Merge from List of geometry topics date September 2011 The following outline is provided as an overview of and topical guide to geometryGeometry &ndash branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Essence of geometry Main Geometry History of geometry Main History of geometry General geometry concepts General concepts Geometric progression Geometric shape Geometry Pi angular velocity velocity linear velocity De Moivre s theorem parallelogram rule Pythagorean theorem similar triangles trigonometric identity unit circle Trapezoid Triangle Theorem point geometry point line mathematics Ray ray plane mathematics plane line mathematics line line segment Measurements bearing navigation Bearing Angle degree angle Degree minute of arc Minute Radian Circumference Diameter Trigonometric functions Trigonometric function Asymptotes Circular functions Periodic functions Law of cosines Law of sines Vectors Main vector geometric Amplitude Dot product Norm mathematics also known as magnitude Position vector Scalar multiplication Vector addition Zero vector Vector spaces and complex dimensions Complex plane Imaginary axis Linear interpolation One to one Orthogonal Polar coordinate system Pole complex analysis Pole Real axis Secant CIrcular sector or sector Semiperimeter Lists List of mathematical shapes List of differential geometry topics List of geometers list of curves list of curve topics See also Portal Geometry List of basic mathematics topics List of mathematics articles Table of mathematical symbols Further reading cite book last Rich first Barnett title Schaum s Outline of Geometry edition 4th publisher McGraw Hill location New York year 2009 isbn 9780071544122 External links outline footer Sister project links Geometry Category Outlines Geometry Category Geometry Category Mathematics related lists Geometry ... more details
Molecular Conductance math G I V math , or the Electrical conductance conductance of a single molecule , is a physical quantity in molecular electronics . Molecular conductance is dependent on the surrounding conditions e.g. pH , temperature, pressure , as well as the properties of measuring device. Many experimental techniques have been developed in an attempt to measure this quantity directly, but theorists and experimentalists still face many challenges. ref Chen F, Hihath J, Huang Z, Li X, Tao NJ. 2007. Measurement of single molecule conductance. Annu. Rev. Phys. Chem. 58 535 64 ref br Recently, a great deal of progress has been made in the development of reliable conductance measuring techniques. These techniques can be divided into two categories molecular film experiments, which measure groups of tens of molecules, and single molecule measuring experiments. Molecular film experiments Molecular film experiments generally consist of the sandwiching of a thin layer of molecules between two electrodes which are used to measure the conductance through the layer. Two of the most successful implementations of this concept have been the bulk electrode approach and in the use of nanoelectrodes. In the bulk electrode approach, a molecular film is typically immobilized onto one electrode and an upper electrode is brought into contact with it allowing for a measure of current flow as a function of applied bias voltage . The nanoelectrode class of experiments, in creatively utilizing ... experimenters a better look at molecular conductance. These fall under the categories ... to detach until eventually one molecule is connected. The atomic level geometry of the tip electrode ... so a histogram approach is required. Forming a junction in which the precise contact geometry is known ... toward the goal of building electronic devices on the molecular level is the ability to measure and control ... in a wide variety of chemical and biosensor applications. References references Category Molecular ... more details
wiktionarypar geometry geometric Geometry is a branch of mathematics dealing with spatial relationships. Geometry or geometric may also refer to Geometric distribution of probability theory and statistics Geometric series , a mathematical series with a constant ratio between successive terms Music Geometry Robert Rich album Geometry Robert Rich album , a 1991 album by American musician Robert Rich Geometry Jega album Geometry Jega album , a 2000 album by English musician Jega See also lookfrom Geometric Disambig pt Geometria desambigua o tr Geometri anlam ayr m ... more details
redirect3 Combinatorial geometry The term combinatorial geometry is also used in the theory of matroid s to refer to a simple matroid , especially in older texts Discrete geometry and combinatorial geometry are branches of geometry that study Combinatorics combinatorial properties and constructive methods of discrete mathematics discrete geometric objects. Most questions in discrete geometry involve ... geometry point s, line geometry lines , plane geometry plane s, circle s, sphere s, polygon ... object. Discrete geometry has large overlap with convex geometry and computational geometry , and is closely related to subjects such as finite geometry , combinatorial optimization , digital geometry , discrete differential geometry , geometric graph theory , toric geometry , and combinatorial topology ... Kepler Kepler and Augustin Louis Cauchy Cauchy , modern discrete geometry has its origins ... Thue , projective configuration s by Reye and Ernst Steinitz Steinitz , the geometry of numbers by Minkowski ... geometry Polyhedron Polyhedra and polytope s Polyhedral combinatorics Convex lattice polytope Lattice ... Graphs Geometry Structural rigidity and flexibility Cauchy s theorem geometry Cauchy s theorem Flexible polyhedron Flexible polyhedra Incidence structure s Configuration geometry Configurations ... group s Triangle group s Digital geometry Discrete differential geometry Geometric set partitioning and transversals See also Discrete and Computational Geometry Discrete mathematics Paul Erd s References cite book author Bezdek, Andr s Kuperberg, W. title Discrete geometry in honor of W ... 3 cite book author K roly Bezdek Bezdek, K roly title Classical Topics in Discrete Geometry publisher ... in discrete geometry publisher Springer location Berlin year 2005 isbn 0 387 23815 8 cite book last1 Pach first1 J nos authorlink1 J nos Pach last2 Agarwal first2 Pankaj K. title Combinatorial geometry ..., Jacob E. and O Rourke, Joseph title Handbook of Discrete and Computational Geometry, Second Edition ... more details
Infobox Album See Wikipedia WikiProject Albums Name Geometry of Love Type studio Artist Jean Michel Jarre Cover Geometry of Love Jarre Album.jpg Released October 2003 Recorded Genre Electronica , Lounge music lounge , Ambient music ambient Length 42 13 Label Warner Music Group Warner Music Producer Jean Michel Jarre Reviews Last album Sessions 2000 br 2002 This album Geometry of Love br 2003 Next album AERO br 2004 Geometry of Love is an album by Jean Michel Jarre , released in 2003. It is his twelfth studio album and his first release on Warner Music Group Warner Music . This album has more in common with the preceding Sessions 2000 album than releases prior, but the style here is still more electronica than jazz . The music was to be lounge music , played in the background or in the chill out area of a Nightclub club . The album was commissioned by Jean Roch, as a soundtrack for his VIP Room nightclub in France . ref Citation title Discography Studio Albums Geometry of Love url http jarreuk.info ... , in 2001. Some of the sounds in Geometry of Love were used earlier on Interior Music released in 2001. Several tracks from Geometry of Love were included on Jarre s 2006 compilation release Sublime Mix . Track listing Pleasure Principle 6 15 Geometry of Love Part 1 3 51 Soul Intrusion 4 45 Electric Flesh 6 01 Skin Paradox 6 17 Velvet Road 5 54 Near Djaina 5 01 Geometry of Love Part 2 4 06 References Notes reflist External links http www.discogs.com Jarre Geometry Of Love release 201348 Geometry of Love at Discogs http jarreuk.com discography studio albums geometryoflove Geometry of Love at JarreUK http www.jarrography.free.fr gallery src.php?cover covers cds albums geometry of love.jpg Geometry of Love at Jarrography Jean Michel Jarre DEFAULTSORT Geometry Of Love Category 2003 albums ... album stub bg Geometry of Love fr Geometry of Love hu Geometry of Love it Geometry of Love ka Geometry of Love pl Geometry of Love pt Geometry of Love ru Geometry of Love sv Geometry of Love tr Geometry ... more details
Variable geometry may refer to Variable geometry ways to alter the shape of an aircraft s wings in flight in order to alter their aerodynamic properties Multi speed Europe , a proposed strategy for European integration disambig Long comment to avoid being listed on short pages ... more details
Spin geometry is the area of differential geometry and topology where objects like spin manifold s and Dirac operator s, and the various associated index theorems have come to play a fundamental role both in mathematics and in mathematical physics . An important generalisation is the theory of Symplectic geometry symplectic Dirac operators in symplectic spin geometry and symplectic topology , which have become important fields of mathematical research. See also Symplectic topology Spinor Spinor bundle Spin manifold Books Cite book last1 Lawson first1 H. Blaine last2 Michelsohn first2 Marie Louise title Spin Geometry publisher Princeton University Press isbn 978 0 691 08542 5 year 1989 postscript None citation last1 Friedrich first1 Thomas title Dirac Operators in Riemannian Geometry publisher American Mathematical Society year 2000 isbn 978 0 8218 2055 1 DEFAULTSORT Differential geometry Category Differential topology Category Differential geometry topology stub physics stub ... more details
Octahedral moleculargeometry Octahedral , EX sub 6 sub square planar moleculargeometry Square planar ... Tetrahedral moleculargeometry Tetrahedral , EX sub 4 sub . If inversion through the center of symmetry ...see also Molecular orbital theory In chemistry , a molecular orbital or MO is a Function mathematics ... generated with the function. Molecular orbitals are usually constructed by combining atomic orbital s or hybrid orbital s from each atom of the molecule, or other molecular orbitals from ... H C C H molecular orbital set Overview Molecular orbitals MOs represent regions in a molecule where an electron is likely to be found. Molecular orbitals are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom. A molecular orbital can specify ... s . Most commonly an MO is represented as a Linear combination of atomic orbitals molecular ... through molecular orbital theory . Most present day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron ... opposite spin. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals see configuration interaction . Formation of molecular orbitals Molecular orbitals arise from allowed interactions between atomic orbital s, which are allowed ..., which is significant if the atomic orbitals are close in energy. Finally, the number of molecular ... the molecule. Qualitative discussion For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the Linear combination of atomic orbitals molecular orbital method ansatz . Here, the molecular orbitals are expressed as linear combination s of atomic orbital s. Linear combinations of atomic orbitals LCAO Molecular orbitals were first ... On the interpretation of some phenomena in molecular spectra Zeitschrift f r Physik , vol. 36, pages ... more details
for the mathematical journal Geometry & Topology In mathematics , geometry and topology is an umbrella term for geometry and topology , as the line between these two is often blurred, most visibly in Riemannian geometry Local to global theorems local to global theorems in Riemannian geometry, and results like the Gauss Bonnet theorem and Chern Weil theory . Sharp distinctions between geometry and topology can be drawn, however, as discussed below. It is also the title of a journal Geometry & Topology that covers these topics. Scope It is distinct from geometric topology , which more narrowly involves applications of topology to geometry. It includes Differential geometry and topology Geometric ... topology as homotopy theory , but some areas of geometry and topology such as surgery theory, particularly algebraic surgery theory are heavily algebraic. Distinction between geometry and topology Pithily, geometry has local structure or infinitesimal , while topology only has global structure. Alternatively, geometry has continuous moduli, while topology has discrete moduli. By examples, an example of geometry is Riemannian geometry , while an example of topology is homotopy theory . The study of metric space s is geometry, the study of topological space s is topology. The terms are not used completely consistently symplectic manifold s are a boundary case, and coarse geometry is global ... study is geometry. The space of homotopy classes of maps is discrete, ref Given point set conditions ... s, hence their study is algebraic geometry . Note that these are finite dimensional moduli spaces. The space ... symplectic topology and symplectic geometry . By Darboux s theorem , a symplectic manifold has no local ... structures on a manifold form a continuous moduli, which suggests that their study be called geometry ... Groups and Symplectic Geometry , by Robert Bryant, p. 103 104 ref References reflist DEFAULTSORT Geometry And Topology Category Topology Category Geometry ... more details
File Nitrobenzene bound within hemicarcerand from Chemical Communications 1997 .jpg thumbnail 200px Molecular encapsulation of a nitrobenzene bound within a hemicarcerand reported by Donald J. Cram Cram and coworkers in Chem. Commun., 1997, 1303 1304. Image Container molecule GA cluster.png 200px thumbnail Container molecule. Green Ga cluster, L ligand, Molecular encapsulation in supramolecular chemistry is the confinement of a guest molecule inside the cavity of a supramolecular host molecule molecular capsule, molecular container or cage compounds . Examples of supramolecular host molecule include carcerand s and endohedral fullerenes . Reactivity of guests An important implication of encapsulating a molecule at this level is that the guest is prevented from contacting other molecules that it might otherwise react with. Thus the encapsulated molecule behaves very differently from the way it would when in solution. The guest molecule tends to be extremely unreactive and often has much different spectroscopic signatures. Compounds normally highly unstable in solution, such as aryne s or cycloheptatetraene have been successfully isolated at room temperature when molecularly encapsulated. Examples One of the first examples of encapsulating a structure at the molecular level was demonstrated by Donald J. Cram Cram and coworkers Ref Cram in which they were able to isolate highly unstable, antiaromatic cylobutadiene at room temperature by encapsulating it within a hemicarcerand. Isolation of cyclobutadiene allowed chemists to experimentally confirm one of the most fundamental predictions of the rules of aromaticity. In another example Ref Fiedler the cage consists of a gallium tetrahedral moleculargeometry tetrahedral cluster compound stabilized by 6 bidentate catechol amide ligand s residing at the tetrahedron edges. The guest is a electron counting 16 electron and thus very ... delivery to cancer cells. Other applications the encapsulation of filaments of a molecular self assembly ... more details
Synthetic or axiomatic geometry is the branch of geometry which makes use of axiom s, theorem s and logical arguments to draw conclusions, as opposed to analytic geometry analytic and algebraic geometry ... they include objects and relationships. In geometry, the objects are things like points , lines and planes ... leads to a different logical system. In the case of geometry, each distinct set of axioms leads to a different geometry. Properties of axiom sets If the axiom set is not Morley s categoricity theorem categorical so that there is more than one model one has the geometry geometries debate to settle ... . And since the Erlangen program of Klein the nature of any given geometry has been seen as the connection ... The geometry of Euclid was synthetic, though not all of his books covered topics of pure geometry . The heyday of synthetic geometry can be considered to have been the 19th century, when analytic methods ... such as Jakob Steiner , in favour of a purely synthetic development of projective geometry . For example ... of dimension three. Projective geometry has in fact the simplest and most elegant synthetic expression of any geometry. In his Erlangen program , Felix Klein played down the tension between synthetic and analytic methods On the Antithesis between the Synthetic and the Analytic Method in Modern Geometry The distinction between modern synthesis and modern analytic geometry must no longer be regarded ... geometry. Although the synthetic method has more to do with space perception and thereby imparts ... to the analytic method, and the formulae of analytic geometry can be looked upon as a precise ... translator 2006 http arxiv.org abs 0807.3161 A comparative review of researches in geometry ref The close axiomatic study of Euclidean geometry led to the construction of the Lambert quadrilateral and the Saccheri quadrilateral . These structures introduced the field of non Euclidean geometry where ... geometry , where parallel lines have an angle of parallelism that depends on their separation. This study ... more details
In real time computer graphics , geometry instancing is the practice of Rendering computer graphics rendering multiple copies of the same polygon mesh mesh in a scene at once. This technique is primarily used for objects such as trees, grass, or buildings which can be represented as repeated geometry without appearing unduly repetitive, but may also be used for characters. Although vertex data is duplicated across all instanced meshes, each instance may have other differentiating parameters such as color, or skeletal animation Pose computer vision pose changed in order to reduce the appearance of repetition. API support for geometry instancing Starting in Direct3D version 9, Microsoft included support for geometry instancing. This method improves the potential runtime performance of rendering instanced geometry by explicitly allowing multiple copies of a mesh to be rendered sequentially by specifying the differentiating parameters for each in a separate stream. The same functionality is exposed in OpenGL using the EXT draw instanced extension. Geometry instancing in offline rendering Geometry instancing in Maya software Maya usually involves mapping a pre animated object or geometry to particles, which can then be rendered in any renderer. Geometry instancing in Maya is useful for creating things like swarms of bees or wasps, in which each one can be detailed, but still behaves in a realisitic way that does not have to be determined by the animator. Because instancing geometry in Maya or any other 3D package only references the original object, file sizes are kept very small and changing the original changes all of the instances. Video cards that support geometry instancing GeForce 6000 and up NV40 GPU or later ATI Radeon 9500 and up R300 GPU or later . External links http www.opengl.org registry specs EXT draw instanced.txt EXT draw instanced documentation http msdn.microsoft.com ... stub Category 3D computer graphics fr Geometry instancing ru Geometry Instancing ... more details
File Fano plane.svg thumb The Fano plane , the projective plane over the field with two elements, is one of the simplest objects in Galois geometry. Galois geometry is the branch of finite geometry that is concerned with Algebraic geometry algebraic and analytic geometry over a finite field a Galois field . ref SpringerLink ref More narrowly, a Galois geometry may be defined as a projective space over a finite field. ref Projective spaces over a finite field, otherwise known as Galois geometries, ... , Harv Hirschfeld Thas 1992 ref Objects of study include vector space s, affine space affine and projective space s over finite fields and various structures that are contained in them. In particular, Arc geometry arc s, Oval projective plane oval s, hyperoval s, unital s, blocking sets, ovoid s, caps, spreads and all finite analogues of structures found in non finite geometries. See also Finite geometry Notes reflist References refbegin Three volume series Citation title Projective Geometries Over Finte Fields first1 J. W. P. last1 Hirschfeld publisher Oxford University Press year 1979 isbn 978 0 19850295 1 postscript , emphasizing dimensions one and two Citation title Finite Projective Spaces of Three Dimensions first1 J. W. P. last1 Hirschfeld publisher Oxford University Press year 1985 isbn 0 19 853536 8 postscript , dimension 3. Citation title General Galois Geometries first1 J. W. P. last1 Hirschfeld first2 J. A. last2 Thas publisher Oxford University Press year 1992 isbn 978 0 19853537 9 postscript , treating general dimension. refend External links http eom.springer.de g g110030.htm Galois geometry at Encyclopaedia of Mathematics, SpringerLink geometry stub Category Finite geometry Category Finite fields Category Algebraic geometry Category Analytic geometry nl Galois meetkunde ... more details
Image pyramid.svg right 240px square pyramid In geometry , an apex Latin for ego ref http www.etymonline.com index.php?search apex Online Etymology Dictionary ref is the Vertex geometry vertex which is in some sense the highest of the figure to which it belongs. In an isosceles triangle , the apex is the vertex where the two sides of equal length meet, opposite the unequal third side. In a Pyramid geometry pyramid or Cone geometry cone , the apex is the vertex opposite the Base geometry base . References MathWorld urlname Apex title Apex reflist Category Polyhedra sn Chisuvi eo Apekso geometrio fr Apex g om trie nl Top meetkunde pl Wierzcho ek geometria ... more details
nofootnotes date May 2011 refimprove date May 2011 In plane geometry , a splitter of a triangle is a line segment having one endpoint at one of the three vertices of the triangle and the other so located on the perimeter as to bisect the perimeter. The three splitters concurrent lines concur at the Nagel point of the triangle. See also Cleaver geometry References Ross Honsberger, Cleavers and Splitters. Chapter 1 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry . Mathematical Association of America , pages 1&ndash 14, 1995. External links http mathworld.wolfram.com Splitter.html Splitter at MathWorld Category Triangle geometry Elementary geometry stub ... more details
notable date October 2010 Geometry Expert GEX is a Chinese software for dynamic diagram drawing and automated geometry theorem proving and discovering. There s a new Chinese version of Geometry Expert, called Mathematics Mechanization Platform MMP Geometer . Java Geometry Expert is free under GNU General Public License . Links http www.mmrc.iss.ac.cn gex GEX Official website Java GEX http woody.cs.wichita.edu gex old , http www.cs.wichita.edu ye new on Wichita State University http woody.cs.wichita.edu help gex jgex.html Java GEX Documentation on Wichita State University Category Theorem proving software systems Category Automated theorem proving Category Interactive geometry software ... more details
October 2010 Infobox Software name Geometry Expressions logo Image Geometry expressions logo.gif screenshot Image Nap demo.png caption Geometry Expressions developer Saltire Software Inc latest release ... and Linux genre interactive geometry software license Proprietary software Proprietary website http www.geometryexpressions.com Official website Geometry Expressions is an Interactive Symbolic Geometry System. Geometry Expressions draws figures that can be defined by either Symbolic Constraints ... with powerful new symbolic constraints. Geometry Expressions can be used as a stand alone program ... Maxima , MuPAD , or Ti Nspire . This allows for convenient incorporation of Geometry Expressions ... in Geometry Expressions. Constructions differ from constraints because they create more objects ... Reflection Translation Rotation Scaling geometry Dilation scaling Locus mathematics Locus Trace ... of a line cannot be calculated. Variables When constraints are made symbolically, Geometry Expressions ... hide all drawn objects and toggle between shown and hidden Materials for Use with Geometry Expressions Books Several books have been written to go with geometry expressions. Most teach or discuss ... gives the details of each class wikitable Title Author s Brief Summary Exploring with Geometry Expressions in High School Mathematics Ian Shepard Activities with geometry expressions that aid discovery of the link between geometry and algebra. Function Transformations Tim Brown Students are familiarized ... x sup 2 sup , y 1 x and y sin x . Connecting Algebra through Geometry and Technology Applying Geometry Expressions in the Algebra II and Pre Calculus Classrooms Jim Wiechmann The playground of Geometry ... that mathematics are created, not just a set of facts. Using Symbolic Geometry to Teach Secondary School Mathematics Geometry Expressions Activities for Algebra 2 and PreCalculus Irina Lyublinskaya ... Examples using Geometry Expressions Philip Todd This book s goal is to demonstrate what you can ... more details
Incidence geometry is an area of mathematics that studies relations of incidence geometry incidence between various geometrical objects such as points, lines, curves, and planes. A specific collection of such objects is called a mathematical structure . One type of mathematical structure of particular importance contains only points and lines and is called an incidence geometry . Definition An incidence geometry is an incidence structure for which the following axioms are true Every pair of distinct points determines a unique line. Every line contains at least two distinct points. For every line, there is at least one point that does not lie on the line. The result of this is that every incidence geometry contains at least three points and three lines. Thus, the simplest incidence geometry that can exist would look something like this File Sample Incidence.jpg center The Fano Plane One famous incidence geometry was developed by the Italian mathematician Fano and is known as the Fano plane File Fano Plane.jpg center Incidence Matrix An incidence geometry can be modeled by an incidence matrix which serves as a visual representation of all incidence relations in the geometry. The rows of the matrix represent points, while the columns represent lines. The incidence matrix for the Fano ... the entire geometry, which is one reason why the study of incidence geometry is important ... theorem incidence geometry de Bruijn Erd s theorem is an important theorem in the field of incidence geometry. It was proposed by two mathematicians, Nicolaas Govert de Bruijn and Paul Erd s . The statement ... lines. More Examples Affine plane incidence geometry Affine planes Projective geometry Projective geometries M bius geometry M bius geometries Polar space s Finite geometry Finite geometries Related ..., Francis 1995 , Handbook of Incidence Geometry Buildings and Foundations , Elsevier B.V. http ... geometry es Geometr a de incidencia no Insidensgeometri ... more details
Molecular electronics , sometimes called moletronics , involves the study and application of molecular ... of conductive polymers as well as Molecular scale electronics single molecule electronic components for nanotechnology . An interdisciplinary pursuit, molecular electronics spans physics, chemistry, and materials science. The unifying feature is the use of molecular building blocks for the fabrication ... such as transistors and molecular scale switches. Due to the prospect of size reduction in electronics offered by molecular level control of properties, molecular electronics has aroused much excitement both in science fiction and among scientists. Molecular electronics provides a potential ... circuits . Molecular electronics comprises two related but separate subdisciplines molecular materials ..., while molecular scale electronics focuses on single molecule applications. ref Cite book last Petty first M.C. coauthors Bryce, M.R. & Bloor, D. title Introduction to Molecular Electronics publisher ... in molecular scale electronics journal Annals of the New York Academy of Sciences volume 852 pages 197 204 year 1998 doi 10.1111 j.1749 6632.1998.tb09873.x ref Molecular scale electronics main Molecular scale electronics Nanoelectronics Molecular scale electronics, also called single molecule electronics ... exclusively of molecular sized compounds are still very far from being realized. However, the continuous ... the molecular components and the bulk material of the electrodes. Molecular electronics operates ... representation of a rotaxane , useful as a molecular switch. One of the biggest problems with measuring ... of nanometers alternative strategies are put into use. These include molecular sized gaps called break ... resistance is highly dependent on the precise atomic geometry around the site of anchoring and thereby ... false S rensen, J.K. . 2006 . Synthesis of new components, functionalized with 60 fullerene, for molecular ... to connect a molecular sized circuit to bulk electrodes in a way that gives reproducible results. Also ... more details
Expert subject Software date October 2008 Expert subject Mathematics date October 2008 Infobox Software name Cabri Geometry logo screenshot caption collapsible author developer Cabrilog released Start date YYYY MM DD latest release version 2.1.1 latest release date Release date and age YYYY MM DD latest preview version latest preview date Release date and age YYYY MM DD frequently updated programming language operating system Mac OS X , Microsoft Windows Windows platform size 40.9 Megabyte MB language English, French, Spanish, Italian, German, Polish, Portuguese, Chinese, Korean, Vietnamese, Japanese, Dutch, Norwegian, Danish, Czech, Slovak , Bosnian status genre Interactive geometry software license Proprietary software Proprietary website URL http www.cabri.com Cabri Geometry is a commercial interactive geometry software produced by the French company Cabrilog for teaching and learning geometry and trigonometry . It was designed with ease of use in mind. The program allows the user to animate geometric figures, proving a significant advantage over those drawn on a blackboard. Relationships between points on a geometric object may easily be demonstrated, which can be useful in the learning process. There are also graphing and display functions which allow exploration of the connections between geometry and algebra. The program can be run under Microsoft Windows Windows or the Mac OS . See also Interactive geometry software alternatives to Cabri Geometry External links http www.cabri.com Cabri Geometry Cabri belongs to the http inter2geo.eu Inter2Geo European project aiming at interoperability between interactive geometry software. Category Interactive geometry software geometry stub science software stub cs Cabri fr Cabri G om tre pt Cabri G om tre ... more details
class wikitable align right width 300 valign top File Complete graph K2.svg 120px BR An edge between two Vertex geometry vertices File Square geometry .svg 120px BR A polygon is bounded by edges, like this Square geometry square has 4 edges. valign top File Hexahedron.png 120px BR Every edge shares two faces in a polyhedron , like this cube . File Hypercube.svg 120px BR Every edge shares three or more faces in a 4 polytope , as seen in this projection of a tesseract . For edge in graph theory Edge graph theory In geometry , an edge is a line segment joining two adjacent vertices in a polygon . Thus applied, an edge is a connector for a one dimensional line segment and two zero dimensional objects. A planar closed sequence of edges forms a polygon and a Face geometry face . In a polyhedron , exactly two faces meet at every edge , while in higher dimensional polytope s, three or more faces meet at an edge . In a polygon, an edge can also be called a Facet geometry facet or side , bounding the polygon. In a polyhedron , an edge can also be considered a Ridge geometry ridge , being the shared boundary between two faces, and in a 4 polytope , an edge can be considered a Peak geometry peak , with a cycle of 3 or more faces and Cell geometry cells wrapping around it. See also Euler characteristic External links GlossaryForHyperspace anchor Edge title Edge mathworld urlname PolygonEdge title Polygonal edge mathworld urlname PolyhedronEdge title Polyhedral edge Category Elementary geometry Category Multi dimensional geometry Category Polytopes 1 Elementary geometry stub ar ca Aresta cs Strana geometrie es Arista geometr a eo Latero eu Ertz geometria fr Ar te g om trie gl Aresta ko hr Brid it Spigolo he ht B lv autne mk nl Ribbe ja no Kant geometri pl Kraw d stereometria pt Aresta simple Side sl Stranica sv Kant geometri uk zh ... more details
BAMBI is a mnemonic device. Its use helps students remember that, in a triangle , three lines the line formed by bisecting the Vertex geometry vertex angle that has a different measure from the other angles, the Altitude triangle altitude from that vertex to the opposite base, and the Median geometry median from that vertex to that base are all the same line if the triangle is Isosceles triangle isosceles B Bisector A Altitude M Median B Base I Isosceles Category Mnemonics Category Geometry ... more details
In geometry , a base is a side of a plane figure or face of solid, particularly one perpendicular to the direction height is measured or on what is considered to the bottom. This usage can be applied to a triangle , parallelogram , trapezoids , Cylinder geometry cylinder , cone , pyramid , parallelopiped or frustum . By extension, the length or area of a base is also called a base. As such, bases are commonly used in formulas for area and volume . See also Area Volume Principal square root References cite book title Plane Geometry first1 C.I. last1 Palmer first2 D.P. last2 Taylor publisher Scott, Foresman & Co. year 1918 pages 38, 315, 353 url http books.google.com books?id k9oZAAAAYAAJ Elementary geometry stub Category Area Category Elementary geometry Category Triangle geometry Category Volume ca Base geometria es Base geometr a eu Oinarri geometria fr Base g om trie it Base geometria nn Grunnlinje ... more details
In differential geometry and the study of Lie group s, a parabolic geometry is a homogeneous space G P which is the quotient of a semisimple Lie group G by a parabolic subgroup P . More generally, the curved analogs of a parabolic geometry in this sense is also called a parabolic geometry any geometry that is modeled on such a space by means of a Cartan connection . Examples The projective space P sup n sup is an example. It is the homogeneous space PGL n 1 H where H is the isotropy group of a line. In this geometrical space, the notion of a straight line is meaningful, but there is no preferred affine parameter along the lines. The curved analog of projective space is a manifold in which the notion of a geodesic makes sense, but for which there are no preferred parametrizations on those geodesics. A projective connection is the relevant Cartan connection that gives a means for describing a projective geometry by gluing copies of the projective space to the tangent spaces of the base manifold. Broadly speaking, projective geometry refers to the study of manifolds with this kind of connection. Another example is the conformal geometry conformal sphere . Topologically, it is the n sphere, but there is no notion of length defined on it, just of angle between curves. Equivalently, this geometry is described as an equivalence class of Riemannian metric s on the sphere called a conformal class . The group of transformations that preserve angles on the sphere is the Lorentz group O n 1,1 , and so S sup n sup O n 1,1 P . Conformal geometry is, more broadly, the study of manifolds with a conformal equivalence class of Riemannian metrics, i.e., manifolds modeled on the conformal sphere. Here the associated Cartan connection is the conformal connection . Other examples include CR geometry ... geometry, the study of manifolds modeled on math SP n P math where math P math is that subgroup ... of Adelaide Category Differential geometry Category Homogeneous spaces ... more details
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