Examples http chemlab.truman.edu CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual MolecularGeometry Category Stereochemistry Category Moleculargeometry ja sv Trigonal geometri ...Image AX3E0 3D balls.png thumb right 200px Idealized structure of a compound with trigonalplanar coordination geometry. In chemistry , trigonalplanar is a moleculargeometry model with one atom at the center and three atoms at the corners of a triangle, called peripheral atoms, all in one plane. ref name March Jerry March Advanced Organic Chemistry 3rd Ed. ref In an ideal trigonalplanar species, all three ligands are identical and all bond angles are 120 . Such species belong to the point group D sub 3h sub . Molecules where the three ligands are not identical, such as formaldehyde H sub 2 sub CO , deviate from this idealized geometry. Examples of molecule s with trigonalplanargeometry include boron trifluoride BF sub 3 sub , formaldehyde H sub 2 sub CO , phosgene COCl sub 2 sub , and sulfur trioxide SO sub 3 sub . Some ions with trigonalplanargeometry include nitrate NO sub 3 sub sup sup , carbonate ion CO sub 3 sub sup 2 sup , and guanidine guanidinium C NH sub 2 sub sub 3 sub sup sup . In organic chemistry, planar, three connected carbon centers that are trigonalplanar are often described as having orbital hybridisation sp sup 2 sup hybridization . ref Holleman, A. F. Wiberg ... Nitrogen inversion is the distortion of pyramidal amine through a transition state that is trigonalplanar. Pyramidalization is a distortion of this molecular shape towards a tetrahedral moleculargeometry . One way to observe this distortion is in pyramidal alkene s. ref name March References references See also AXE method Moleculargeometry VSEPR External links http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu Indiana University Molecular Structure ... more details
Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual MolecularGeometry Category Stereochemistry Category Moleculargeometry ja sv Trigonal pyramidal ...Infobox moleculargeometry Image File Pyramidal 3D balls.png Symmetry group Cyclic symmetries C sub 3v sub Electron direction 4 Atom direction 3 Bond angle 109.5 , 107 mu Examples ammonia NH sub 3 sub , phosphorus trichloride PCl sub 3 sub In chemistry , a trigonal pyramid is a moleculargeometry with one atom at the Apex geometry apex and three atoms at the corners of a trigonal base. When all three atoms at the corners are identical, the molecule belongs to Molecular symmetry point group C sub 3v sub . One example of a molecule with a trigonal pyramidal geometry is ammonia NH sub 3 sub . Some molecules and ions with trigonal pyramidal geometry include the xenon trioxide molecule, XeO sub 3 sub , the chlorate ion, ClO sub 3 sub sup sup , the sulfite ion, SO sub 3 sub sup 2 sup , and the phosphite ion, PO sub 3 sub sup 3 sup . In organic chemistry, molecules which have a trigonal pyramidal geometry are sometimes described as orbital hybridisation sp sup 3 sup hybridized . The AXE method ... Trigonal pyramidal geometry in ammonia The nitrogen molecule in ammonia has 5 valence electron s and bonds with three hydrogen atoms to complete the octet rule octet . This would result in the geometry ... AXE Method Moleculargeometry References reflist External links http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu IUMSC Indiana University Molecular ... . However, the three hydrogen atoms are repelled by the electron lone pair in a way that the geometry is distorted to a trigonal pyramid regular 3 sided pyramid with bond angles of 107 . In contrast, boron trifluoride is flat, adopting a trigonalplanargeometry because the boron does not have a lone pair of electrons. In ammonia the trigonal pyramid undergoes rapid nitrogen inversion . ref name ... more details
Infobox moleculargeometry Image File Trigonal bipyramidal 3D balls.png Symmetry group Dihedral symmetry in three dimensions D sub 3h sub Electron direction 5 Atom direction 5 Bond angle 90 , 120 mu 0 Examples PF5 PF sub 5 sub In chemistry a trigonal bipyramid formation is a moleculargeometry with one atom at the center and 5 more atoms at the corners of a triangular dipyramid . This is one of the few cases where bond angles surrounding an atom are not identical see also pentagonal dipyramid , which is simply because there is no geometrical arrangement which can result in five equally sized bond angles in three dimensions. File Trigonal bipyramidal 3D balls ax eq.png thumb left 200px ax axial br eq equatorial Behavior Isomers with a trigonal bipyramidal geometry are able to interconvert through a process known as Berry mechanism Berry pseudorotation . Pseudorotation is similar in concept to the movement of a conformational diastereomer, though no full revolutions are completed. In the process of pseudorotation, two equatorial ligands both of which have a shorter bond length than the third shift toward the molecule s axis, while the axial ligands simultaneously shift toward the equator ... Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual Category Stereochemistry Category Moleculargeometry MolecularGeometry es Geometr a molecular bipiramidal trigonal ja sv Trigonal bipyramidal geometri ... s apicophilicity is observed. See also AXE method Moleculargeometry External links http www.3dchem.com ... such as PF5 PF sub 5 sub . Examples Phosphorus pentachloride is a molecule with a trigonal bipyramidal geometry. The phosphorus atom shares a plane with three chlorine atoms which are at 120 degrees ... apical or axial positions . The triiodide ion is also based upon a trigonal bipyramid, but with the equatorial ... University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules l3d.html ... more details
and complex ions MolecularGeometry DEFAULTSORT Square PlanarMolecularGeometry Category Stereochemistry Category Moleculargeometry ja sv Plankvadratisk geometri ... planargeometry can thus be derived from the octahedral diagram. The removal of the two ligands ... s stabilize this geometry. See also AXE method Moleculargeometry References reflist External ...Image Square planar 3D balls.png thumb right 200px Idealized structure of a compound with square planar coordination geometry. The square planarmoleculargeometry in chemistry describes the stereochemistry spatial arrangement of atoms that is adopted by certain chemical compound s. As the name suggests, molecules of this geometry have their atoms positioned at the corners of a square on the same plane about a central atom. Relationship to other geometries Linear chemistry Linear The addition of two ligands to linear compounds, ML sub 2 sub , can afford square planar complexes. For example, AuCl sub 2 sub sup nowiki &minus nowiki sup adds chlorine to give square planar AuCl sub 4 sub sup nowiki &minus nowiki sup . Tetrahedral moleculargeometry In principle, square planargeometry can be achieved by flattening a tetrahedron. As such, the interconversion of tetrahedral and square planar geometries provides an intramolecular pathway for the isomerization of tetrahedral compounds. This pathway does not operate readily for hydrocarbons, but tetrahedral nickel II complexes, e.g. NiBr sub 2 sub triphenylphosphine PPh sub 3 sub sub 2 sub , undergo this change reversibly. Octahedral geometry ... 035471 6 ref Examples Numerous compounds adopt this geometry, examples being especially numerous for transition ... as predicted by VSEPR theory . The geometry is prevalent for transition metal complexes with d ... homogeneous catalysts are square planar in their resting state, such Wilkinson s catalyst and Crabtree ... IUMSC Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry ... more details
Description Chemical structure of the trigonalplanarmoleculargeometry. Author, date of creation selfmade by en User Rune.welsh Rune Welsh , November 1, 2005 Source Copyright Released to the Public Domain Comments high resolution b w PNG ChemDraw Irfanview. Licensing PD self date November 2005 ... more details
, carbon dioxide has a linear molecular shape. Trigonalplanar Just from its name, it can easily be said that molecules with the trigonalplanar shape are somewhat triangular and in one Plane geometry ...Cleanup reason the article is muddled and incomplete. Molecular structure covers more than moleculargeometry . date January 2011 Image Water molecule dimensions.svg thumb 200px Geometry of the water molecule water molecule Moleculargeometry or molecular structure is the three dimension al arrangement ... , magnetism , and biological activity . ref McMurray ref ref Cotton&Wilkinson6th ref Moleculargeometry determination The moleculargeometry can be determined by various spectroscopy spectroscopic ... chemistry methods to high accuracy. The moleculargeometry can be different as a solid, in solution ... it is connected to its neighboring atoms. The moleculargeometry can be described by the positions ... hardly influences the moleculargeometry. But, as a quantum mechanical motion, it is thermally excited ... formed by the first three atoms and the plane formed by the last three atoms. Moleculargeometry is determined ... s and Pi bond s. The geometry can also be understood by molecular orbital theory where the electrons .... The bond angle is 90 degrees. An example of an octahedral moleculargeometry octahedral molecule is sulfur ... like shapes . Unlike the linear and trigonalplanar shapes but similar to the tetrahedral orientation ... 0 center center 3 center trigonalplanar center 120 center center BF sub 3 sub center center Image ... References Reflist External links http www.tutor pages.com Chemistry MolecularGeometry Polar Or Nonpolar.html MolecularGeometry & Polarity Tutorial 3D visualization of molecules to determine polarity. MolecularGeometry DEFAULTSORT MolecularGeometry Category Moleculargeometry ar ca ... spectroscopy can give information about the molecule geometry from the details of the vibrational ... and electron diffraction can give molecular structure for crystalline solids based on the distance ... more details
CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual MolecularGeometry Category Moleculargeometry ja ... planargeometry. Thus even though the geometry is rarely seen as the ground state, it is accessed by a low energy distortion from a trigonal bipyramid. Pseudorotation also occurs in square pyramidal molecules. Molecules with this geometry, as opposed to trigonal bipyramidal, exhibit heavier vibration. The mechanism used is similar to the Berry mechanism. Examples Some molecular compounds that adopt square pyramidal geometry are XeOF sub 4 sub , ref Square Pyramidal MolecularGeometry . VSEPR ... AXE method Square pyramid Hypervalent molecule Moleculargeometry References references External ... square pyramidal geometries. ref Square Pyramidal Geometry . http intro.chem.okstate.edu 1314F97 ... IUMSC Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules ... more details
Infobox moleculargeometry Image File seesaw 3D balls.png Symmetry group Cyclic symmetries C sub 2V sub Electron direction 5 Atom direction 4 Bond angle 90 , 120 , 180 mu 0 Examples Sulfur tetrafluoride SF sub 4 sub Seesaw is a type of moleculargeometry where the central atom has one lone pair of electrons, and there are four bonding groups also connected to that central atom. Behavior Seesaw molecules behave similarly to trigonal bipyramidal ones in that they go through a phase of Berry pseudorotation . The four atoms in motion act as a lever about the central atom for example, the four fluorine atoms of sulfur tetrafluoride rotate around the sulfur atom. ref http www.ch.ic.ac.uk rzepa bpr Illustration of the Berry Pseudorotation ref Examples The following compounds and ions have seesaw geometry ref Seesaw MolecularGeometry, AX4E1 . 25 Dec 2007 http www.up.ac.za academic chem mol geom seesaw.htm ref Sulfur tetrafluoride SF sub 4 sub Selenium tetrafluoride SeF sub 4 sub IF sub 2 sub O sub 2 sub sup sup IOF sub 3 sub ClF sub 4 sub sup sup Tellurium tetrafluoride TeF sub 4 sub XeO sub 2 sub F sub 2 sub Commented out because image was deleted Image Seesaw.gif thumbnail 100px See also Moleculargeometry AXE method References reflist External references http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu IUMSC Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules l3d.html Point Group Symmetry Point Group Symmetry Interactive Examples http chemlab.truman.edu CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual http intro.chem.okstate.edu 1314F00 Lecture Chapter10 VSEPR.html MolecularGeometry DEFAULTSORT Seesaw MolecularGeometry Category Moleculargeometry chemistry stub es Geometr a molecular de balanc n ja ... more details
In chemistry , the term bent can be applied to certain molecule s to describe their moleculargeometry . H sub 2 sub O is an example of a bent molecule. The bond angle between the two hydrogen atoms is approximately 104.45 inverse cosine of 1 4 . ref G. L. Miessler and D. A. Tarr Inorganic Chemistry 3rd Ed, Pearson Prentice Hall publisher, ISBN 0 13 035471 6. ref Nonlinear triatomic molecules and ions are common for compounds containing only main group elements, prominent examples being nitrogen dioxide , Sulfur dichloride SCl sub 2 sub , and the Carbene CH sub 2 sub . This geometry is almost always consistent with VSEPR theory . See also AXE method Moleculargeometry References reflist External links http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules l3d.html Point Group Symmetry Interactive Examples http chemlab.truman.edu CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual MolecularGeometry Category Stereochemistry Category Moleculargeometry es Geometr a molecular angular ja sv B jd geometri ... more details
In chemistry , the Linear moleculargeometry describes the arrangement of three or more atoms placed at an expected bond angle of 180 . Linear organic molecules, e.g. acetylene, are often described by invoking sp orbital hybridization for the carbon centers. Many linear molecules exist, prominent examples include CO2 CO sub 2 sub , Hydrogen cyanide HCN , and xenon difluoride . Linear anions include azide N sub 3 sub sup nowiki &minus nowiki sup and thiocyanate SCN sup nowiki &minus nowiki sup . Linear cations include Nitronium ion NO sub 2 sub sup sup . ref Greenwood, N. N. & Earnshaw, A. 1997 . Chemistry of the Elements 2nd Edn. , Oxford Butterworth Heinemann. ISBN 0 7506 3365 4. ref See also VSEPR theory AXE Method AXE method Moleculargeometry References references External links http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu IUMSC Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules l3d.html Point Group Symmetry Point Group Symmetry Interactive Examples http chemlab.truman.edu CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual MolecularGeometry Category Moleculargeometry es Geometr a molecular lineal ja sv Linj r geometri ... more details
Image T shaped 3D balls.png thumb right 200px Idealized structure of a compound with T shaped coordination geometry. In chemistry, T shaped molecular geometry describes the structures adopted by some compounds where a central atom has three ligand s. Ordinarily, three coordinated compounds adopt trigonal planar or pyramidal geometries. Example of a T shaped molecules are the halogen trifluorides, such as ClF3 ClF sub 3 sub . ref Greenwood, N. N. & Earnshaw, A. 1997 . Chemistry of the Elements 2nd Edn. , Oxford Butterworth Heinemann. ISBN 0 7506 3365 4. ref According to VSEPR theory T shaped geometry results from three ligands and two lone pairs of electrons bonded to the central atom. The three atoms bond at 90 angles on one side of the central atom, producing the T shape. ref Chemistry Dictionary and Glossary. 2005. http www.ktf split.hr glossary no en o.php?def T shaped 20molecular 20shape ref AXE Type AX sub 3 sub E sub 2 sub . According to Valence Bond Theory, T shaped molecules are assigned sp sup 3 sup d hybridization. It is generally accepted that d orbitals do not contribute to the bonding in such molecules, which can be more simply described using Molecular Orbital Theory . See also AXE method References references External links http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu IUMSC Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules l3d.html Point Group Symmetry Point Group Symmetry Interactive Examples http chemlab.truman.edu CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated Trigonal Planar Visual MolecularGeometry Category Molecular geometry ja T sv T formad geometri ... more details
Image Pentagonal bipyramidal 3D balls.png thumb right 200px Idealized structure of a molecule with pentagonal bipyramidal coordination geometry. In chemistry , a pentagonal bipyramid or dipyramid is a molecular geometry with one atom at the centre with seven ligand s at the corners of a pentagonal dipyramid . A perfect pentagonal bipyramid belongs to the molecular point group D sub 5h sub . The pentagonal bipyramid is a case where bond angles surrounding an atom are not identical see also Trigonal bipyramid molecular geometry . ref Cotton, F. Albert Wilkinson, Geoffrey Murillo, Carlos A. Bochmann, Manfred 1999 . Advanced Inorganic Chemistry 6th Edn. New York Wiley Interscience. ISBN 0 471 19957 5. ref Other seven coordinate geometries include the mono capped octahedron and mono capped trigonal prism. A variety of transition metal complexes adopt heptacoordination, but the symmetry is usually lower than D sub 5h sub . Examples Iodine heptafluoride IF sub 7 sub with 7 bonding groups Peroxo Cr IV complexes, e.g. Cr O sub 2 sub sub 2 sub NH sub 3 sub sub 3 sub where the peroxo groups occupy four of the planar positions. References Reflist External links http www.ch.ic.ac.uk rzepa bpr Figure 5.html Images of IF sub 7 sub http www.3dchem.com 3D Chem Chemistry, Structures, and 3D Molecules http www.iumsc.indiana.edu IUMSC Indiana University Molecular Structure Center MolecularGeometry Category Stereochemistry Category Molecular geometry ja ... more details
also Octahedral cluster s AXE method Moleculargeometry Bailar twist References references External ... The concept of octahedral coordination geometry was developed by Alfred Werner to explain the stoichiometries ... two diastereomers in an organic compound, at least two carbon centers are required. Trigonal prismatic geometry For compounds with the formula MX sub 6 sub , the chief alternative to octahedral geometry is a trigonal prismatic geometry , which has symmetry group symmetry D sub 3h sub . In this geometry, the six ligands are also equivalent. There are also distorted trigonal prisms, with C ... of and complexes, which is usually slow, is proposed to proceed via a trigonal prismatic ... IUMSC Indiana University Molecular Structure Center http www.phys.ncl.ac.uk staff njpg symmetry Molecules ... CHEM121Labs MolecularModeling1.htm Molecular Modeling http intro.chem.okstate.edu 1314F97 Chapter9 3BP.html Animated TrigonalPlanar Visual MolecularGeometry Category Moleculargeometry Category Coordination chemistry es Geometr a molecular octa drica ja pt Geometria molecular octa drica sv ... more details
Molecular Structure Center http www.cartage.org.lb en themes Sciences Chemistry Miscellenous Helpfile ComplexIons mainpage.htm http chemlab.truman.edu CHEM121Labs MolecularModeling1.htm Molecular Modeling MolecularGeometry DEFAULTSORT Tetrahedral MolecularGeometry Category Moleculargeometry ja ... , a difference attributed to the influence of the lone pair. Transition metal chemistry Again the geometry ... at carbon. Nitrogen inversion in ammonia also entails transient formation of planar NH sub 3 sub . Inverted tetrahedral geometry Geometrical constraints in a molecule can cause a severe distortion of idealized tetrahedral geometry. In compounds featuring inverted carbon, for instance, the carbon ... sub 5 sub H sub 4 sub potential energy surface , Lewars E.1 Journal of Molecular Structure THEOCHEM ... more details
Multiple issues wikify December 2010 orphan January 2011 Infobox moleculargeometry Examples Image File Pentagonal pyramidal 3D balls.png Symmetry group Electron direction Atom direction Bond angle mu A pentagonal pyramidal structure is most commonly recognized as a pyramid with a base shaped like a pentagon . It is one of the few molecular geometries with uneven bond angle s. Image AX6E1 2D.png thumbnail 100px Examples XeOF sub 5 sub sup 1 sup , IOF sub 5 sub sup 2 sup References http mathworld.wolfram.com PentagonalPyramid.html MolecularGeometry DEFAULTSORT Pentagonal Pyramidal MolecularGeometry Category Moleculargeometry ja ... more details
Planar may refer to Wiktionary Planar computer graphics , computer graphics pixel information from several bitplanes Planar graph , graph that can be drawn so that no edges intersect or that can be embedded in the plane Plane geometry , a name for something made up of flat planes or pertaining to planes Planar Systems , U.S. digital display manufacturing corporation based in Hillsboro, Oregon Zeiss Planar , photographic lens designed by Paul Rudolph at Carl Zeiss in 1896 Planar device, computer hardware circuit in conventional PCI integrated into a motherboard See also Planer , tool disambig de Planarit t ... more details
border 1 bgcolor ffffff cellpadding 5 align right style margin left 10px width 250 bgcolor e7dcc3 colspan 2 Trigonal trapezohedron align center colspan 2 Image Trigonal trapezohedron.png 240px Trigonal trapezohedron br Click on picture for large version. bgcolor e7dcc3 Type trapezohedra bgcolor e7dcc3 Faces 6 rhombus rhombi bgcolor e7dcc3 Edges 12 bgcolor e7dcc3 Vertices 8 bgcolor e7dcc3 Face configuration 3,3,3,3 bgcolor e7dcc3 Symmetry group Symmetry group Three dimensions D sub 3d sub bgcolor e7dcc3 Dual polyhedron trigonal antiprism bgcolor e7dcc3 Properties convex, face transitive Image Hexahedron.jpg thumb right A cube is a special case with square faces In geometry , the trigonal trapezohedron or deltohedron is the first in an infinite series of face uniform polyhedra which are dual polyhedron dual to the antiprism s. It has six faces which are congruence geometry congruent rhombus rhombi . Trigonal trapezohedrons are a subset of the rhombohedron s. The cube is a special case with square faces. External links mathworld urlname Trapezohedron title Trapezohedron Polyhedron navigator DEFAULTSORT Trigonal Trapezohedron Category Space filling polyhedra Category Zonohedra Category Polyhedra Polyhedron stub eo Triangula kajtopluredro fr Trap zo dre trigonal ... more details
theorem , an important result in Euclidean geometry Euclidean and projective geometry . Image Oxyrhynchus ... fragment of Euclid s Elements Geometry lang grc wikt geo earth , wikt metri measurement ... position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences ... century BC geometry was put into an axiomatic system axiomatic form by Euclid , whose treatment Euclidean geometry set a standard for many centuries to follow. Archimedes developed ingenious techniques ... of geometry is called a geometer. The introduction of coordinates by Ren Descartes and the concurrent development of algebra marked a new stage for geometry, since geometric figures, such as plane curve s, could now be represented analytic geometry analytically , i.e., with functions and equations ..., the theory of perspective graphical perspective showed that there is more to geometry than just the metric properties of figures perspective is the origin of projective geometry . The subject of geometry ... with Euler and Carl Friedrich Gauss Gauss and led to the creation of topology and differential geometry .... Since the 19th century discovery of non Euclidean geometry , the concept of space has undergone a radical ... space , point etc. still have their intuitive meaning and abstract spaces. Contemporary geometry ... structure, allowing one to speak about length. Modern geometry has multiple strong bonds with physics , exemplified by the ties between pseudo Riemannian geometry and general relativity . One of the youngest ... of geometry makes it initially more accessible than other parts of mathematics, such as algebra or number ... provenance for example, in fractal geometry and algebraic geometry . ref It is quite common in algebraic geometry to speak about geometry of algebraic variety algebraic varieties over finite field ... to the ordinary sphere s or Cone geometry cone s. ref Overview Image Chinese pythagoras.jpg thumb 300px ... Pei Suan Ching 500 200 BC. The recorded development of geometry spans more than two millennia ... more details
views Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three dimensional space to points on a two dimensional projection plane . The projected point on the plane is chosen such that it is Line geometry collinear with the corresponding three dimensional point and the centre of projection . The lines connecting these points are commonly referred to as projectors . The centre of projection can be thought of as the location of the observer while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed e.g., photographic negative, photographic print, computer monitor . When the centre of projection is at a finite distance from the projection plane, a Perspective graphical perspective projection is obtained. When the centre of projection is at infinity, all the projectors are parallel, and the corresponding subset of planar projections are referred to as parallel projections . Mathematical formulation Mathematically, planar projections are linear transformations acting on a point in three dimensional space math mathbf a x,y,z math to give a point math mathbf b u,v math on the projection plane. These transformations consist of various function composition compositions of the five transformations orthographic projection , rotation mathematics rotation , Shear mapping shear , Translation geometry translation and Projective transformation perspective . Map uses It is also used in maps to show the planet Earth and other planets or objects in space. This is good for maps of close up areas. math stub Category Graphical projections ... more details
Infobox lens design scheme Planar 1896.png author Paul Rudolph physicist Paul Rudolph year 1896 elements 6 groups 4 aperture f 4.5 The Zeiss Planar is a photographic lens designed by Paul Rudolph physicist Paul Rudolph at Carl Zeiss AG Carl Zeiss in 1896 . Rudolph s original was a six element symmetrical design. While very sharp, the lens suffered from Lens flare flare due to its many air to glass surfaces. Before the introduction of Anti reflective coating lens coating technology the four element Tessar , with slightly inferior image quality, was preferred due to its better contrast. In the 1950s, when effective anti reflective lens coatings became available, coated Planars were produced with much improved flare. These lenses used the Zeiss T coating system, which had been invented in 1935. ref http www.zeiss.com C12567A100537AB9 Contents Frame CBE2C3659882006AC1256D01002B5E45 Zeiss.de New Visual Glasses Better Objectives ref They performed very well as normal and medium long focus lenses for small and medium format cameras. One of the most notable Planar lenses is the high speed f 2.0 110 mm lens for the 2000 and 200 series medium format Hasselblad cameras. File Planar lenses 7050.jpg thumb left Carl Zeiss T Planar 50 1.4, 50 1.7 Image Planar 50 1.4.png thumb center Carl Zeiss T Planar 50 1.4 lens. See also Photographic lens design References references Carl Zeiss lenses http www.sony mea.com microsite dslr 09 carlZeissLens index.html?HPID carlZeissLensMicrosite DSLR Thumbnails Carl Zeiss SLR Lenses Planar T 1,4 50 http www.propix.in carl zeiss planar 14 50.html Category Zeiss lenses Planar photography stub de Planar Objektiv fr Planar ja pl Zeiss Planar ru zh ... more details
In mathematics , a planar lamina is a closed surface of mass math m math and surface density math rho x,y math such that math m int int rho x,y ,dx ,dy math , over the closed surface . Planar laminas can be used to determine moments of inertia , or center of mass . Category Measure theory math stub ... more details
Unsourced image removed Image Antenna flat panel.png thumb 400px A planar array fractal antenna In telecommunication s and radar , a planar array is an antenna electronics antenna in which all of the elements, both driven element active and passive radiator parasitic , are in one plane. A planar array provides a large aperture antenna aperture and may be used for directional beam control by varying the relative phase waves phase of each element. A planar array may be used with a reflecting screen behind the active plane. ref FS1037C MS188 ref A planar array with a reflecting screen is related to a Radar absorbent material radar absorber . Both are supposed not to reflect incoming radiation of the desired wavelength. Radar absorbers have the advantage that they can use magnetic materials to avoid reflections at the interface to air at least for some frequencies. For antennas to be broadband, the transition from air vacuum to the metal of the screen has to be a gradual one. Radar absorbers have the advantage that they do not have to collect the received energy. The antenna needs a Three dimensional space 3D tree of twin lead s and choke electronics chokes to connect a single cable to a large number of micro antennas. Micro dipole antennas are only resonant at a single high frequency, to be broadband the arms of adjoining antennas have to be connected. Footnotes reflist Category Radio frequency antenna types electronics stub ... more details
Planar chirality is the special case of Chirality mathematics chirality for two dimension s. Most fundamentally, planar Chirality mathematics chirality is a Mathematics mathematical term, finding use in chemistry , physics and related physical sciences, for example, in astronomy , optics and metamaterials . Recent occurrences in latter two fields are dominated by microwave applications and micro and nanostructure d planar interfaces for visible and infrared light . Planar chirality in chemistry Image Planar chiral ferrocene derivative.PNG thumb right An planar chiral derivative of ferrocene , used for kinetic resolution of some racemic secondary alcohol s ref cite journal last1 Ruble first1 J. C. last2 Latham first2 H. A. last3 Fu first3 G. C. year 1997 title Effective Kinetic Resolution of Secondary Alcohols with a Planar Chiral Analogue of 4 dimethylamino pyridine. Use of the Fe C sub 5 ... dimethylbiphenyl is perhaps the simplest example of this case. Planar chirality is also exhibited ... paracyclophane s. Nature rarely provides planar chiral molecules cavicularin being an exception. Assigning the configuration of planar chiral molecules To assign the configuration of a planar chiral ... ref Planar chirality in optics and metamaterials The study of planar chiral Metamaterial metamaterials has revealed that planar chirality is associated with an optical effect the directionally asymmetric .... Planar chiral metamaterials, which are also anisotropic and lossy exhibit different total transmission ... the effect is referred to as circular conversion dichroism. Like the twist of a planar chiral pattern appears reversed for opposite directions of observation, planar chiral metamaterials have ..., N. I. title Asymmetric propagation of electromagnetic waves through a planar chiral structure journal ... Planar metamaterial with transmission and reflection that depend on the direction of incidence ... reflist Chiral synthesis DEFAULTSORT Planar Chirality Category Stereochemistry ... more details
Infobox company company name Planar Systems, Inc. company logo Image PlanarArcLogo std NoTag Sml.gif ... data 722392 000119312510254224 dex991.htm title Planar Announces Fiscal Fourth Quarter and Full Year 2010 Financial Results date November 9, 2010 publisher Planar Systems accessdate 2009 11 09 ref ... & Projectors industry Technology homepage http www.planar.com www.planar.com Planar Systems, Inc ... of electroluminescent EL digital displays. Planar also makes a variety of other specialty displays ... K. Perkel. History 1980s Planar was founded in 1983 by Jim Hurd, Chris King, John Laney and others ... 1999 ref In 1986, a division spun off from Planar to work on projection technology, InFocus . ref http ... Hobbled by Japan s Lead New York Times , December 18, 1990 Section D page 1 ref Planar s executives took the company public in 1993, listing the stock on the NASDAQ boards ref Planar Systems gets in step with area trend to go public . The Oregonian , October 30, 1993 ref Planar acquired Tektronix s avionics display business, creating the short lived Planar Advance in 1994. ref Planar Inc. maps ... panel LCDs in Lake Mills, Wisconsin, was sold to Planar in 1997. ref Standish of Lake Mills Sold to LCD ... LCD manufacturing shifted to East Asian countries. 2000s File Planar headquarters 1195 Compton.JPG thumb Company headquarters On April 23, 2002, DOME Imaging Systems was purchased by Planar and became ... 12674 Planar Systems Acquires DOME Imaging Systems Photonics.com May 1, 2002 ref Planar acquired Clarity ... 07 17 daily17.html Planar buys Clarity for 46M Portland Business Journal July 19, 2006 ref On May 23, 2007, Planar acquired Runco International , a leading brand in the high end, custom home theater market. ref http www.cepro.com article planars acquisition of runco no end to the party Planar s Acquisition of Runco No End to the Party CEPro , May 24, 2007 ref On August 6, 2008, Planar sold its medical ... 6, 2008 ref Operations Planar s EL manufacturing plant in Hillsboro, was closed in 2002 and these operations ... more details
class wikitable align right colspan 2 Example graphs Planar Nonplanar align center Image Butterfly graph.svg ... center Image CGK4PLN.svg 100px br The complete graph br K sub 4 sub is planar because it can be redrawn ... center Image Biclique K 3 3.svg 100px br K sub 3,3 sub In graph theory , a planar graph is a graph ... in such a way that no edges cross each other. A planar graph already drawn in the plane without edge intersections 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 a point in 2D space, and from every edge to a plane ... is called a planar map . Although a plane graph has an external or unbounded face, none of the faces of a planar map have a particular status. A generalization of planar graphs are graphs which can be drawn on a surface of a given genus mathematics genus . In this terminology, planar graphs have graph ... provided a characterization of planar graphs in terms of Forbidden graph characterization forbidden graphs , now known as Kuratowski s theorem A graph mathematics Finite graph finite graph is planar ... as Theorem P include A finite graph is planar if and only if it does not contain a subgraph that is homeomorphism ... to K sub 3,3 sub and is therefore not planar. Instead of considering subdivisions, Wagner s theorem deals with minor graph theory minors A finite graph is planar if and only if it does not have K sub ... of finite planar graphs. Other planarity criteria In practice, it is difficult to use Kuratowski s criterion to quickly decide whether a given graph is planar. However, there exist fast algorithm ... O n linear time whether the graph may be planar or not see planarity testing . For a simple, connected, planar graph with v vertices and e edges, the following simple planarity criteria hold Theorem ... &le 2 v &minus 4. In this sense, planar graphs are sparse graph s, in that they have only O v ..., has 6 vertices, 9 edges, and no cycles of length 3. Therefore, by Theorem 2, it cannot be planar. Note ... more details
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