a homography (assuming a pinhole camera model). This...

incidence poset of a planar map (planar graph with fixed plane embedding) is at most four. Felsner later proved in "The order dimension of planar maps revisited...

two papers a mile-stone in PLED development. Their device have similar planar structure, i.e. the active layer (perovskite) is sandwiched between two...

The Debye sheath (also electrostatic sheath) is a layer in a plasma which has a greater density of positive ions, and hence an overall excess positive...

for extreme-UV lithography". spie.org. "Fast Simulation Methods for Non-Planar Phase and Multilayer Defects in DUV and EUV Photomasks for Lithography"...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

dimensions also has a complete skeleton. K1 through K4 are all planar graphs. However, every planar drawing of a complete graph with five or more vertices must...

or planar bedding consists of cross-bedded units that are extensive horizontally relative to the set thickness and that have essentially planar bounding...

given a planar Boolean circuit (i.e. a Boolean circuit whose underlying graph is planar) containing only NAND gates with exactly two inputs. Planar Circuit...

configuration of this structure is something of a truss, space frame or planar frame. Awnings are also often constructed of aluminium understructure with...

mask design, is the representation of an integrated circuit in terms of planar geometric shapes which correspond to the patterns of metal, oxide, or semiconductor...

Part of a series on Graphical projection Planar projections Parallel projection Orthographic projection Isometric projection Oblique projection Perspective...

Planar approximation of angular distance on sky...

centers in Au(III) complexes, like other d8 compounds, are typically square planar, with chemical bonds that have both covalent and ionic character. Gold(I...

or flat embedding; these graphs form a three-dimensional analogue of the planar graphs. Complementarily, an intrinsically linked graph is a graph that does...

liquid (2D liquid) is a collection of objects constrained to move in a planar space or other two-dimensional space in a liquid state. The movement of...

longitude; and x {\displaystyle x} and y {\displaystyle y} are the projected (planar) coordinates for a given ( φ , λ ) {\displaystyle (\varphi ,\lambda )} coordinate...

used for the assembly of a part. It could also be used to group nominally planar geometrical features that are constrained to lie inside the same flatness...

a reference wave, holographic principles enabled the use of a compact, planar feeding structure and suppression of undesired lobes. This was extended...

degree Δ or Δ+1. For some graphs, such as bipartite graphs and high-degree planar graphs, the number of colors is always Δ, and for multigraphs, the number...

Bangladesh University of Engineering and Technology. He is an author of the book Planar Graph Drawing. He is known for his contribution in graph drawing, graph...

In structural geology, a fold is a stack of originally planar surfaces, such as sedimentary strata, that are bent or curved ("folded") during permanent...

circuit boards and these filters have the advantage of largely being planar. Precision planar filters are manufactured using a thin-film process. Higher Q factors...

affected only by self-cancelling tangential forces. Gaudí evolved from planar to spatial geometry, and then to ruled geometry. These forms allowed the...

The Campanella in Campanella 3, though the controls are different (with planar 2D motion to dodge obstacles as a common theme). Eggs are a recurring theme...

Example of a MST: The minimum spanning tree of a planar graph. Each edge is labeled with its weight, which here is roughly proportional to its length....

In liquid crystals homogeneous alignment, sometimes called planar alignment, is the state of alignment where molecules align in parallel to a substrate...

double bonds. This unsaturated arrangement means the bicyclic molecule is planar. Guanine, along with adenine and cytosine, is present in both DNA and RNA...

by the German chemist Arthur Rudolf Hantzsch (1857–1935). Imidazole is a planar 5-membered ring, that exists in two equivalent tautomeric forms because...

and the stationary part away from the user that contains a portion of the planar pantograph. The function of the bridge is to form a base for the vertical...

interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs. When there are no holes or added points, triangulations...

range of up to 1,600 nmi (1,800 mi; 3,000 km) US Navy Raytheon AN/TPS-72 Planar array E/F-band air search radar Westinghouse Electric AN/TPS-73 S-band multi-functional...

elements from a Planar-type double Gauss lens, resulting in the designs shared by the Schneider Kreuznach Xenotar (1952) and Zeiss Planar (1953) & Biometar...

deploying few-modes optical planar waveguides. Especially, if modes can be easily converted from conventional single-mode planar waveguides into few-mode...

August 2010. Retrieved 22 August 2010. Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, ACM Computing Surveys...

theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and 3n edges. The friendship graph...

behind V IV: below H, in front of V These labels are the same as used in 2D planar geometry (), as seen from infinitely far to the "left", taking H and V to...

application is still to add shadows to 3D applications. It is also used for planar reflections. Other rendering techniques, such as portal rendering, use the...

isomers also occur in inorganic coordination compounds, such as square planar MX 2 Y 2 {\displaystyle {\ce {MX2Y2}}} complexes and octahedral MX 4 Y 2...

{\displaystyle c} ; γ {\displaystyle \gamma } is a numerical factor, which in planar problems assumes the value 2 / 2835 {\displaystyle 2/2835} ; g {\displaystyle...

In graph theory, Grinberg's theorem is a necessary condition for a planar graph to contain a Hamiltonian cycle, based on the lengths of its face cycles...

internally disjoint regions of the Euclidean plane. The map graphs include the planar graphs, but are more general. Any number of regions can meet at a common...

Graphical projection Ingrid Carlbom; Joseph Paciorek; Dan Lim (December 1978). "Planar Geometric Projections and Viewing Transformations". ACM Computing Surveys...

Concepts Affine transformation Back-face culling Clipping Collision detection Planar projection Reflection Rendering Beam tracing Cone tracing Checkerboard rendering...

contents) Ahmed, Sherif Sayed (2014). Electronic Microwave Imaging with Planar Multistatic Arrays. Logos Verlag Berlin. p. 1. ISBN 978-3-8325-3621-3. Extract...

compounds anthracene and phenanthrene. PAHs are uncharged, non-polar and planar. Many are colorless. Many of them are also found in fossil fuel deposits...

In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. In the two-dimensional case...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

achieve a goal, and is sometimes represented by a diagram. For spatial or planar topologic or topographic sets see map. Plans can be formal or informal:...

4 planar points which are all orthocenters of triangles formed by the other 3...

aromatic, however, because various types of ring strain destabilize an all-planar geometry. Although not aromatic itself, [10]annulene can transition between...

tectonics, the movement of large regions of the Earth's crust in the manner of planar rigid bodies, are key to understanding the formation of the Himalayas. The...

} Planar extension tests are carried out on thin specimens which are constrained from deforming in one direction. For planar extension in the...

exhibit significantly faster switching times and higher current density than planar CMOS (complementary metal–oxide–semiconductor) technology, resulting in...

The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K5 nor the...

small-space complexity classes, parameterized complexity, and algorithms for planar graphs. Mahajan is originally from Mumbai, the daughter of a government...

inequality that relates the length L of a closed curve and the area A of the planar region that it encloses. The isoperimetric inequality states that 4 π A...

Magnetic levitation using a planar Halbach array and concentric structure windings...

not cover the surface of a circle finitely many times. In addition to the planar regular polygons there are infinitely many regular skew polygons. Skew polygons...

tetrahedrally bonded carbon, which is about 109.47°. However, cyclopentane is not planar in its normal conformations. It puckers in order to increase the distances...

Concepts Affine transformation Back-face culling Clipping Collision detection Planar projection Reflection Rendering Beam tracing Cone tracing Checkerboard rendering...

the atoms within the pyrimidinedione ring system are sp2 hybridized and planar. The imidazole ring also has a resonance. Therefore, the fused 5,6 ring...

example the equator and meridians of a globe); the spherical analog of planar circles, which curve relative to the surface, are called small circles (for...

containing the number 4. It is the sum of 47 + 94 + 141. 282 is the number of planar partitions of 9. This means that 282 is the number of ways to separate 9...

important research contributions are within transport processes across planar and curved interfaces, the understanding of nucleation phenomena, thermodynamics...

Many d8 complexes of the first row metals exist in tetrahedral or square planar geometry. In some cases these geometries exist in measurable equilibria...

antennas. Radomes can be constructed in several shapes – spherical, geodesic, planar, etc. – depending on the particular application, using various construction...

invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar graphs with...

one another entirely, in which case their paths will diverge along other planar conic sections. If one object is very much heavier than the other, it will...

Traditional implementations assumed the buffer was being created on a planar cartesian coordinate space (i.e., created by a map projection) using Euclidean...

4-benzoquinone, it is a yellow solid. Like the parent benzoquinone, chloranil is a planar molecule that functions as a mild oxidant. Chloranil is produced by chlorination...

3-space. To define the connected sum for two oriented knots: Consider a planar projection of each knot and suppose these projections are disjoint. Find...

A planar arrangement of the ring carbons would be too strained, and therefore the stable conformations of the trans form have a bent (non-planar) ring...

cation. Square planar complexes of the formula [M(en)2](n+) are also well known. Representative square planar complexes are M = Pd2+, Pt2+...

Projection of a tetrahedral molecule onto a planar surface....

based on real-world situational biomechanics. They usually involve multi-planar, multi-joint movements which place demand on the body's core musculature...

ended in 1993. The exterior of the building consists of sharply angled planar surfaces. The architecture of the building has been likened to Deconstructivism...

k-quasi-planar if it has no k pairwise crossing edges. Using this terminology, if a topological graph is 2-quasi-planar, then it is a planar graph. It...

Spiric sections as planar sections of a torus...

edges cross, its covering graph is said to be upward planar. A number of results on upward planarity and on crossing-free Hasse diagram construction are...

the plane of focus (PoF) is parallel to the lens and image planes. If a planar subject (such as the side of a building) is also parallel to the image plane...

atom is substituted for the nitrogen atom. Whereas the pyrrole molecule is planar, the arsole molecule is not, and the hydrogen atom bonded to arsenic extends...

be removed, leaving a planar subgraph. The removed vertex is called the apex. A k-apex graph is a graph that can be made planar by the removal of k vertices...

Rolleiflex 600x series Rolleiflex 6008 SRC 1000 professional, with Zeiss 4/120 Planar HFT lens Overview Maker Rollei Type Medium format single-lens reflex camera...

indicatrix is to relate how distances on the sphere change when mapped to a planar surface. Specifically, the desired relation is the transform T {\displaystyle...

Hamiltonian cycles, the existence of Hamiltonian cycles in 4-vertex-connected planar graphs Tutte's theorem on perfect matchings, a characterization of the graphs...

two-dimensional shape of the largest area that can be maneuvered through an L-shaped planar region with legs of unit width. The area thus obtained is referred to as...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

β-catenin buildup, keeping the concentration of β-catenin in the cell low. The planar cell polarity pathway (PCP) is the most notable β-catenin independent pathway...

technique using gamma rays. It is very similar to conventional nuclear medicine planar imaging using a gamma camera (that is, scintigraphy), but is able to provide...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

problems in order to facilitate solution. Three-dimensional analogues and planar boundary/area problems on other shapes, including the obvious rectangular...

silicon integrated circuit was enabled by the planar process developed by Jean Hoerni. In turn, Hoerni's planar process was inspired by the surface passivation...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

coordination geometry, whereas the tetrahalides are usually tetrahedral. Square planar tetrahalides are known as are examples with 2- and 3-coordination. Alfred...

series–parallel graphs, and include also the maximal outerplanar graphs. Planar 3-trees are also known as Apollonian networks. The graphs that have treewidth...

scattering. This works at a wide range of angle of incidence, unlike a planar mirror, which does this only if the mirror is exactly perpendicular to the...

point 81 to 83 °C (178 to 181 °F; 354 to 356 K) Structure Molecular shape planar Dipole moment zero Hazards Occupational safety and health (OHS/OSH): Main...

Video representing negative refraction of light at uniform planar interface....

In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into...

lines are the trajectory of inbound and outbound photons at (0,0). The planar-cosmology topological segmentation is the future F, the past P, space left...

probability theory and stochastic processes, including graphons, random planar maps, the Schramm–Loewner evolution, and their applications to quantum gravity...

3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented...

In biochemistry, intercalation is the insertion of molecules between the planar bases of deoxyribonucleic acid (DNA). This process is used as a method for...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

stripline format. This does not imply an industry preference, although planar transmission line formats (that is, formats where conductors consist of...

hyperbolic space of an arbitrary dimension always lie on the same plane. Hence planar hyperbolic triangles also describe triangles possible in any higher dimension...

triangulation to allow the data field to be contoured. A triangular cell is always planar, because it is a 2-simplex (i.e. specified by n+1 vertices in an n-dimensional...

compute locations using multilateration. Projected coordinate system (or planar, grid) A standardized cartesian coordinate system that models the surface...

butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices and 6 edges. It can be constructed by...

computing and related fields. In 2010, researchers produced microfabricated planar ion traps for theoretical use in a trapped ion quantum computer. "Visiting...

Stanford University Thesis Flatland Photonics: Circumventing Diffraction with Planar Plasmonic Architectures (2009, Awarded Francis and Milton Clauser Prize...

slope number. As Keszegh, Pach & Pálvölgyi (2011) showed, every planar graph has a planar straight-line drawing in which the number of distinct slopes is...

Awards Prix Versailles 2019 LEAF Award (2009, 2011, 2013, 2014, 2015, 2017, 2018) Practice Studio MK27 Buildings Gama-Issa House Jungle House Planar House...

restricted to very simple and regularly shaped of often only a small number of planar slices into the outside object. breakaway : a cutaway realized by a single...

the company introduced the STAX Spirit S5 wireless planar magnetic headphones, which combined planar magnetic driver technology with wireless Bluetooth...

geometry that asks for the convex shape of smallest area that can cover every planar set of diameter one. The diameter of a set by definition is the least upper...

progressive deterioration of high-voltage components and equipment. The study of planar Lichtenberg figures along insulating surfaces and 3D electrical trees within...

Tutte embedding or barycentric embedding of a simple, 3-vertex-connected, planar graph is a crossing-free straight-line embedding with the properties that...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

greater attention to the contrasting qualities of surface (open, closed, planar, broken etc.) while less attention was paid to story-telling and convincing...

Retrieved April 22, 2010. Shor, Peter Williston (September 1985). Random Planar Matching and Bin Packing (Ph.D. thesis). MIT. OCLC 14107348. Shor, Peter...

planar magnetic loudspeakers and in 1987 introduced the world's first full-range push-pull (with electromagnets on both sides of the membrane) planar...

three sides and one of the angles of a spherical triangle, analogous to the planar law of cosines for a triangle in the Euclidean plane. A spherical triangle...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

Rolleiflex SL 2000 F Rolleiflex SL2000F motor with Planar 1.4/50 lens Overview Maker Rollei (Franke & Heidecke) Type Modular SLR Released 1981 (1981) Lens...

{\displaystyle V_{th}} with significantly greater efficacy than in bulk planar devices. In particular, this architecture enables dynamic body biasing (DBB)...

Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert...

associate with a ligand to form the square planar four-coordinate complex. Reductive elimination of square planar complexes can progress through a variety...

AN/SPY-6(V)1 was selected in October 2025. Each ship will be equipped with four planar arrays, providing a 360° situational awareness. Each of those arrays are...

rhombohedral system. The carbonate ions (CO2− 3) are arranged in a triangular planar configuration, and the manganese ions (Mn2+) are surrounded by six oxygen...

mathematics, the Y-Δ transform plays an important role in theory of circular planar graphs. The Y-Δ transform is known by a variety of other names, mostly based...

(Philco-Ford) 1947 1976 Philips 1930 c. 1930 present Pioneer 1985 2010 Planar Systems 1983 present Polaroid - - Polytron 1975 present ProLine - - Now...

{a}}h}{r}}} For a planar end cap at the base, t = 0 {\displaystyle t=0} : v ^ = − a ^ {\displaystyle {\hat {v}}=-{\hat {a}}} for a planar end cap at the...

structure Monoclinic Coordination geometry 4 (Au) Molecular shape Square planar (around Au) Thermochemistry Std enthalpy of formation (ΔfH⦵298) -169.8 kJ/mol...

in its service life, with the most significant one being adopting a new planar array radar, Emerson AN/APQ-159 with a range of 20 nmi to replace the original...

trigonal planar molecular geometry. The structure of the trimer of the metaborate ion ([B3O6]3−). This anion is a cyclic molecule and has a trigonal planar molecular...

grid. A 2 × 2 {\displaystyle 2\times 2} grid graph is a 4-cycle. Every planar graph H is a minor of the h × h grid, where h = 2 | V ( H ) | + 4 | E (...

125px.com. "Planar T* f/1.4 - 50 mm" (PDF). Carl Zeiss – via 125px.com. "Planar T* f/1.7 - 50 mm" (PDF). Carl Zeiss – via 125px.com. "Planar T* f/1.2 -...

Benedictusberg Abbey church by Hans van der Laan has plastic ratio proportions. Planar symmetries have for millennia been exploited in artworks such as carpets...

did still remain in production until the 1960s, by which time the silicon planar transistor was dominating the market. While point-contact transistors usually...

polynomial-time algorithms for Max-Cut in general graphs are known. However, in planar graphs, the maximum cut problem is dual to the route inspection problem...

actually appears to the eye. Instead, he formulated the theory based on planar projections, or how the rays of light, passing from the viewer's eye to...

key-fob designs. Planar Inverted-F Antennas (PIFA) are a form of printed PCB antenna in which the radiating element is implemented as a planar conductive plate...

glass or microporous polymer membranes with appropriate surface chemistry. Planar shallow electroosmotic pumps are made of parallel shallow microchannels...

the slight negative charge of the aromatic system on another molecule. Planar monocyclic molecules containing 4n π electrons are called antiaromatic and...

wall-mounted, and in-wall hybrid speakers using electrostatic loudspeaker and planar magnetic thin film loudspeaker technology. MartinLogan was founded by Gayle...

measurement convention used to describe the plane orientation or attitude of a planar geologic feature. A feature's strike is the azimuth (relative to north)...

Retrieved 2014-05-06. "Sony Ziris Canvas Custom Video Wall Solution" (PDF). "Planar AD22 Specifications" (PDF). "Userful Artistic Mosaic Video Wall". "Datapath...

A flow-based generative model is a generative model used in machine learning that explicitly models a probability distribution by leveraging normalizing...

simplest anastigmatic lens designs. It was designed by H. Dennis Taylor. A Planar (1896) design is one with 4 groups of 6 elements and a flat field design...

projection maps a family of confocal spherical conics onto two families of planar ellipses and hyperbolas. The projection has been used for all maps of the...

edges, and have an order-6 dihedral group of symmetries. Both graphs are 1-planar. Karam, Kaio; Campos, C. N. (2014), "Fulkerson's conjecture and Loupekine...

Harvard in 1962. In their extensive evaluation of Maxwell's equations at the planar interface between a linear and nonlinear medium, several rules for the interaction...

processing through photolithography. The reason to use either of these planar faces depends on the application for which the silicon wafer will be used...

Coordination number Type of void Crystal structure Examples 0.1547 3 Trigonal planar α-B2O3 structure B2O3 0.2247 4 Tetrahedral Zincblende structure ZnS, CuCl...

Smallest rectangle which encloses some planar set of points...

−86.65·10−6 cm3/mol Viscosity 1.04 cP at 65 °C Structure Molecular shape Planar Hazards GHS labelling: Pictograms Signal word Warning Hazard statements...

systems to be aromatic and close to planar. Due to a balance between angle strain (~20°) and aromaticity, a planar conformation and distorted conformation...

thesis was titled "A spectrometric study of high-energy electrons using planar-doped barrier (PBD) launchers", and her research focused on developing a...

uniform presentation of the chromaticity as (another than in CIE 1931) planar Euclidean shape. This presentation is a projective transformation of the...

disilenes each silicon atom has planar coordination but the substituents are twisted so that the molecule as a whole is not planar. In diplumbenes the Pb=Pb...

tetrahydrate are known. Both are orange-yellow solids consisting of the planar [AuCl4]− anion. Often, chloroauric acid is handled as a solution, such as...

of two major ways to organize graphics data in memory, the other being planar organization, where each pixel is made of individual bits stored in their...

interpreted in this way as the number of perfect matchings in a graph. For planar graphs (regardless of bipartiteness), the FKT algorithm computes the number...

Concepts Affine transformation Back-face culling Clipping Collision detection Planar projection Reflection Rendering Beam tracing Cone tracing Checkerboard rendering...

planar magnetic or electrostatically-driven loudspeakers, and should not be confused with planar or true ribbon loudspeakers. In contrast to a planar...

Isochrons and a stable limit cycle of the planar system x ˙ = x − y − x ( x 2 + y 2 ) ; y ˙ = x + y − y ( x 2 + y 2 ) {\displaystyle {\dot {x}}=x-y-x(x^{2}+y^{2});{\dot...

Type of planar curve with tree-like structure...