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	Mirror symmetry - Wikipedia, the free encyclopedia
		The discovery of mirror symmetry is connected with names such as Lance Dixon, Wolfgang Lerche, Cumrun Vafa, Nicholas Warner, Brian Greene, Ronen Plesser, Philip Candelas, Monika Lynker, Rolf Schimmrigk and others.
		Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry is a special example of T-duality: the Calabi-Yau manifold may be written as a fiber bundle whose fiber is a three-dimensional torus.
		Mirror symmetry has also become a very powerful tool in mathematics, and although mathematicians have proved many rigorous theorems based on the physicists' intuition, a full mathematical understanding of the phenomenon of mirror symmetry is lacking.
	en.wikipedia.org /wiki/Mirror_symmetry (272 words)

	Reflection symmetry - Wikipedia, the free encyclopedia
		Reflection symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.
		The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical.
		The triangles with this symmetry are isosceles, the quadrilaterals with this symmetry are the kites and the isosceles trapezoids.
	en.wikipedia.org /wiki/Reflection_symmetry (371 words)

	Mirror symmetry - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-01)
		It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden dimensions of string theory.
		Mirror symmetry allowed the physicists to calculate many quantities that seemed virtually incalculable before, by invoking the "mirror" description of a given physical situation, which can be often much easier.
		One possible mathematical framework is provided by the homological mirror symmetry conjecture.
	www.sciencedaily.com /encyclopedia/mirror_symmetry (272 words)

	Symmetry and Symmetry Breaking
		The extension of the concept of continuous symmetry from “global” symmetries (such as the Galilean group of spacetime transformations) to “local” symmetries is one of the important developments in the concept of symmetry in physics that took place in the twentieth century.
		Symmetries may be used to explain (i) the form of the laws, and (ii) the occurrence (or non-occurrence) of certain events (this latter in a manner analogous to the way in which the laws explain why certain events occur and not others).
		Another reason for attributing symmetries to nature is the so-called geometrical interpretation of spatiotemporal symmetries, according to which the spatiotemporal symmetries of physical laws are interpreted as symmetries of spacetime itself, the “geometrical structure” of the physical world.
	plato.stanford.edu /entries/symmetry-breaking (9807 words)

	Symmetry:two sides to every story
		The symmetry of gaming dice is necessary to ensure that all six numbers always have an equal probability of coming up.It was the beauty of symmetry, rather than its usefulness,that first attracted human curiosity.
		The thalidomide tragedy had its origins in a type of symmetry now known to be of fundamental importance in the chemistry of life: "chirality" [Ref Video:BB10 RI Lecture "Man in the Mirror"].
		Symmetry amid complexity was essential to Islamic advances in astronomy and mathematics, particularly trigonometry and geometry,around the end of the first millennium AD.This enlightened fascination is revealed in the ceramic extravaganzas on mosque ceilings.
	www.geocities.com /Omegaman_UK/symmetry.html (2036 words)

	Why Humans are sensitive to mirror symmetry?
		The sensitivity to vertical mirror symmetry is a result of a small portion of the neurons in the optical nerves going to the wrong side in the optical chasm, but connect correctly (in the toplogical sense) to the LGN on the wrong side.
		While the 'stray neurons' are 'stray', the sensitivity to mirror symmetry may have evolutionary advantage, because it makes detecting animals (which are in general mirror symmteric) easier.
		A preference for mirror symmetry in other angles and locations is explained by the general advantage of mirror symmtery (explained in the first two paragraphs), and by learning from experience about its significance.
	www.human-brain.org /mirror.html (711 words)

	Mirror symmetry (Site not responding. Last check: 2007-11-01)
		The discovery of mirror symmetry is connected with names such as BrianGreene, Ronen Plesser, Philip Candelas, and others.
		Mirror symmetry allowed the physicists to calculate many quantities that seemed virtually incalculable before, by invoking the"mirror" description of a given physical situation, which can be often much easier.
		Mirror symmetry has also become a verypowerful tool in mathematics, and the mathematicians have proved many rigorous theorems based on the mirror symmetryintuition.
	www.therfcc.org /mirror-symmetry-179271.html (212 words)

	Mirror Symmetry/Mirror Images
		Then have them turn the mirror (not their head) so they can see the person next to them, then turn the mirror so they can see the ceiling, then their shoes, then a poster on the wall, etc. Ask the students to look at the geometric figure sheet.
		At this point, ask the students to find all of the lines of symmetry (the cut where one part of the figure is the mirror image of the other part) of all of the figures on the sheet.
		Have the students arrange the mirrors so they can see exactly four images, and check the angle, then five images, and check the angle, then six images, and check the angle, then eight images, and check the angle, then ten images, and check the angle.
	www.iit.edu /~smile/ph9517.html (662 words)

	Geometry.Net - Scientists Books: Yau Shing-tung
		Mirror Symmetry IV: Proceedings of the Conference on Strings, Duality, and Geometry, Centre De Recherches Mathematiques of the University De Montreal...
		The literature on mirror symmetry has been dubbed "physical mathematics" by some mathematicians because of the physical constructions employed that are not based on rigorous mathematics.
		The challenge of defining mirror symmetry rigorously is brought out in many articles in the book, with toric varieties showing the most promise: the enlarged Kahler moduli space of a given manifold is isomorphic to the complex structure moduli space of its mirror.
	www.geometry.net /scientists_bk/yau_shing-tung.html (873 words)

	Symmetry around a Point in the Plane
		Symmetry is the set of mathematical rules that describe the shape of an object.
		Also note, though, that we can now draw a mirror plane at right angles to the original plane, and d is a mirror image of a, and c is a mirror image of b.
		The six-fold rotation rotates the mirror plane to b, c, d, e, and f, but a-d, b-e and c-f are the same: flipping a mirror plane 180 degrees merely flips it over onto itself.
	www.uwgb.edu /dutchs/SYMMETRY/2DPTGRP.HTM (1498 words)

	Mirror Symmetry
		The image to the right is a depiction of the universe as a mirror image of God, drawn by Robert Fludd in the early 17th century.
		In 1956 physicists Chen Ning Yang and Tsung Dao Lee realised that although mirror symmetry had been shown to be true for the strong, electromagnetic and gravitational interactions, they believed that it had never been tested for the weak interaction.
		This violation of mirror symmetry occurs down to the molecular level.
	www.upscale.utoronto.ca /GeneralInterest/Harrison/Parity/Parity.html (2113 words)

	Jurate Macnoriute SYMMETRY IN THE QUARTERS OF PICTURE (Site not responding. Last check: 2007-11-01)
		Symmetry in the quarters of picture Many years ago I noticed a case of symmetry in the quarters of picture which relates principles of symmetry with the whole of picture.
		Thus symmetry of objects of different values is a case of manifestation of dissonance principle.
		Thus we may think that existence of symmetry in the quarters of picture is one way of manifestation of poetics and musicality.
	www.freehomepages.com /jumac/s9e.html (1185 words)

	M5337 Orbifolds Sphere Patterns
		Then every plane of mirror symmetry of the chair cuts the sphere in a line of mirror symmetry of the sphere, and every rotatinal symmetry of the chair is a rotational symmetry of the surface of the sphere.
		The mirror string in the symmetry group of our chair is a great circle on the surface of the celestial sphere.
		The symmetry group of a brick is discopic, like that of the table, except that the top of a brick is the same as the bottom.
	www.geom.uiuc.edu /education/math5337/Orbifolds/sphere_patterns.html (1043 words)

	Peter van der Helm: Natural selection of visual symmetries (Site not responding. Last check: 2007-11-01)
		Reflectional symmetry corresponds to mirror symmetry which, together with a kind of broken symmetry, forms the holographic regularity called bilateral symmetry; radial, rotational, and translational symmetries are variants of the holographic regularities called repetition and alternation.
		The symmetry structure of a body grows cell by cell, and the repetition structure of a queue of penguins grows penguin by penguin, so that the holographic growth steps can be said to specify the constituent parts of each regularity.
		First, in scene perception in general, mirror symmetry is preeminently a cue for the presence of a living object.
	www.nici.kun.nl /~peterh/doc/wynncom.html (1286 words)

	Mirror symmetry
		Mirror symmetry is therefore a special case of string equivalence in which the explicit isomorphism takes the form noted above.
		Recall that in [14] a construction of pairs of mirror manifolds was presented which relied crucially on the existence of special points in moduli space at which the associated Calabi--Yau has enhanced discrete symmetries.
		For this reason, such deformation arguments have only been used to establish mirror symmetry for a continuously connected (in the sense of conformal field theory) family of Calabi--Yau spaces containing at least one point at which the explicit construction of [14] could be applied.
	www.cgtp.duke.edu /~drm/condensation/node6.html (691 words)

	Mirror Symmetry
		The aim of the book is to provide a pedagogical introduction to the field of mirror symmetry from both a mathematical and physical perspective.
		After covering the relevant background material, the main part of the monograph is devoted to the proof of mirror symmetry from various viewpoints.
		It is the first book on the subject which tries to put together the mathematical and the physical aspects of mirror symmetry in a systematic way, and it has inherited the pedagogical style of the school where it originated.
	www.claymath.org /publications/Mirror_Symmetry (282 words)

	Math 5337 Wallpaper Patterns Kali Exercises
		mirror strings, the kaleidoscopic points, and the gyration points of the pattern you are given by the other group.
		If there are lines of mirror symmetry in your pattern, you only need to look on one side of them for gyration points.
		If there are no lines of mirror symmetry in your pattern, there's another way to restrict your search for gyration points to a finite region.
	www.geom.uiuc.edu /~math5337/Wallpaper/kali_exercise.html (739 words)

	Fields Institute - Calabi-Yau Varieties and Mirror Symmetry
		Mirror symmetry is a conjecture in string theory that certain "mirror pairs" of Calabi-Yau manifolds give rise to isomorphic physical theories.
		Geometry around mirror symmetry and string theory has been pursued by many mathematicians (complex geometers, toric geometers, and others), and great progress has been witnessed in understanding geometric aspects of the problem.
		Further investigation on p-adic analysis in physics (pertinent to mirror symmetry to begin with) ought to be carried out.
	www.fields.utoronto.ca /programs/scientific/01-02/cyms (1320 words)

	Mirror symmetry (Site not responding. Last check: 2007-11-01)
		The discovery of mirror symmetry is connected with names such as Brian Greene, Ronen Plesser, Philip Candelas, and others.
		Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry is a special example of T-duality : the Calabi-Yau manifold may be written as a fiber bundle whose fiber is a three-dimensional torus.
		A smooth surface, usually made of glass with reflective material painted on the underside, that reflects light so as to give an image of what is in front of it.
	www.serebella.com /encyclopedia/article-Mirror_symmetry.html (1216 words)

	2. Symmetry and mirror (Site not responding. Last check: 2007-11-01)
		The symmetry of our body is called bilateral.Bilateral symmetry occurs when the two halves of the whole are each other's mirror images.
		For example,if the two mirrors are at 90 degree upside they give a non reversed image of yourself.
		Now put another mirror in front of this device and the whole plane will be filled with a symmetrical tiling.
	zito.web.cern.ch /zito/aleph/symmetry/node02.html (162 words)

	Perception abstract: Mirror symmetry opposes splitting of chromatically homogeneous surfaces
		Three experiments were designed to test: (a) the main hypothesis, that mirror symmetry enhances perception of a single figure; (b) the role of orientation; (c) the effect of the number of axes of symmetry.
		The results show that (i) there is a good general correlation between mirror symmetry and perception of a single figure; (ii) vertical and horizontal axes of symmetry are the most effective; and (iii) the more axes of symmetry a surface has, the more likely is the perception of a single figure.
		These results suggest that mirror symmetry is an important factor in the perception of chromatically homogeneous displays.
	www.perceptionweb.com /perabs/p31/p3218.html (293 words)

	symmetry student page (Site not responding. Last check: 2007-11-01)
		An image has Reflectional Symmetry if there is at least one line which splits the image in half so that one side is the mirror image of the other.
		Reflectional symmetry is also called line symmetry or mirror symmetry because there is a line in the figure where a mirror could be placed, and the figure would look the same.
		Translational symmetry results from moving a figure a certain distance in a certain direction also called translating (moving) by a vector (length and direction).
	www.geom.uiuc.edu /~demo5337/s97a/students.html (228 words)

	All Elementary Mathematics - Study Guide - Geometry - Symmetry. Symmetry of plane figures...
		A symmetry center is a center of a ball; a symmetry plane is a plane of any large circle; a symmetry axis is a diameter of a ball.
		A round cone has an axial symmetry; a symmetry axis is an axis of a cone.
		Its symmetry axis is any of its diagonals; a symmetry center is a point of their intersection.
	www.bymath.com /studyguide/geo/sec/geo22.htm (450 words)

	Research of David R. Morrison
		Mirror symmetry and rational curves on quintic threefolds: A guide for mathematicians, J. Amer.
		Mirror symmetry and moduli spaces of superconformal field theories, Proc.
		Mirror symmetry and the type II string, Trieste Conference on S-Duality and Mirror Symmetry, Nuclear Phys.
	www.cgtp.duke.edu /~drm/research.html (669 words)

	Homological Mirror Symmetry Literature \| The String Coffee Table
		In terms of the topological A- and B-model truncations of the full 2D SCFT, mirror symmetry relates the A-model on one CY to the B-model on another.
		A nice overview of the field of mirror symmetry in the math community is given on the website of a mirror symmetry workshop that took place at the Fields institute in 2001
		You can see from the text on that website that mirror symmetry is related to a lot of hot topics, not the least to Wiles’ proof of the Taniyama-Shimura-Weil conjecture.
	golem.ph.utexas.edu /string/archives/000839.html (873 words)

	Introduction to Symmetry (Science U)
		There are actually four distinct kinds of symmetry, corresponding to four basic ways of moving a tile around in the plane, illustrated to the right.
		This is simply because if we do one symmetry followed by another, then we could have just move the tiling directly from its initial postion to its final position, and it would still match up.
		The symmetry group of a tiling is just the collection of all its symmetries.
	www.scienceu.com /geometry/articles/tiling/symmetry.html (812 words)

	Bilateral or Mirror symmetry
		Bilateral symmetry is the most common type of symmetry.
		Roughly speaking, an object has bilateral symmetry if it can be divided into two halves, each the mirror image of the other.
		Indeed, the figure has no symmetry at all even though it appears to satisfy the dictionary definition of symmetry.
	nothung.math.uh.edu /~mike/hti/handouts/notes/node5.html (248 words)

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