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Topic: Reflection symmetry

	Symmetry - Wikipedia, the free encyclopedia
		A glide reflection symmetry (in 3D: a glide plane symmetry) means that a reflection in a line or plane combined with a translation along the line / in the plane, results in the same object.
		Symmetry is used in the design of the overall floor plan of buildings as well as the design of individual building elements such as doors, windows, floors, frieze work, and ornamentation; many facades adhere to bilateral symmetry.
		Symmetry is also an important consideration in the formation of scales and chords, traditional or tonal music being made up of non-symmetrical groups of pitches, such as the diatonic scale or the major chord.
	en.wikipedia.org /wiki/Symmetry (2842 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 geometric kites and the isosceles trapezoids.
	en.wikipedia.org /wiki/Reflection_symmetry (372 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.
		Curie was led to reflect on the question of the relationship between physical properties and symmetry properties of a physical system by his studies on the thermal, electric and magnetic properties of crystals, these properties being directly related to the structure, and hence the symmetry, of the crystals studied.
		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).
	plato.stanford.edu /entries/symmetry-breaking (9818 words)

	Math Forum: Types of Symmetry in the Plane
		A reflection of an "R" is a backwards "R".
		A glide reflection combines a reflection with a translation along the direction of the mirror line.
		The reflection of a figure in the plane about a line moves its reflected image to where it would appear if you viewed it using a mirror placed on the line.
	mathforum.org /sum95/suzanne/symsusan.html (946 words)

	Symmetry as a Compositional Determinant: Chapter 2: Definitions
		Symmetry is here to be defined as a congruence which results from the operations of reflection, rotation, or translation.
		If the entire figure is reflected about this axis, the result is congruent with the original, and therefore satisfies the condition for reflective symmetry.
		Another possible symmetry operation is a rotation around a point, or a line in three variables, exhibited by the letter Z. This letter may be rotated 180 degrees around a point to create an image identical to the original.
	solomonsmusic.net /diss2.htm (2268 words)

	Your Heading Goes Here
		Symmetry is the ability to move an object so that its image is an exact copy of the original object.
		This type of symmetry is seen by viewing an object as if a mirror is placed on a line and the reflection from the mirror is the other side.
		With rotational symmetry, an object moves around a point a certain number of degrees, without changing the original appearance of the object.
	homepages.ius.edu /TEHURST (414 words)

	Symmetry in Science and Religion, by Thomas J McFarlane
		Symmetry is the archetypal key that unlocks the true nature of the world.
		[18] This symmetry of subject and object is revealed in the ultimate mystical insight: the recognition of the imaginary nature of the subject-object distinction, and hence the underlying identity of subject and object.
		And through the recognition of symmetry in our lives, the true nature of creation comes into focus until it is all seen to be the symmetrical play of imagined distinctions in utter unity.
	www.integralscience.org /sacredscience/SS_symmetry.html (2387 words)

	Reflection - Search Results - ninemsn Encarta (Site not responding. Last check: 2007-11-03)
		Reflection, phenomenon of light and other wave motions in which the light or other wave motion is returned after impinging on a surface, or the...
		An object is said to have reflection symmetry if it can be divided, in imagination, into two halves that are mirror images of one another.
		If a light ray that is travelling through a homogeneous medium is incident on the surface of a second homogeneous medium, part of the light is...
	au.encarta.msn.com /Reflection.html (117 words)

	HYLE 3 (1997): Symmetry and Complexity-Fundamental Concepts of Research in Chemistry
		Pasteur recognized that the relationship between symmetry of reflection and optical activity is not a function of the crystal structure of a substance.
		The next symmetry element is inversion in which a molecule remains unchanged during a reflection of all atomic coordinates (x, y, z) at the point of inversion to (-x, -y, -z).
		In general, mathematical symmetries are defined by so-called automorphisms that means self-mappings of figures or structures whereby the structure remains invariant (example: rotation or reflection of polygons in the plane).
	www.hyle.org /journal/issues/3/mainzer.htm (7464 words)

	Symmetry (Site not responding. Last check: 2007-11-03)
		Actually, this is only one kind of symmetry: we call this "reflection symmetry".
		Besides reflection symmetry, there is another kind of symmetry called rotation symmetry.
		The design below does not have reflection symmetry, because there is no way that you can fold it over and have one half match the other.
	www.punahou.edu /acad/sanders/geometrypages/GP04Symmetry.html (485 words)

	Symmetry around a Point in the Plane
		Symmetry is the set of mathematical rules that describe the shape of an object.
		Rotation symmetry without reflection is often used in graphic design to portray the idea of speed, power, or dynamic action.
		Some objects have no symmetry at all: a computer keyboard, a left glove, the letters G Q d p J L. In a 360 degree rotation, the object matches its original appearance only once, after a full 360 degrees.
	www.uwgb.edu /dutchs/symmetry/2dptgrp.htm (1498 words)

	Symmetry, Design and Patterns (Site not responding. Last check: 2007-11-03)
		Reflective symmetry occurs when a pattern can be folded across a mirror so one half lies on top of the other.
		SYMMETRY: Thus to summarize, when you take a copy of an image or a shape in a repeated pattern and move it in some way so that it lies exactly on top of the original, that figure is said to have symmetry.
		Symmetry means "the same" or "identical." The terms we defined above are examples of different types of symmetry on a flat surface (planar symmetry).
	www.uh.edu /hti/cu/1999/v05/07.htm (2463 words)

	The Aesthetics of Symmetry
		Symmetry has several variants, but the basic symmetrical operations are Translation, Rotation, and Reflection.
		Let's put together an equation where a higher rating indicates complete randomness (or a symmetry that is too challenging to discern), and a lower rating shows boredom.
		I therefore propose an equation for determining the Interest level of a particular symmetrical design: I = M/sn, where "I" is the Interest level, "s" is a number for the symmetry operation, "M" is a number for the complexity of the underlying motif, and "n" is the number of times that the motif is repeated.
	home.earthlink.net /~jdc24/symmetry.htm (1210 words)

	Illuminations: Symmetries IV
		Symmetries IV Of all the different symmetries, this is the hardest for students to understand and to identify.
		A glide reflection is a symmetry transformation that consists of a translation followed by a reflection across the translation line.
		Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.
	illuminations.nctm.org /index_d.aspx?id=475 (799 words)

	TeacherSource . Math . Graphic Design \| PBS
		Reflection symmetry is sometimes called "mirror" or "flip" symmetry.
		A butterfly (see below) may have reflection symmetry because one side is a mirror image of the other.
		Organize the letters according to which ones have reflection symmetry into three groups: the letters that have reflection symmetry with a vertical line of symmetry (like the letter A), those with a horizontal line of symmetry, and those with both vertical and horizontal lines of symmetry.
	www.pbs.org /teachersource/mathline/concepts/designandmath/activity2.shtm (511 words)

	SYMMETRY IN WHEELS (Site not responding. Last check: 2007-11-03)
		Reflection Symmetry: is transformation in which each point of a figure has an image that is the same distance from the line of reflection as the original point.
		A figure has reflective symmetry if, when the figure is folded along the line of symmetry the two halves of the figure match (they are mirror images of each other).
		Reflections, rotations, and translations are used to move a geometric figure without changing its size or shape.
	www.uh.edu /hti/cu/1999/v05/05.htm (2602 words)

	Symmetry and Point Groups (Site not responding. Last check: 2007-11-03)
		Symmetry is especially important in carrying out molecular orbital calculations.
		Symmetry elements are geometric entities that are used to minipulate molecules so as to transform them from one spatial orientation into another, indistinguishable, orientation.
		The point group or symmetry group is the name given to the collection of symmetry elements possessed by a molecule.
	chemistry.umeche.maine.edu /Modeling/symmetry.html (1161 words)

	Logo License
		This unit examines the use of reflective, rotational, and translational symmetry in the design of logos.
		The concept of symmetry is fundamental to mathematics and is used extensively in various guises.
		By symmetry, there are essentially only three squares: a corner square, a square in the middle of a side and the centre square.
	www.nzmaths.co.nz /Geometry/Symmetry/LogoLicense.aspx (1758 words)

	Symmetry Tutorial - Reflection (Site not responding. Last check: 2007-11-03)
		If a geometric plane is drawn through a molecule, we can reflect through that plane to generate a new configuration.
		The reflection operation can be pictured as follows: take each atom in the molecule and move it toward the plane along a line perpendicular to that plane.
		Continue moving the atom through the plane to a point equidistant from the plane on the opposite side of the plane.
	www.otterbein.edu /home/fac/DNHJHNS/symmetry/reflection.html (87 words)

	[No title]
		I will explain what a line of symmetry is and have students come up one at a time to the overhead and draw a line of symmetry through one of the examples until all are completed.
		Place an emphasis on the line of symmetry and that the object that on one side must be reflected across the line of symmetry to the other side.
		After students have completed their Reflection Symmetry Worksheets they can As Needed design their own reflecting picture, shape, or scene that is symmetrical across a line of symmetry.
	www.europa.com /~paulg/edug55x/GeomUnit.doc (1906 words)

	Symmetry in Tessellations (Site not responding. Last check: 2007-11-03)
		In the example below, point A is a point of 3-fold rotational symmetry, while point B is a point of 2-fold rotational symmetry.
		A tessellation possesses glide reflection symmetry if it can be translated by some vector and then reflected about that vector and remain unchanged.
		A special case of glide rereflection symmetry is simple reflection or mirror symmetry, where the vector has a value of zero.
	members.cox.net /tessellations/Symmetry.html (278 words)

	Geometry Session 7: Symmetry
		If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry.
		The line that you reflect over is called the line of symmetry.
		In Problems A1 and A2, sketch the figures or print the PDF files of the figures and show the lines of symmetry as dashed lines.
	www.learner.org /channel/courses/learningmath/geometry/session7/part_a (262 words)

	The Geometry Junkyard: Symmetry and Group Theory
		Associating the symmetry of the Platonic solids with polymorf manipulatives.
		Ron Lifshitz provides a light introduction to the symmetry of periodic and aperiodic crystals, and the complications introduced by including permutations of colors in a coloring as part of a symmetry operation.
		Spherical Julia set with dodecahedral symmetry discovered by McMullen and Doyle in their work on quintic equations and rendered by Don Mitchell.
	www.ics.uci.edu /~eppstein/junkyard/sym.html (1155 words)

	"inQuiry Almanack" - Minutes from ME - March, 1997
		Draw a good-sized version of the letter A on a piece of paper, place the edge of the mirror across the vertical center of the letter and you see that the reflected image in the mirror balances and exactly completes the letter.
		The letters O and X are completed by the reflection from a mirror held either vertically or horizontally.
		When you are tired of interpreting codes and spelling and reflecting it's nice to lighten up and relax by creating your own symmetrical project.
	www.fi.edu /qa97/me3 (267 words)

	Glide reflection symmetries of the square tiling
		Inspection of Figure 17, shows that no line of symmetry of the square tiling can be a glide line.
		Since translation through half a diameter of a square tile is not a symmetry of the square tiling, it follows easily that this symmetry of the square tiling is a glide reflection symmetry.
		Also verify that points of intersection between lines and glide lines of symmetry are centers of rotational symmetries of the tiling.
	nothung.math.uh.edu /~mike/hti/handouts/notes/node25.html (177 words)

	Key Relationships and Extra problems for Math 402
		A reflection over a single line an odd number of times is the same as reflecting over the line once.
		A reflection over a single line an even number of times is the same as doing nothing (the identity transformation).
		A reflection followed by a reflection is a translation if and only if the two lines do not intersect.
	www.wiu.edu /users/mfjro1/wiu/stu/m402/m402-Fall99/f99page1.htm (532 words)

	Symmetry - Reflection and Rotation
		The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry).
		The Line of Symmetry does not have to be up-down or left-right, it can be in any direction.
		With Rotational Symmetry, the image is rotated (around a central point) so that it appears 2 or more times.
	www.mathsisfun.com /geometry/symmetry.html (184 words)

	Reflection Symmetry
		Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to recognise, because one half is the reflection of the other half.
		it is not perfect symmetry, because the image is changed a little by the lake surface.
		The Line of Symmetry (also called the Mirror Line) does not have to be up-down or left-right, it can be in any direction.
	www.mathsisfun.com /geometry/symmetry-reflection.html (143 words)

	Geometry Session 7: Symmetry
		Symmetry is one of the most important ideas in mathematics.
		There can be symmetry in an algebraic calculation, in a proof, or in a geometric design.
		It's such a powerful idea that when it's used in solving a problem, we say that we exploit the symmetry of the situation.
	www.learner.org /channel/courses/learningmath/geometry/session7 (115 words)

	An Intuitive Notion of Line Symmetry
		A simple test to determine if a figure has line symmetry is to fold the figure along the supposed line of symmetry and see if the two halves of the figure coincide.
		The figures in the photo are only a sampling of the geometric figures which possess symmetry.
		A figure has line symmetry if there is a line on which the figure may be folded so that the two parts of the figure will coincide.
	regentsprep.org /Regents/math/symmetry/Lsymmet.htm (289 words)

	Biology 104 Spring 2002 - Symmetry (Site not responding. Last check: 2007-11-03)
		Another example, which especially interested Pierre Curie, was that crystals whose distribution of charges lacks a certain kind of symmetry (inversion through a point) are apt to generate electric fields when compressed, and conversely to shrink when subjected to electric fields.
		An interesting exception is the development of echinoderm adults (5 planes of reflection symmetry) from pluteus (or equivalent) larvae that have only one plane of reflection symmetry.
		The other abnormality: Half such people have "situs inversus viscerum", which is a right-left reflection of the anatomy of the heart, stomach, spleen and all other internal organs that don't have reflection symmetry.
	www.bio.unc.edu /courses/2003spring/biol104/symmetry.htm (1668 words)

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