The Orthographic Conference of 1901 also called the Berlin II Orthographic Conference was a German spelling reform for the German Empire , it was largely based on the Prussian school spelling, but also based on the Orthographic Conference of 1876. The standardized of German spelling in the German speaking countries the countries of Germany, Austria, Switzerland was used uniformly until 1996, apart from the displacement of in Switzerland in the 1920s with ss. The conference got rid of numerous existing double and triple forms. Soon after the conference, the reforms were criticized by various people who believed there should be further reform, but it took 95 years until the next change with the German spelling reform implemented in 1996 . See also German spelling German spelling reform of 1996 Spelling reform Otto Basler German orthography reform of 1944 References Format footnotes date October 2011 references Reich Ministry for Science and Education eds Rules for the German spelling words and directory, Berlin German schoolbook publisher, 1944 Otto Basler . Rules and glossary, Munich Leibniz later Oldenbourg , 1948 and elsewhere Wolfgang Kopke Spelling and constitutional reform, T bingen Mohr, 1995 Theodor Ickler The only real spelling reform in Germany, in Sueddeutsche Zeitung No. 129, 8 Juni 1998, S. 9 June 1998, p. 9 Hanno Birken Bertsch and Reinhard Markner Spelling Reform and National Socialism. A chapter from the political history of the German language, G ttingen Wallstein, 2000. ISBN 3 89244 450 1 External links http www.perseus.tufts.edu cgi bin ptext?doc Perseus 3Atext 3A1999.04.0059 3Aentry 3D 2319181 Lewis and Short Latin Dictionary G Category German orthography Category Orthography reform German Category Spelling reform de Reform der deutschen Rechtschreibung von 1901 ... more details
Image proj map.png thumb right Commutativity of this diagram is the universality of projection , for any map f and set X. Generally speaking, in mathematics , a projection is a mapping of a Set mathematics set or of a structure mathematics mathematical structure which is idempotent , which means that a projection is equal to its Function composition composition with itself. A projection may also refer .... Originally, the notion of projection was introduced in Euclidean geometry to denotes the projection ... are The projection from a point onto a plane or central projection If C is the point, called center of projection , the projection of a point P different of C is the intersection with the plane ... any image by the projection. The projection onto a plane parallel to a direction D The image of a point ... other projections, called projection map s have been defined for the need of cartography. The 3D projection ... the two kinds of projections and of defining the image by a central projection of any point different of the center of projection are at the origin of projective geometry . The original notion of projection has been extended or generalized to various mathematical situations, frequently, but not always ... sup projection set theory projection map , written proj sub j sub , that takes an element x ... equivalence relation is known as the canonical projection. The evaluation map sends a function f ... product math prod i in X Y i math , and the evaluation map is a projection map from the cartesian ... a canonical projection morphism to each factor. This projection will take many forms in different categories. The projection from the Cartesian product of set mathematics sets , the product topology ..., the mapping that takes a point x , y , z in three dimensions to the point x , y , 0 in the plane is a projection. This type of projection naturally generalizes to any number of dimensions n for the source and k n for the target of the mapping. See orthogonal projection , projection linear algebra . In the case ... more details
Refimprove date February 2012 A projection clock also called ceiling clock is an analog signal analog or digital clock equipped with a Image projector projector that creates an enlarged image of the clock face on any suitable projection screen , most often the ceiling. The advantage of a projection clock is that the clock can be placed almost anywhere. Depending on the projector used, the image can be in monochrome or color. The image generated by most projection clocks is large enough that a nearsightedness nearsighted person can see it from distance without glasses or contact lenses. Projection clocks are also used in advertising and merchandising . High brightness analog projection clocks can superimpose a business logo on top of the clock face, while there are low brightness projection clocks designed for home use that project for example a logo in addition to the time. Projection clocks may be connected to and synchronize with an Atomic clock to self adjust their time accurately. History Projection clocks were patented at least twice once in 1909, and another time in 1940. ref http www.roger russell.com project project.htm Dead link date February 2012 ref Both patents have expired by now. Early projection clocks were universally analog but with the widespread adoption of digital clocks, digital projection clocks became the standard. Technology A projection clock usually needs a backlight like an incandescent light bulb incandescent bulbs or light emitting diode LEDs . There are low brightness and high brightness clocks. While the projection created by low brightness clocks ... indoor places. Low brightness projection clocks Most modern projection clocks use a red ... reading when ambient light is too bright for the projection to be seen. They are often integrated into alarm clocks. High brightness projection clocks Modern high brightness projection clocks are in most ... to combine analog and digital information on the projected image. Projectors used in projection ... more details
Image Usgs map albers equal area conic.PNG frame right An Albers projection shows areas accurately, but distorts shapes. File Albers projection SW.jpg 450px thumb Albers projection the world, standard parallels 20 N and 50 N. The Albers equal area conic projection , or Albers projection named after Heinrich C. Albers , is a Map projection Conical conic , Map projection Equal area equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels. The Albers projection is the standard projection for British Columbia . ref cite web title British Columbia Map Projection Standard publisher BC Integrated Land Management Bureau url http www.ilmb.gov.bc.ca risc pubs other mappro map.htm accessdate 2010 08 05 ref It is also used by the United States Geological Survey and the United States Census Bureau . ref cite web title Projection Reference publisher Bill Rankin url http www.radicalcartography.net ?projectionref accessdate 2009 03 31 ref Snyder ref name snyder Cite book author Snyder, John P. title Map Projections &ndash A Working Manual. U.S. Geological Survey Professional Paper 1395 publisher United States Government Printing Office, Washington, D.C. year 1987 This paper can be downloaded from http pubs.er.usgs.gov pubs pp pp1395 USGS pages. ref Section 14 describes generating formul for the projection, as well as the projection s characteristics. Formul also appear at http mathworld.wolfram.com AlbersEqual AreaConicProjection.html Mathworld s page on the Albers projection . References ... s page on the Albers projection http www.radicalcartography.net ?projectionref Table of examples and properties ... geomatics techweb yt albers projection.html Yukon Albers Projection http www.uff.br mapprojections Albers en.html An interactive Java Applet to study the metric deformations of the Albers Projection ... fr Projection d Albers nl Projectie van Albers pt Proje o de Albers ru ... more details
Image Bottomley projection.gif thumb 250px right A Bottomley projection A Bottomley projection is an equal area map projection . The projection is math x frac rho sin E sin phi 1 , math math y tfrac pi 2 rho cos E , math where math rho tfrac pi 2 phi , math math E frac lambda sin phi 1 sin rho rho math and &phi is the latitude, &lambda is the longitude from the central meridian, and &phi sub 1 sub is the given parallel of the projection which determines its shape, all in radians. Parallels i.e. lines of latitude are concentric ellipse elliptical arcs of constant eccentricity mathematics eccentricity , centred on the north pole . On the central meridian geography meridian , shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the sinusoidal projection and the Werner projection . It was introduced by Henry Bottomley as an alternative to the Bonne projection to reduce the extent of extreme distortion at the edges and give a more satisfying overall shape. External links http www.cybergeo.eu index3977.html Cybergeo article Category Cartographic projections Category Equal area projections Cartography stub ... more details
Projection pursuit is a type of statistical technique which involves finding the most interesting possible projections in multidimensional data. Often, projections which deviate more from a Normal distribution are considered to be more interesting. As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections this is the pursuit aspect that motivated the technique known as matching pursuit . The projection pursuit concept was developed by Jerome H. Friedman and John Tukey in 1974. See also Projection pursuit regression Targeted projection pursuit References cite journal title A Projection Pursuit Algorithm for Exploratory Data Analysis author J. H. Friedman and J. W. Tukey journal IEEE Transactions on Computers month Sep. year 1974 volume C 23 issue 9 pages 881 890 issn 0018 9340 url http www.slac.stanford.edu cgi wrap getdoc slac pub 1312.pdf doi 10.1109 T C.1974.224051 cite journal title Projection pursuit author P. J. Huber journal The Annuals of Statistics month Jun. year 1985 volume 13 issue 2 pages 435 475 url http www.stat.rutgers.edu rebecka Stat687 huber.pdf doi 10.1214 aos 1176349519 cite journal doi 10.2307 2981662 author M. C. Jones and R. Sibson title What is Projection Pursuit? journal Journal of the Royal Statistical Society, Series A General year 1987 volume 150 issue 1 pages 1 37 jstor 2981662 Category Exploratory data analysis Category Multivariate statistics stat stub de Projection Pursuit fr Poursuite de projection ru ... more details
File Cassini projection SW.jpg thumb Cassini projection of the world. The Cassini projection is a map projection described by C sar Fran ois Cassini de Thury in 1745 . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp. 74 76, ISBN 0 226 76747 7. ref It is the Transversality transverse aspect of the equirectangular projection , in that the globe is first rotated so the central meridian becomes the equator , and then the normal equirectangular projection is applied. Composing these operations math x arcsin cos phi sin lambda , math math y arctan left frac tan phi cos lambda right math where math lambda math is the longitude from the central meridian and math phi math is the latitude. When programming these equations, the inverse tangent function used is actually the atan2 function, with the first argument math sin phi math and the second math cos phi cos lambda math . The use of the Cassini projection has largely been superseded by the Transverse Mercator projection, at least with central mapping agencies. Distortions Things along the central meridian, and at right angles to it, are not distorted. Elsewhere, the distortion is largely in a north south direction, and varies by the square of the central meridian. As such, the greater the longitudinal extent of the area, the worse the distortion becomes. Due to this, the Cassini projection works best on long, narrow areas, and worst on wide areas. References references External links http www.radicalcartography.net ?projectionref Table of examples and properties of all common projections , from radicalcartography.net http www.ordnancesurvey.co.uk oswebsite freefun geofacts geo1164.html Ordnance Survey GeoFacts on the Cassini Projection DEFAULTSORT Cassini Projection Category Cartographic projections Cartography stub ... more details
Image Dot Product.svg thumb 300px right If 0 90 , as in this case, the scalar projection of a on b coincides with the Euclidean norm length of the vector projection . File Projection and rejection.png thumb 200px Vector projection of a on b a sub 1 sub , and vector rejection of a from b a sub 2 sub . The scalar projection of a vector geometric vector math mathbf a math on or onto a vector math mathbf b math , also known as the scalar resolute or scalar component of math mathbf a math in the direction of math mathbf b math , is given by math s mathbf a cos theta mathbf a cdot mathbf hat b , math where the operator math cdot math denotes a dot product , math hat mathbf b math is the unit vector in the direction of math mathbf b math , math mathbf a math is the Euclidean norm length of math mathbf a math , and math theta math is the angle between math mathbf a math and math mathbf b math . The scalar projection is a scalar mathematics scalar , equal to the Euclidean norm length of the orthogonal projection of math mathbf a math on math mathbf b math , with a minus sign if the projection has an opposite direction with respect to math mathbf b math . Multiplying the scalar projection of math mathbf a math on math mathbf b math by math mathbf hat b math converts it into the above mentioned orthogonal projection, also called vector projection of math mathbf a math on math mathbf b math ... b math is known, the scalar projection of math mathbf a math on math mathbf b math can be computed ... projection math s , math becomes math s mathbf a cos theta mathbf a frac mathbf a cdot mathbf b mathbf a , mathbf b frac mathbf a cdot mathbf b mathbf b , math Properties The scalar projection has ... of the corresponding vector projection if the angle is smaller than 90 . More exactly, if the vector projection is denoted math mathbf a 1 math and its length math mathbf a 1 math math s mathbf a 1 math .... See also Scalar product Cross product Vector projection Category Vectors Mathanalysis stub ca Projecci ... more details
File Mollweide projection SW.jpg 450px thumb Mollweide projection of the world. Image Tissot indicatrix world map Mollweide proj.svg thumb 450px The Mollweide projection with Tissot s indicatrix of deformation The Mollweide projection is a Map projection pseudocylindrical map projection generally used for global maps of the world or sky . Also known as the Babinet projection , homalographic projection , homolographic projection , and elliptical projection . As its more explicit name Mollweide equal area projection indicates, it sacrifices accuracy of angle and shape in favor of accurate proportions ..., for instance small maps depicting global distributions. The projection was first published by mathematician .... It was popularized by Jacques Babinet in 1857, giving it the name homalographic projection . The variation ... as seen by the Wilkinson Microwave Anisotropy Probe . Projected using the Mollweide projection. Image ... Data Analysis Project . Projected using the Mollweide projection. The projection is math x frac ... be bypassed otherwise, division by zero may result. Properties The Mollweide is a Map projection Pseudocylindrical pseudocylindrical projection in which the equator is represented as a straight horizontal ..., although not as severe as in the sinusoidal projection . Shape distortion may be diminished by using an interrupted version. A sinusoidal interrupted Mollweide projection discards the central ... projection uses multiple disjoint central meridians, giving the effect of multiple ellipses ..., has inspired the creation of several other projections, including the Goode homolosine projection Goode s homolosine , van der Grinten projection van der Grinten and the Boggs eumorphic projection Boggs ... 252 ref See also Aitoff projection Hammer projection References reflist External links http www.uff.br ... and angle of the Mollweide Map Projection http mathworld.wolfram.com MollweideProjection.html Mollweide Projection at Mathworld Category Cartographic projections Category Equal area projections ca Projecci ... more details
Unreferenced stub auto yes date December 2009 Orphan date October 2008 Calligraphic projection is a system, often used for laser lighting display s, whereby one or more laser beams draws an image on a screen by reflecting the laser beam from one or more mirrors attached to a deflecting mechanism. Analog oscilloscope s have customarily employed this kind of vector graphics , as did a number of computer graphics terminals in the 1970s, such as the Tektronix 4014 . Calligraphic projection is sometimes called Jules Antoine Lissajous Lissajous projection, after the mathematical figure and mathematician . See also Lissajous curve calligraphy DEFAULTSORT Calligraphic Projection Category Entertainment Category Laser image generation Compu graphics stub Optics stub ... more details
Unreferenced date December 2009 The Projection Principle is a stipulation proposed by Noam Chomsky as part of the Phrase Structure Component of Generative grammar Generative Transformational Grammar . Under the Projection Principle, the properties of lexical items must be preserved while generating the phrase structure of a sentence. The Principle, as formulated by Chomsky in Knowledge of Language Its Nature, Origin and Use 1986 , states that lexical structure must be represented categorically at every syntactic level . For example, the verb strangle , apart from the subject, has an obligatory argument, its object, which must appear in the sentence. The following subcategorization frame for the verb strangle specifies its properties the underlined gap for the location of the verb is followed by the noun phrase NP strangle Verb, NP It is out of this frame that a sentence like the following can be generated Fabio strangled Prince Jamal. A sentence without the object, in violation of the verb s subcategorization frame and the Projection Principle, would be ill formed sup sup Fabio strangled. Before the Projection Principle was proposed, phrase structures were generated in separation from the properties of lexical entries. These were hypothesized to enter the slots in pre generated structures waiting to be filled by the lexical material. According to more recent theories, phrase structures are not generated by phrase structure rules, but are projected from the lexical entries. The Projection Principle therefore obviates the need for phrase structure rules in the generative component. Category Grammar Category Noam Chomsky de Projektionsprinzip fr Principe de projection pa projection principle ... more details
File GS 50 projection with lines of constant scale.svg thumb right GS 50 projection, with lines of constant scale factore superimposed. All 50 States, including islands and passages between Alaska, Hawaii, and the conterminous 48 States are shown with scale factors ranging only from 1.02 to 0.98 GS50 is a map projection that was developed by John P. Snyder of the USGS in 1982. The GS50 projection provides a Conformal map conformal projection suitable only for maps of the 50 United States. Scale map Scale varies less than 2 throughout the area covered. Distortion is very low as well. It is not a standard projection in the sense that it uses complex polynomials of the tenth order rather than a trigonometric formulation, though it was developed from an oblique stereographic projection . References cite journal last1 Snyder first1 John P. year 1985 title Bulletin 1629 pages 79 92, 147 51 publisher United States Geological Survey cite journal last1 Snyder first1 John P. year 1987 title Professional Paper 1395 publisher United States Geological Survey accessdate 2011 06 22 pages 203 212 url http onlinepubs.er.usgs.gov djvu PP PP 1395.pdf format pdf Category Cartographic projections ... more details
The Natta projection is a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula . This concept is named after Giulio Natta . In a hydrocarbon molecule with all carbon atoms making up the backbone in a tetrahedral molecular geometry , the zigzag backbone is in the paper plane with the substituents either sticking out of the paper chemical bond depicted triangular in bold or retreating into the paper chemical bond depicted triangular in stripe pattern . The Natta projection is useful for representing the tacticity of a polymer. Image Isotacticpolymer.gif center isotactic polymers See also Haworth projection Newman projection Fischer projection References cite book title Polymer Synthesis Theory and Practice Fundamentals, Methods, Experiments author Dietrich Braun, Harald Cherdron, Matthias Rehahn, H. Ritter, B. Voit publisher Springer year 2005 isbn 3540207708 page 10 Category Stereochemistry ar es Proyecci n de Natta it Proiezione di Natta he hu Natta projekci ru ... more details
File Sinusoidal projection SW.jpg 450px thumb Sinusoidal projection of the world. Image Tissot indicatrix world map sinusoidal proj.svg thumb right 450px The sinusoidal projection with Tissot s indicatrix of deformation The sinusoidal projection is a pseudocylindrical Map projection Equal area equal area map projection , sometimes called the Sanson Flamsteed or the Mercator equal area projection . Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570. The projection is defined by math x left lambda lambda 0 right cos varphi math math y varphi , math where &phi is the latitude, &lambda is the longitude, and &lambda sub 0 sub is the central meridian. ref http pubs.er.usgs.gov usgspubs pp pp1395 Map Projections A Working Manual , United States Geological Survey USGS Professional Paper 1395, John P. Snyder, 1987, pp. 243 248 ref The north south scale is the same everywhere at the central meridian geography meridian , and the east west scale is throughout the map the same as that correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian ... projection shows relative sizes accurately, but distorts shapes and directions. Distortion can be reduced ... projection around the north pole are the Werner projection Werner and the intermediate Bonne projection Bonne and Bottomley projection Bottomley projections. The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid developed by the NASA s Moderate Resolution ... de Sinusoidal Projektion es Proyecci n sinusoidal fr Projection sinuso dale ko it Proiezione ... more details
Image Glucose Haworth.png thumb right A Haworth projection of the structure for Glucose &alpha small D small glucopyranose A Haworth projection is a common way of representing the cyclic Structural formula structure of monosaccharide s with a simple three dimensional perspective. The Haworth projection was named after the English chemist Sir Norman Haworth . A Haworth projection has the following characteristics ref GoldBookRef title Haworth representation url http goldbook.iupac.org H02749.html ref Carbon is the implicit type of atom. In the example on the right, the atoms numbered from 1 to 6 are all carbon atoms. Carbon 1 is known as the Anomer Anomeric Carbon . Hydrogen atoms on carbon are implicit. In the example, atoms 1 to 6 have extra hydrogen atoms not depicted. A thicker line indicates atoms that are closer to the observer. In the example on the right, atoms 2 and 3 and their corresponding OH groups are the closest to the observer. Atoms 1 and 4 are farther from the observer. Atom 5 and the other atoms are the farthest. The groups below the plane of the ring in Haworth projections are equivalent to those on the right hand side of a Fischer projection . See also Structural formula Fischer projection Natta projection Newman projection References references Category Carbohydrate chemistry Category Carbohydrates Category Stereochemistry ar bg cs Haworthova projekce da Haworth projektion de Haworth Formel fr Projection de Haworth id Proyeksi Haworth it Proiezione di Haworth he hu Haworth projekci nl Haworthprojectie ja pl Projekcja Hawortha ru sr Hauortova projekcija zh ... more details
The GSO projection named after Ferdinando Gliozzi, Jo l Scherk , and David Olive David A. Olive is an ingredient used in constructing a consistent model in superstring theory. The Projection 28linear algebra 29 projection is a selection of a subset of possible vertex operators in the worldsheet conformal field theory CFT usually those with specific worldsheet fermion number and periodic function periodicity conditions. Such a projection is necessary to obtain a consistent worldsheet CFT. For the projection to be consistent, the set A of operators retained by the projection must satisfy Closure The operator product expansion OPE of any two operators in A contains only operators which are in A . Mutual locality There are no branch cuts in the OPE of any two operators in the set A . Modular invariance The partition function on the two torus of the theory containing only the operators in A respects modular invariance . Starting from the same worldsheet CFT, different choices in the GSO projection will lead to string theories with different physical particles and properties in spacetime . For example, the Type II string theory Type II and Type 0 string theory Type 0 string theories result from different GSO projections on the same worldsheet theory. Furthermore, the two distinct Type II theories, IIA and IIB, differ in their GSO projections. In building models of realistic string vacua as opposed to toy model s , one typically chooses a GSO projection which eliminates the tachyon ic ground state of the string and preserves spacetime supersymmetry . References Joseph Polchinski Polchinski, Joseph 1998 . String Theory , Cambridge University Press. A modern textbook. Vol. 2 Superstring theory and beyond. ISBN 0 521 63304 4. string theory stub Category String theory fr Projection GSO ko GSO it Proiezione GSO ... more details
File Projection and rejection.png thumb 200px Projection of a on b a sub 1 sub , and rejection of a from b a sub 2 sub . File Projection and rejection 2.png thumb 248px When 90 180 , a sub 1 sub has an opposite direction with respect to b . The vector projection of a vector math mathbf a math on or onto ... mathbf a math in the direction of math mathbf b math is the orthogonal projection of math mathbf ... projection of math mathbf a math onto math mathbf b math , and math mathbf hat b math is the unit vector in the direction of math mathbf b math . In turn, the scalar projection is defined as math ... theta math is the angle between math mathbf a math and math mathbf b math . The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection ...&lpg PA83&dq projection 20rejection 20vector&hl it&pg PA83 v onepage&q projection 20rejection ... projection of math mathbf a math onto the plane geometry plane or, in general, hyperplane orthogonal to math mathbf b math . Both the projection math mathbf a 1 math and rejection math mathbf a 2 math ... implies that the rejection is given by math mathbf a 2 mathbf a mathbf a 1. math The vector projection ... on angle Scalar projection Main Scalar projection The scalar projection of math mathbf a math ... between math mathbf a math and math mathbf b math . A scalar projection can be used as a scale factor to compute the corresponding vector projection. Vector projection The vector projection ... math a 1 math is the corresponding scalar projection, as defined above, and math mathbf hat b math ... b mathbf a , mathbf b cos theta , math Scalar projection By the above mentioned property of the dot product, the definition of the scalar projection becomes math a 1 mathbf a cos theta mathbf a frac mathbf a cdot mathbf b mathbf a , mathbf b frac mathbf a cdot mathbf b mathbf b , math Vector projection Similarly, the definition of the vector projection becomes math mathbf a 1 a 1 mathbf hat b frac ... more details
File Hammer projection SW.jpg 450px thumb Hammer projection of the world. The Hammer projection is an equal area map projection , described by Ernst Hammer cartographer Ernst Hammer in 1892 . Directly inspired by the Aitoff projection , Hammer suggested the use of the equatorial form of the Lambert azimuthal equal area projection instead of Aitoff s use of the azimuthal equidistant projection math x mathrm laea x left frac lambda 2, phi right math math y frac 1 2 mathrm laea y left frac lambda 2, phi right math where math mathrm laea x math and math mathrm laea y math are the x and y components of the equatorial Lambert azimuthal equal area projection. Written out explicitly math x frac 2 sqrt 2 cos phi sin left frac lambda 2 right sqrt 1 cos phi cos left frac lambda 2 right math math y frac sqrt 2 sin phi sqrt 1 cos phi cos left frac lambda 2 right math The inverse is calculated with the intermediate variable math z equiv sqrt 1 left frac1 4 x right 2 left frac1 2 y right 2 math The longitude and latitudes can then be calculated by math begin align lambda & 2 arctan left frac zx 2 2z 2 1 right phi & arcsin zy end align math where math lambda math is the longitude from the central meridian and math phi math is the latitude . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp.130 133, ISBN 0 226 76747 7. ref ref Weisstein, Eric W. http mathworld.wolfram.com Hammer AitoffEqual AreaProjection.html Hammer Aitoff Equal Area Projection. From MathWorld A Wolfram Web Resource ref Visually, the Aitoff and Hammer projections are very similar. The Hammer has seen more use because of its equal area property. The Mollweide projection is another equal area projection of similar aspect, though with straight parallels of latitude, unlike the Hammer s curved parallels. See also Mollweide projection Aitoff projection References references External ... Aitoff Projection . Category Cartographic projections Category Equal area projections ca Projecci ... more details
File Aitoff projection SW.jpg 450px thumb An Aitoff projection of the world. The Aitoff projection is a modified azimuthal map projection . Proposed by David A. Aitoff in 1889 , it is the equatorial form of the azimuthal equidistant projection , but stretched into a 2 1 ellipse while halving the longitude from the central meridian math x mathrm azeq x left frac lambda 2, phi right , math math y frac 1 2 mathrm azeq y left frac lambda 2, phi right math where math mathrm azeq x math and math mathrm azeq y math are the x and y components of the equatorial azimuthal equidistant projection. Written out explicitly, the projection is math x frac 2 cos phi sin left frac lambda 2 right mathrm sinc alpha , math math y frac sin phi mathrm sinc alpha , math where math alpha arccos left cos phi cos left frac lambda 2 right right , math and math mathrm sinc alpha math is the unnormalized sinc function with the discontinuity removed. In all of these formulas, math lambda math is the longitude from the central meridian and math phi math is the latitude. Three years later, Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal area projection in the same manner as Aitoff, producing the Hammer projection . While Hammer was careful to cite Aitoff, there has been some confusion since, wherein Aitoff has been attributed to Hammer s projection. ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp.130 133, ISBN 0 226 76747 7. ref See also Mollweide projection Hammer projection References references External links http www.radicalcartography.net ?projectionref Table of common projections http www.uff.br mapprojections Aitoff en.html An interactive Java Applet to study the metric deformations of the Aitoff Projection . http map.gsfc.nasa.gov Wilkinson Microwave Anisotropy Probe WMAP Category Cartographic projections ca Projecci d Aitoff de Aitov Projektion es Proyecci n de Aitoff fa ja ... more details
File Werner projection SW.jpg 450px thumb Werner projection of the world. The Werner projection is a pseudoconic equal area map projection sometimes called the Stab Werner or Stabius Werner projection. Like other heart symbol heart shaped projections, it is also categorized as cordiform . Stab Werner refers to two originators Johannes Werner 1466&ndash 1528 , a parish priest in Nuremberg , refined and promoted this projection that had been developed earlier by Johannes Stabius Stab of Vienna around 1500. The projection is a limiting form of the Bonne projection , having its standard parallel at one of the poles 90 N S . ref citation title Flattening the Earth Two Thousand Years of Map Projections first John P last Snyder year 1993 pages 60 2 ISBN 0 226 76747 7 . ref ref citation author mask 8 url http pubs.er.usgs.gov usgspubs pp pp1395 contribution Map Projections A Working Manual publisher United States Geological Survey title Professional Paper number 1395 first John P last Snyder year 1987 pages 138 0 . ref Distances along each parallel and along the central meridian are correct, as are all distances from the north pole. References references External links citation url http www.radicalcartography.net ?projectionref title Table of examples and properties of all common projections publisher Radical Cartography . Category Cartographic projections Category Equal area projections Category Equidistant projections es Proyecci n Werner ru ja ... more details
About the alchemical concept Projection disambiguation Projection Image Alchemik Sedziwoj Matejko.JPG thumb 300px Depiction of Michal Sedziw j Sedziw j performing a transmutation for Sigismund III by Jan Matejko , 1867 Projection was the ultimate goal of Western alchemy . Once the Philosopher s stone or powder of projection had been created, the process of projection would be used to transmute a lesser substance into a higher form, often lead into gold . Typically, the process is described as casting a small portion of the Stone into a molten base metal. Claims and demonstrations The seventeenth century saw an increase in tales of physical transmutation and projection. These are variously explained as examples of charlatanism, fiction, pseudo scientific error, or missed metaphor. The following is a typical account of the projection process described by Jan Baptista van Helmont in his De Natura Vitae Eternae . ref Rosemary Guiley. The Encyclopedia of Magic and Alchemy. 2006. p.328 ref quote I have seen and I have touched the Philosopher s Stone more than once. The color of it was like ... I call a grain that which takes 600 to make an ounce. I made projection with this fourth part of a grain wrapped in paper upon eight ounces of quicksilver heated in a crucible. The result of the projection ... is recorded as making a projection of the red stone onto mercury, making gold. His wealth is given ..., some alchemists of this time period give accounts of fraudulent projection demonstrations, distinguishing .... Accounts are given of double bottomed crucibles used to conceal hidden gold during projection ... and entertainment Main Alchemy in art and entertainment The concept of projection appears in various ... where the following dialogue can be found, commenting on fraudulent applications of projection ... ref quote i When do you make projection? Son, be not hasty, I exalt our med cine, By hanging him ... in the Holy Roman Empire . University of Chicago Press, 2007. Notes reflist Alchemy DEFAULTSORT Projection ... more details
In information theory , the information projection or I projection of a probability distribution q onto a set of distributions P is math p underset p in P arg min operatorname D mathrm KL p q math where math D mathrm KL math is the Kullback Leibler divergence from p to q . Viewing the Kullback Leibler divergence as a measure of distance, the I projection math p math is the closest distribution to q of all the distributions in P . See also Sanov s theorem noreferences date October 2011 Category Information theory probability stub ... more details
ref improve date November 2011 File Mercator projection SW.jpg thumb 450px right Mercator projection ... of the texts The Mercator projection is a Map projection Cylindrical cylindrical map projection ... the standard map projection for nautical purposes because of its ability to represent lines ... of small objects which makes the projection conformal projection conformal , the Mercator projection ... projection Cylindrical cylindrical projections , circle of latitude parallel s and meridian geography ... is the same as the north south scale, making the projection conformal map conformal . A Mercator .... Being a conformal projection, angles are preserved around all locations. However scale ... projection is practically unusable. All lines of constant bearing navigation bearing rhumb lines rhumbs ... and straight rhumb lines, make this projection uniquely suited to marine navigation courses ... projection represented a major breakthrough in the nautical cartography of the 16th century. However ... was known, could the Mercator projection be fully adopted by navigators. Several authors are associated with the development of Mercator projection German Erhard Etzlaub c. 1460&ndash 1532 , who ... designed a projection identical to Mercator s . Portuguese mathematician and cosmographer Pedro Nunes ... the construction of several large scale nautical charts in the cylindrical equidistant projection ... Edward Wright c. 1558&ndash 1615 , who formalized the mathematics of Mercator projection ... the Mercator projection with its modern logarithmic formula, later deduced by calculus. Mathematics of the projection Image Gudermannian.svg thumb 231px right Relation between vertical position ... function . Mathematically, the Mercator projection is completely characterization mathematics ... 1 sec varphi 1 tan varphi 2 sec varphi 2 right math Derivation of the projection Image Usgs map mercator.svg right frame The Mercator projection is a cylindrical projection. Assume a spherical Earth ... more details
File Robinson projection SW.jpg thumb 450px right Robinson projection of the world. Image Tissot indicatrix world map Robinson proj.svg thumb 450px The Robinson projection with Tissot s indicatrix of deformation The Robinson projection is a map projection of a world map , which shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image. ref name impossible cite web title The Impossible Quest for the Perfect Map url http www.nytimes.com 1988 10 25 science the impossible quest for the perfect map.html?pagewanted all&src pm publisher The New York Times accessdate 1 May 2012 author John Noble Wilford date October 25, 1988 ref The Robinson projection is an accomplishment of Arthur H. Robinson in 1961, and has been in use by Rand McNally since the 1960s and was used by the National Geographic Society between 1988 and 1998. ref name impossible Since 1998, the National Geographic Society has used the Winkel tripel projection . Strengths and weaknesses The Robinson projection is neither Map projection Equal area equal area nor conformal map conformal , abandoning both for a compromise. The creator ... in any pseudocylindrical projection. However, at the time it was developed, the projection effectively ... ref name impossible Specification The projection is defined by the table class wikitable Latitude ... parallel of latitude. See also Winkel Tripel &mdash projection currently used by the National Geographic. Further reading Arthur H. Robinson 1974 . A New Map Projection Its Development and Characteristics .... 214 216. External links Commons cat Maps with Robinson projection http www.radicalcartography.net ... deformations of the Robinson Projection . http findarticles.com p articles mi hb3006 is 2 31 ai n29118548 ?tag content col1 Numerical evaluation of the Robinson projection , from Cartography and Geographic ... de Robinson fr Projection de Robinson it Proiezione di Robinson nl Robinsonprojectie ja pt ... more details
Deleted image removed Image Stereographic Projection Northern Hemisphere.png thumb right Stereographic projection of the northern hemisphere of the Earth from the south pole onto the plane tangent at the north pole Views Image Stereographic projection in 3D.png thumb right 3D illustration of a stereographic projection from the north pole onto a plane below the sphere The stereographic projection , in geometry ... mathematics plane . The projection is defined on the entire sphere, except at one point &mdash the projection ..., then, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable ..., so does the stereographic projection it finds use in diverse fields including complex analysis , cartography , geology , and photography . In practice, the projection is carried out by computer ... juxta ac mathematicis utiles , by Francois d Aguilon Fran ois d Aiguillon . It demonstrates how the projection is computed. The stereographic projection was known to Hipparchus , Ptolemy and probably earlier to the Ancient Egypt Egyptians . It was originally known as the planisphere projection. ref ... projection, mapping each hemisphere as a circular disk. ref According to Snyder 1993 , although he acknowledges he did not personally see it ref The equator ial aspect of the stereographic projection ... projection its current name in his 1613 work Opticorum libri sex philosophis juxta ac mathematicis ... Image Stereoprojzero.svg thumb right Stereographic projection of the unit sphere from the north ... thumb 300px right This section focuses on the projection of the unit sphere from the north pole onto ... intersects the plane z 0 in exactly one point P nowiki nowiki . Define the stereographic projection ... z on the sphere and X , Y on the plane, the projection and its inverse are given by the formulas ..., the projection and its inverse are math R, Theta left frac sin varphi 1 cos varphi , theta ... on the sphere and polar coordinates R , on the plane, the projection and its inverse are math ... more details
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