for cross sections in architecture and engineering Multiview orthographic projection Crosssection Views In geometry , a crosssection is the intersection set theory intersection of a figure in 2 dimensional space with a line, or of a body in 3 dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross sections. Cavalieri s principle states that solids with corresponding cross sections of equal areas have equal volumes. The cross sectional area math A math of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has math A pi r 2 math when viewed along its central axis, and math A 2 rh math when viewed from an orthogonal direction. A sphere of radius r has math A pi r 2 math when viewed from any angle. More generically, math A math can be calculated by evaluating the following surface integral math A iint limits mathrm top d mathbf A cdot mathbf hat r , math where math mathbf hat r math is a unit vector pointing along the viewing direction toward the viewer, math d mathbf A math is a surface element with outward pointing normal, and the integral is taken only over the top most surface, that part of the surface that is visible from the perspective of the viewer. For a convex body , each ray through the object from the viewer s perspective crosses just two surfaces. For such objects, the integral may be taken over the entire surface math A math by taking the absolute value of the integrand so that the top and bottom of the object do not subtract away, as would be required by the Divergence Theorem applied ... simple Crosssectiongeometry sv Tv rsnitt ... A d mathbf A cdot mathbf hat r math See also commons category Cross sections Descriptive geometry ... geometry Category Technical drawing Category Methods of representation Geometry stub ar ... more details
wiktionary crosssectionCrosssection may refer to Crosssectiongeometry , the intersection of a 3 dimensional body with a plane Multiview orthographic projection CrosssectionCross sectional views in architecture & engineering Radar crosssection , the unit of measure of how detectable an object is with a radar Crosssection physics , the likelihood of an interaction event between two particles Absorption crosssection Neutron crosssection Nuclear crosssection Photoionisation crosssection Scattering crosssectionSection fiber bundle , in differential and algebraic geometry and topology, a section of a fiber bundle or sheaf Cross sectional data , a type of one dimensional data set in statistics and econometrics Stratigraphy , the study of geological cross sections Core sample Thin sectionCrosssection biology , a sample such as that created by a microtome disambiguation de Querschnitt ms Keratan rentas ru ... more details
Unreferenced date December 2009 Orphan date February 2009 Optical CrossSection or OCS is a value which describes the maximum amount of optical flux reflected back to the source. The standard unit of measurement is math frac m 2 sr math . It is dependent on the geometry and the reflectivity at a particular wavelength of an object. Optical crosssection is useful in fields such as LIDAR . In the field of Radar this is referred to Radar CrossSection . Object such as license plates on automobiles has a high optical crosssection to maximize the laser return to the speed detector gun . Flat mirror Optical crosssection of a flat mirror with a given reflectivity at a particular wavelength math r lambda math can be express by this formula. math mbox OCS r lambda frac D 4 1.4884 lambda 2 math Where math D math is the cross sectional diameter of the beam. Note that the direction of the light has to be perpendicular to the mirror surface for this formula to be valid, else the return from the mirror would no longer go back to it source. In order to maximize the return a corner reflector is used. The alignment of a corner reflector with respect to the source is not as critical as the alignment of a flat mirror. Other optical devices Optical crosssection is not limited to reflective surfaces. Optical devices such as telescopes and cameras will return some of the optical flux back to the source, since it has optics that reflect some light. The Optical crosssection of a camera can vary over time due to the camera shutter opening and closing. See also Radar crosssection External links http www.multilingualarchive.com ma enwiki en Optical crosssection Optical crosssection DEFAULTSORT Optical CrossSection Category Optics ... more details
The scattering crosssection , sub scat sub , is a hypothetical area which describes the likelihood ... section is different from the cross sectional area geometrical crosssection of a particle, and it depends ... amount of scattering in a sparse medium is determined by the product of the scattering crosssection and the number of particles present. In terms of area, the total crosssection is the sum of the cross sections due to absorption crosssection absorption , scattering and luminescence math sigma sigma A sigma S sigma L. math The total crosssection is related to the absorbance of the light ... crosssection and the physical size of the particles, as the scattering crosssection depends ... of an approaching vehicle. That is to say that the scattering crosssection of the water droplets ... is the same. Meteorological range The scattering crosssection is related to the meteorological ... Scattering crosssection, sub scat sub file S05490 ref Units Its SI unit is the square meter , m , although smaller units are usually used in practice. The name crosssection arises because it has ... the path length in centimetre s. To avoid the need for conversion factors, the scattering crosssection ... , the differential crosssection is defined as follows let a beam of intensity math I 0 math measured ... define the differential crosssection to be math d sigma over d Omega frac I s I 0 . math Note that this quantity ... area, math d sigma math in space. The differential crosssection is simply math d sigma over d Omega ... math f theta, phi frac e i k r r . math We then have as the definition of differential crosssection ... a scattered particle within a given solid angle. The integral crosssection is the integral of the differential crosssection on the whole sphere of observation 4 math pi math steradian math sigma int d Omega , d sigma over d Omega . math A crosssection is therefore a measure of the effective surface ... 24 sup b . The crosssection of two elementary particle particles i.e. observed when the two particles ... more details
Deleted image removed Image Crosssection all Pt.JPG thumb right 400px The graph displays the crosssection of all the level of platinum Pt . Photoionisation crosssection in the context of condensed matter physics refers to the probability of a particle usually an electron being emitted from its electronic state . Crosssection in photoemission The photoemission is a useful experimental method for the determination and the study of the electronic states. Sometimes the small amount of deposited material over a surface has a weak contribution to the photoemission spectra , which makes its identification very difficult. The knowledge of the crosssection of a material can help to detect thin layers or 1D nanowires over a Substrate materials science substrate . A right choice of the photon energy can enhance a small amount of material deposited over a surface, otherwise the display of the different spectra won t be possible. ref prl See also ARPES Synchrotron radiation Crosssection physics absorption crosssection Nuclear crosssection References note prl A. Dallmeyer and al . Phys. Rev. B 61, R5133 R5136 2000 External links http ulisse.elettra.trieste.it services elements WebElements.html Elettra s photoemission cross sections calculations Category Electromagnetism Category Condensed matter physics Category Physics physics stub ... more details
A crosssection is the effective area which governs the probability of some scattering or absorption ... of a crosssection is used to express the likelihood of interaction between particles. When particles in a beam are thrown against a foil made of a certain substance, the crosssection math sigma math ... of the area of the section of the solid the crosssection , represented by math sigma math ... . Scattering main Scattering crosssection The scattering crosssection , sub scat sub , is a hypothetical ... by a particle. In general, the scattering crosssection is different from the cross sectional area geometrical crosssection of a particle, and it depends upon the wavelength of light and the permittivity ... by the product of the scattering crosssection and the number of particles present. In terms of area, the total crosssection is the sum of the cross sections due to absorption crosssection ... crosssection is related to the absorbance of the light intensity through Beer Lambert Beer ... Nuclear physics File Crosssection illustration simple.svg right Main neutron crosssection In nuclear physics , it is convenient to express the probability of a particular event by a crosssection ... be expressed in terms of the equivalent stopping crosssection of the atoms. This notion can be extended ... as the equivalent crosssection of beryllium for this type of reaction. See also Scattering theory Radar The monostatic radar crosssection is defined as 4 times the radio differential crosssection at 180 degrees. Cross sectional area Rutherford scattering neutron crosssection References More ... astr.gsu.edu Hbase nuclear nucrea.html c3 Nuclear CrossSection http hyperphysics.phy astr.gsu.edu Hbase nuclear crosec.html c1 Scattering CrossSection http www nds.iaea.org IAEA Nuclear ... Reaction CrossSection http www.iupac.org goldbook C01161.pdf IUPAC Goldbook Definition Collision CrossSection Category Fundamental physics concepts Category Nuclear physics Category Particle physics ... more details
The nuclear crosssection physics crosssection of a nucleus is used to characterize the probability that a nuclear reaction will occur. The concept of a nuclear crosssection can be quantified physically ... unit for measuring a nuclear crosssection denoted as is the barn unit barn , which is equal to 10 sup 28 sup m or 10 sup 24 sup cm . Cross sections can be measured for all possible interaction processes together, in which case they are called total crosssection s, or for specific processes, distinguishing elastic scattering and inelastic scattering of the latter, amongst neutron crosssection s the absorption crosssection s are of particular interest. In nuclear physics it is conventional to consider the impinging particles as point particle s having negligible diameter. Cross ... by the interposition of a known thickness of a particular material. The crosssection obtained in this way is called the total crosssection and is usually denoted by a or sub T sub . The typical nuclear radius is of the order of 10 sup 12 sup cm. We might therefore expect the cross sections for nuclear ... by the n, math gamma math reaction the crosssection in some cases is as much as 1,000 barns, while ... are in the neighborhood of 0.001 barn. Macroscopic crosssection Nuclear cross sections are used in determining ... flux, units 1 area time math sigma x math microscopic crosssection for reaction math x math , units ... of 1 volume math Sigma x equiv sigma x rho A math macroscopic crosssection 1 length Types of reactions ... crosssection math sigma t math , which gives the probability of a neutron to undergo any sort of reaction ... neutron crosssection for reaction x as the proportionality constant between a neutron .... The distinction between macroscopic and microscopic crosssection is that the former ... of a type of nuclei. See also Neutron crosssection Scattering crosssection References More footnotes ... Crosssection measurements with a neutron generator journal The Nucleus volume 42 issue 1 2 pages ... more details
N math is the atomic density in cm sup 3 sup See also Crosssection physics Photoionisation crosssection Nuclear crosssection Scattering crosssection Neutron crosssection Mean free path Compton ...Image Photon Cross Sections.png thumb right 300px Cross sections values for all elements with atomic number Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to compton edge s which were also shown. Absorption crosssection is a measure for the probability of an absorption process. More generally, the term crosssection physics crosssection is used in physics to quantify the probability of a certain particle particle interaction, e.g., scattering , absorption electromagnetic radiation electromagnetic absorption , etc. Note that light in this context is described as consisting of elementary particle particle s, i.e., photon s. In the context of ozone shielding of ultraviolet light , absorption crosssection is the ability of a molecule to absorb a photon of a particular wavelength and polarization waves polarization . Analogously, in the context of nuclear engineering it refers to the probability of a particle usually a neutron being absorbed by a nucleus. Although the units are given as an area, it does not refer to an actual size area, at least partially because the density or state of the target molecule will affect the probability of absorption. Quantitatively, the number dN of photons absorbed, between the points x and x dx along the path of a beam is the product of the number N of photons penetrating to depth x times the number n of absorbing molecules per unit volume times the absorption crosssection math frac dN dx N n sigma math . The absorption crosssection is closely related to mass absorption coefficient . For a given particle and its energy, the absorption crosssection of the target material can be calculated from mass absorption coefficient using math sigma mu rho m a N A math where math ... more details
physics , the concept of a neutron crosssection is used to express the likelihood of interaction ... power plant . The standard unit for measuring the crosssection is the barn unit barn , which ... crosssection, and therefore the probability of an interaction, depends on the target type ... temperature. Target type dependence The neutron crosssection is defined for a given type of target particle. For example, the capture crosssection of hydrogen 2 referred to as deuterium is much ..., is expressed with the help of the total crosssection sub T sub . However, it may be useful ... sections sub S sub and sub A sub are defined and the total crosssection is simply the sum of the two partial cross sections ref name DOE math sigma T sigma S sigma A math Absorption crosssection ... in element or isotope. Scattering crosssection The scattering crosssection can be further subdivided ... of the scattering crosssection and for a natural sample, presence of different isotope s of the same ... crosssection varies with the atomic number of the element in question. A very prominent example is hydrogen and its isotope deuterium . The total crosssection for hydrogen is over 10 times that of deuterium ... U235 fission crosssection For a given target and reaction, the crosssection is strongly dependent on the neutron speed. In the extreme case, the crosssection can be, at low energies, either null the energy for which the crosssection becomes significant is called threshold energy or, on the contrary, much larger than the crosssection at high energies. Therefore, a crosssection should be defined ... average crosssection here for more details. As an example, the plot on the right shows that the Nuclear fission fission crosssection of the uranium 235 is low at high neutron energies but becomes ... section at temperature T and sub 0 sub the crosssection at temperature T sub 0 sub T and T sub ... right 450px Interpretation of the reaction rate with the help of the crosssection Let us imagine ... more details
R is the ratio of the hadron ic crosssection physics crosssection to the muon crosssection in electron positron collisions math R frac sigma 0 e e rightarrow mathrm hadrons sigma 0 e e rightarrow mu mu , math where the superscript 0 indicates that the crosssection has been corrected for initial state radiation. R is an important input in the calculation of the anomalous magnetic dipole moment . ref http arxiv.org abs hep ph 9502298 S. Eidelman and F. Jegerlehner, Z. Phys. C67 585 1995 . ref Experimental values have been measured for center of mass energies from 400 MeV to 150 GeV. ref W. M. Yao et al., J. Phys. G 33, 1 2006 Section 40 ref R also provides experimental confirmation of the electric charge of quark s, in particular the charm quark and bottom quark, and the existence of three quark colors. ref W. M. Yao et al., J. Phys. G 33, 1 2006 Section 9.7 ref A naive calculation of R yields math R 3 sum q e q 2, math where the sum is over all quark flavors with mass less than the beam energy. e sub q sub is the electric charge of the quark, and the factor of 3 accounts for the three colors of the quarks. Quantum chromodynamics QCD corrections to this naive formula have been calculated. ref S.G. Gorishny et al. , Phys. Lett. B259 144 1991 ref Notes reflist Category Scattering Category Particle physics particle stub ... more details
In physics , and especially scattering theory , the momentum transfer crosssection is an effective scattering crosssection physics crosssection useful for describing the average momentum transfered from a particle when it collides with a target. Essentially, it contains all the information about a scattering process necessary for calculating average momentum transfers but ignores other details about the scattering angle. The momentum transfer crosssection math sigma mathrm tr math is defined in terms of an azimuthally symmetric and momentum independent differential crosssection math frac mathrm d sigma mathrm d Omega theta math by math sigma mathrm tr int 1 cos theta frac mathrm d sigma mathrm d Omega theta mathrm d Omega math math int int 1 cos theta frac mathrm d sigma mathrm d Omega theta sin theta mathrm d theta mathrm d phi math . Explanation The factor of math 1 cos theta math arises as follows. Let the incoming particle be traveling along the math z math axis with vector momentum math vec p mathrm in q hat z math . Suppose the particle scatters off the target with polar angle math theta math and azimuthal angle math phi math plane. Its new momentum is math vec p mathrm out q cos theta hat z q sin theta cos phi hat x q sin theta cos phi hat y math . By conservation of momentum, the target has acquired momentum math Delta vec p vec p mathrm in vec p mathrm out q 1 cos theta hat z q sin theta cos phi hat x q sin theta cos phi hat y math . Now, if many particles scatter off the target, and the target is assumed have azimuthal symmetry, then the radial math x math and math y math components of the transfered momentum will average to zero. The average momentum transfer will be just math q 1 cos theta hat z math . If we do the full averaging over all possible scattering ... sigma mathrm tot math where the total crosssection is math sigma mathrm tot int frac mathrm d sigma mathrm d Omega theta mathrm d Omega math . Therefore, for a given total crosssection, one does not need ... more details
Image Sigma invader RCS.png thumb 300px Typical RCS diagram A 26 Invader Radar crosssection RCS is a measure of how detectable an object is with a radar . A larger RCS indicates that an object is more easily detected. An object reflects a limited amount of radar energy. A number of different factors determine how much electromagnetic energy returns to the source such as material of which the target is made absolute size of the target relative size of the target in relation to the wavelength of the illuminating radar the incident angle angle at which the radar beam hits a particular portion of target ... the calculation of a RCS because the RCS is a property of the target reflectivity. Radar crosssection ... from the radar to the target meters math sigma math radar crosssection of the target meters squared ... at the target. This power density is intercepted by the target with radar crosssection math sigma ... . The faceted appearance reduces radar crosssection for Stealth ship stealth . Main Stealth technology ... threat direction, with some sort of smooth transition between. To calculate the radar crosssection ... coefficients of corners and points. The crosssection can then be calculated, using the diffraction ... SciTech Publishing year 2004 title Radar CrossSection ref ref cite web author IEEE Transactions on Antennas and Propagation year 2008 title A Method to Measure Radar CrossSection Parameters of Antennas ... and Knott. Radar CrossSection . SciTech Publishing, 2004. ISBN 1 891121 25 1. Harrington, Roger F ... PDF http ieeexplore.ieee.org xpls abs all.jsp?arnumber 4685914 Method to measure radar crosssection ... courses radar crosssection reduction Radar CrossSection Reduction Course A GA Tech ... highly classified. Definition Informally, the RCS of an object is the cross sectional area of a perfectly ... The radar cross sectional area of an object does not necessarily bear a direct relationship with the physical cross sectional area of that object but depends upon other factors. Somewhat less ... more details
The United States National Radar Crosssection Facility is located at Holloman AFB , New Mexico . See also Portal United States Air Force F 117A Nighthawk HAVE BLUE References http www.eglin.af.mil library factsheets factsheet.asp?id 6478 Eglin AFB Public Affairs 46th Test Wing Fact Sheet DEFAULTSORT National Radar CrossSection Facility Category United States Air Force USAF stub ... 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 metria measurement ..., and the properties of space. Geometry arose independently in a number of early cultures as a body ... science emerging in the West as early as Thales 6th Century BC . By the 3rd century BC geometry was put into an axiomatic system axiomatic form by Euclid , whose treatment Euclidean geometry ... geometry in digital imaging . Academic Press . p.1. ISBN 0127039708 ref Archimedes developed ... works in the field 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 ... century. Furthermore, 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 was further enriched by the study of intrinsic structure of geometric objects ... geometry . In Euclid s time there was no clear distinction between physical space and geometrical space. Since the 19th century discovery of non Euclidean geometry , the concept of space ... geometry considers manifold s, spaces that are considerably more abstract than the familiar ... with additional 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 ... the visual nature of geometry makes it initially more accessible than other parts of mathematics ... traditional, Euclidean 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 ... more details
NOTOC selfref For the sectioning of Wikipedia articles, see Help Section wiktionarypar sectionSection may refer to Section botany Section music Archaeological section Histological section , a thin slice of tissue used for microscopic examination Section, an instrumental group within an orchestra Organization orchestra Memory segment , a division of computer memory Statigraphic section , layers of rocks Caesarean section , method of child birth Sleeping car Open section accommodation Pullman section , a type of sleeping car accommodation Sectioning , also known outside the United Kingdom as involuntary commitment Writing Section typography , a division of a chapter or document Section sign , in typography Section bookbinding , papers folded during bookbinding Mathematics Section category theory , also in homological algebra, and including Section fiber bundle , in topology Part of a sheaf mathematics Section group theory Land area Section United States land surveying 640 acres Section of a Dominion Land Survey Western Canada Section as a part of the Alberta Township System Forest section , a division of a forest range in India Social organisations Section Alpine club Section military unit Section Scouting Section One , an elite, top secret counter terrorist organization in the television series La Femme Nikita Places Section, Alabama , a town in the United States See also Crosssection disambiguation Division disambiguation Part disambiguation Segment disambiguation disambig ar de Sektion fr Section it Sezione he io Seciono ru nl Sectie ja pl Sekcja pt Sec o ... more details
see also Grind The term Blade geometry refers to the physical properties of a sword blade crosssection or grind and taper. Crosssection The crosssection of a blade is the primary way of determining its function and place in history. Early Middle Ages Early Viking and medieval European blades tended to have a lenticular crosssection. This is primarily a lozenge or apple seed type of design that lacks a strong central ridge in the middle of the blade. The flexibility these blades have illustrates the purpose that they served, as primarily cutting weapons, that could also be used with the thrust. Late Middle Ages With the improvement in the defensive capabilities of armor in the High Middle Ages High and Late Middle Ages, the crosssection of the sword blade adapted to suit the needs of warriors. Swords began to favour rigidity over flexibility as more rigid blades allowed for the stronger thrusts that were used to pierce armour. These blades were made with a diamond crosssection, which could be more or less acute, depending on the purpose of the blade. Weapons such as the Estoc , for example, would have little to no cutting edge, but they would be very rigid and strong on the thrust. This is opposed by the Longsword which was usually a multi purpose weapon used for both thrusting and cutting. The diamond crosssection could also be hollow ground for additional strength on the thrust. A hollow ground blade has a very strong central ridge which provides its rigidity and thrusting power. Taper There are two types of physical blade taper, distal and profile. Distal tapering refers to a blade s crosssection thinning from its base to its tip. This is used to create the handling characteristics of individual blades and the amount of distal taper varies depending upon the intended purpose of the blade. Many modern replica blades are not made with any distal taper, resulting ... feature properties.html DEFAULTSORT Blade Geometry Category Swords Category Blade weapons de Klingenform ... more details
In mathematics , projective geometry is the study of geometric properties that are invariant under projective transformation s. This means that, compared to elementary geometry, projective geometry has ... at infinity to traditional points, and vice versa. br Properties meaningful in projective geometry ... by a transformation matrix and translation geometry translation s the affine transformation ...? It is not possible to talk about angle s in projective geometry as it is in Euclidean geometry ... clearly in perspective drawing . One source for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel geometry parallel lines can be said to meet in a point at infinity , once the concept is translated into projective geometry ... in a perspective drawing. See projective plane for the basics of projective geometry in two dimensions. While the ideas were available earlier, projective geometry was mainly a development of the nineteenth century. A huge body of research made it the most representative field of geometry of that time ... theory , the Italian school of algebraic geometry , and Felix Klein s Erlangen programme leading to the study of the classical groups built on projective geometry. It was also a subject with a large number of practitioners for its own sake, under the banner of synthetic geometry . Another field that emerged from axiomatic studies of projective geometry is finite geometry . The field of projective geometry is itself now divided into many research subfields, two examples of which are projective algebraic geometry the study of Algebraic variety Projective varieties projective varieties and projective differential geometry the study of differential geometry differential invariants of the projective transformations . Overview Projective geometry is an elementary non Metric mathematics metrical form of geometry, meaning that it is not based on a concept of distance. In two dimensions it begins ... more details
. In differential geometry , a cylinder is defined more broadly as any ruled surface spanned by a one parameter family of parallel lines. A cylinder whose Crosssectiongeometrycrosssection is an ellipse ... cylinder math 1 a b . Even more general is the generalized cylinder the Crosssectiongeometrycrosssection can be any curve. The cylinder is a degenerate quadric because at least one of the coordinates ... cylinder respectively. Common use In common use a cylinder is taken to mean a finite section of a right ... of one base and the height is measured along the positive x axis. A plane section at a distance of math ... int 0 r s , , ds , d phi , dz math math pi ,r 2 ,h , math Cylindric section Image Cylindric section.svg thumb 120px Cylindric section. Cylindric sections are the intersections of cylinders with planes ... web title MathWorld Cylindric section url http mathworld.wolfram.com CylindricSection.html ref Other ... . Projective geometry File Canterra Tower Calgary.JPG thumb In projective geometry , a cylinder is simply a cone whose apex geometry apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky. In projective geometry , a cylinder is simply a cone geometry cone whose apex geometry apex is at infinity. This is useful in the definition of degenerate ... of two or three perpendicular cylinders Prism geometry References reflist 2 External links commons Cylinder geometry Wikisource1911Enc Cylinder http www.mathguide.com lessons SurfaceArea.html ... cylinders Volume of a cylinder at MATHguide http www.mathsisfun.com geometry cylinder.html Spinning ... animation at Math Open Reference http www.cut the knot.org Curriculum Geometry CutCylinder.shtml ... Category Elementary shapes Category Euclidean solid geometry Category Surfaces Category Greek ... more details
Unreferenced stub auto yes date December 2009 Infobox Television show name Landscape of Geometry image Image Landscape of Geometry Opening Title 1.jpg 200px caption show name 2 genre format creator developer writer director creative director presenter starring David Stringer judges voices narrated theme music composer opentheme endtheme composer country Canada language English language English num seasons 1 num episodes 8 list episodes Landscape of Geometry Episode list executive producer producer editor location cinematography camera runtime company distributor channel TVOntario picture format audio format first run first aired 1 January 1982 last aired 1 January 1983 status Ended preceded by followed by related website production website Landscape of Geometry was an educational television show that illustrated the principles and applications of geometry . The series was produced and broadcast by TVOntario in 1982&ndash 83 and was hosted by David Stringer . Episode list Eight episodes were produced. They were The Shape of Things It s Rude to Point Lines That Cross Lines That Don t Cross Up, Down, and Sideways Trussworthy Cracked Up The Range of Change All episodes were 15 minutes in length. DEFAULTSORT Landscape Of Geometry Category TVOntario shows Category Canadian children s television series Category Mathematics education television series Canada tv prog stub ... 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 ... Circles Conic section Conics Ellipse Parabola Hyperbola Arcs on circles and conics Regular polygon ... 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 ... more details
Groups , section 5. DEFAULTSORT Anabelian Geometry Category Algebraic geometry ...Distinguish Noncommutative geometry Anabelian geometry is a proposed theory in mathematics , describing the way the algebraic fundamental group G of an algebraic variety V , or some related geometric object, determines how V can be mapped into another geometric object W , under the assumption that G is very far from being an abelian group , in a sense to be made more precise. The word anabelian an alpha privative an before abelian was introduced in Esquisse d un Programme , an influential manuscript of Alexander Grothendieck , circulated in the 1980s. ref Alexander Grothendieck, 1984. http people.math.jussieu.fr leila grothendieckcircle EsquisseFr.pdf Esquisse d un Programme , 1984 manuscript , published in Geometric Galois Actions , L. Schneps, P. Lochak, eds., London Math. Soc. Lecture Notes 242 , Cambridge University Press , 1997, pp. 5&ndash 48 English transl., ibid., pp. 243&ndash 283. ref While the work of Grothendieck was for many years unpublished, and unavailable through the traditional formal scholarly channels, the formulation and predictions of the proposed theory received much attention, and some alterations, at the hands of a number of mathematicians. Those who have researched in this area have obtained some expected and related results, and in the 21st century the beginnings of such a theory started to be available. Formulation of a conjecture of Grothendieck on curves The anabelian question has been formulated as cquote how much information about the isomorphism class of the variety X is contained in the knowledge of the etale fundamental group ? ref http www.math.jussieu.fr leila SchnepsLM.pdf, p. 2. ref A concrete example is the case of curves, which ... line and n 4, when the isomorphism class of C is determined by the cross ratio in K of the four points removed almost, there being an order to the four points in a cross ratio, but not in the points ... more details
proved using calculus By similarity, the linear dimensions of a crosssection parallel to the base ... distance from the plane of the base to the crosssection. Since the area of any crosssection is proportional to the square of the shape s Scaling geometry scaling factor, the area of a crosssection at height y is B math tfrac h y 2 h 2 math , or since both B and h are constants ... Volume See also Cone geometry Volume label 1 Cone geometry Volume The volume of a pyramid also any ... of the apex, provided that h is measured as the perpendicular distance from the plane geometry plane ... of Indian mathematics and Indian astronomy , used this method in the Aryabhatiya section 2.6 . ref ... similar to the one above see Cone geometry Volume volume of a cone . The volume can also be calculated ... Bipyramid Cone geometry Trigonal pyramid chemistry Frustum References references External links MathWorld ... dual polyhedra Category Prismatoid polyhedra Category Pyramids Pyramid geometry Category Pyramids ... more details
coordinate geometry. ref Apollonius of Perga , in Apollonius of Perga De Sectione Determinata On Determinate Section , dealt with problems in a manner that may be called an analytic geometry of one ... date September 2011 In Analytical Geometry a section of a line can be given by the formula where c ...File Punktkoordinaten.PNG thumb 450px Cartesian coordinates. Analytic geometry , or analytical geometry has two different meanings in mathematics. The Analytic geometry Modern analytic geometry modern and advanced meaning refers to the geometry of analytic variety analytic varieties . This article focuses on the classical and elementary meaning. In classical mathematics, analytic geometry , also known as coordinate geometry , or Cartesian geometry , is the study of geometry using a coordinate system ... geometry synthetic approach of Euclidean geometry , which treats certain geometric notions as Primitive .... Analytic geometry is widely used in physics and engineering , and is the foundation of most modern fields of geometry, including algebraic geometry algebraic , differential geometry differential , discrete geometry discrete , and computational geometry computational geometry. Usually the Cartesian coordinate system is applied to manipulate equation s for Plane mathematics plane s, Line geometry straight line s, and Square geometry square s, often in two and sometimes in three dimensions. Geometrically ... in school books, analytic geometry can be explained more simply it is concerned with defining and representing ... results about the linear continuum of geometry relies on the Cantor Dedekind axiom . History The Ancient ... had introduced analytic geometry. ref cite book first Carl B. last Boyer authorlink Carl Benjamin ... had analytic geometry. Such a judgment is warranted only in part, for certainly Menaechmus ... pages 142 quote The Apollonian treatise On Determinate Section dealt with what might be called an analytic geometry of one dimension. It considered the following general problem, using the typical ... more details
A toric section is an intersection of a Plane mathematics plane with a torus , just as a conic section is the intersection of a Plane mathematics plane with a cone geometry cone . Mathematical formulae In general, toric sections are fourth order quartic curve quartic plane curve s of the form math left x 2 y 2 right 2 a x 2 b y 2 cx dy e 0. math Spiric sections A special case of a toric section is the spiric section , in which the intersecting plane is parallel to the rotational symmetry axis of the torus . They were discovered by the ancient Greek geometer Perseus geometer Perseus in roughly 150 BC . Well known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli . Villarceau circles Another special case is the Villarceau circles , in which the intersection is a circle despite the lack of any of the obvious sorts of symmetry that would entail a circular crosssection. General toric sections More complicated figures such as an annulus mathematics annulus can be created when the intersecting plane is perpendicular or wikt oblique oblique to the rotational symmetry axis. geometry stub Category Algebraic curves Category Toric sections it Sezione torica sl Presek torusa zh ... more details
In geometry , the link of a vertex geometry vertex of a 2 dimension al simplicial complex is a Graph theory graph that encodes information about the local structure of the complex at the vertex. It is a graph theoretic analog to a sphere centered at a point. Example File Tetrahedron.svg thumb The tetrahedron is a 2 complex. File Graphe complet K3.png thumb The link of a vertex of a tetrahedron is the triangle. The link of a vertex of a tetrahedron is a triangle the three vertices of the link corresponds to the three edges incident to the vertex, and the three edges of the link correspond to the faces incident to the vertex. In this example, the link can be visualized by cutting off the vertex with a plane formally, intersecting the tetrahedron with a plane near the vertex the resulting crosssection is the link. Definition Let math scriptstyle X math be a simplicial complex. The link math scriptstyle operatorname Lk v,X math of a vertex math scriptstyle v math of math scriptstyle X math is the graph constructed as follows. The vertices of math scriptstyle operatorname Lk v,X math correspond to edges of math scriptstyle X math which are incident to math scriptstyle v math . Two such edges are adjacent in math scriptstyle operatorname Lk v,X math if they are Incidence geometry incident to a common 2 cells at math scriptstyle v math . In general, for an abstract simplicial complex and a face math scriptstyle F math of math scriptstyle X math , denoted math scriptstyle operatorname Lk F,X math is the set of faces math scriptstyle G math such that G math cap math F math emptyset math and G math cup math F math in math X. Because math X math is simplicial, there is a set isomorphism between math scriptstyle operatorname Lk F,X math and math X F G in X math such that F math subset G math . The graph math scriptstyle operatorname Lk v,X math is often given the topology of a ball ... 3 540 64324 9 topology stub Category Geometry mk ... more details
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