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Topic: Rotational symmetry

Related Topics

spontaneous symmetry breaking

symmetry of second derivatives

bilateral symmetry

CP symmetry

radial symmetry

P symmetry

T symmetry

CPT symmetry

mirror symmetry

rotational symmetry

gauge symmetries

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	Totally Tessellated: Symmetry and Transformations, page 2/4
		The distance to the center of rotation is kept constant.
		If we can perform a rotation to a tessellation that such that the result is the same as the original tessellation, then the tessellation has rotational symmetry.
		After rotation around the red point through a certain number of degrees (60 to be exact), you find that the copy exactly matches the original.
	library.thinkquest.org /16661/background/symmetry.2.html (210 words)

	math lessons - Symmetry
		Pentamerism is a body symmetry exhibited primarily by starfish; it is rotational symmetry with respect to an angle of 72°.
		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.
	www.mathdaily.com /lessons/Symmetric (1756 words)

	Introduction & Symmetry Operations
		The axis along which the rotation is performed is an element of symmetry referred to as a rotation axis.
		The plane of the mirror is an element of symmetry referred to as a mirror plane, and is symbolized with the letter m.
		Note that crystals that have a center of symmetry will exhibit the property that if you place it on a table there will be a face on the top of the crystal that will be parallel to the surface of the table and identical to the face resting on the table.
	www.tulane.edu /~sanelson/eens211/introsymmetry.htm (2609 words)

	Rotational symmetry - Wikipedia, the free encyclopedia
		Rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space.
		rotational symmetry with respect to an angle of 100°, then also with respect to one of 20°, the greatest common divisor of 100° and 360°.
		Rotational symmetry with respect to any angle is, in two dimensions, circular symmetry.
	en.wikipedia.org /wiki/Rotational_symmetry (1345 words)

	NBS Monograph 115: 2. Symmetry prop. rotational energy levels
		The rotational levels of all diatomic molecules can be classified as + or - according to their parity, i.e., according to the behavior of the complete molecular wave function (apart from translation) when the laboratory-fixed Cartesian coordinates of all particles are replaced by their negatives.
		When one of these symmetry operations acts on a function containing the electron coordinates, its effect is to replace, everywhere in the function, each coordinate by the quantity found in table 3 at the intersection of the appropriate row and column.
		It turns out that a consistent and useful scheme of geometric symmetry operations can be obtained if a sense-reversing operation is defined to have the same effect on the Eulerian angles as does the pure rotation obtained from the sense-reversing operation by multiplication by the inversion [15, 16].
	physics.nist.gov /Pubs/Mono115/chap2.00.html (1030 words)

	Symmetry around a Point in the Plane
		Rotation symmetry without reflection is often used in graphic design to portray the idea of speed, power, or dynamic action.
		In the case of the three-fold axis, the rotation rotates the mirror plane from a to b and then to c.
		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)

	Circle Symmetry
		As you’ll discover, rotational symmetry is more circular, and with a bit of practise it can start to feel natural.
		Examples of rotational symmetry are everywhere (flowers, logos, games), and the study of symmetry serves as a wonderful bridge between the sciences and the arts: the same ideas that appear in geometry, graphing and chemistry also appear in architecture, art and dance.
		One way of thinking of rotational symmetry is that each person is doing the exact same shape and facing toward the center of the circle.
	www.mathdance.org /circlesymmetry/circlesymmetry.html (1135 words)

	symmetry concept from the Astronomy knowledge base (Site not responding. Last check: 2007-10-16)
		CPT invariance (3 facts) - A symmetry which is believed to hold true for all particles throughout the course of universal history.
		A symmetry, in general, is a property that allows a system to behave in the same way even though it has undergone some change.
		A gauge symmetry is something like a rotation, in which the amount of rotation can vary randomly from one point of space to the next.
	www.site.uottawa.ca:4321 /astronomy/symmetry.html (654 words)

	Intro to Minerals: Crystal Class and System
		Rotational symmetry arises when a structural element is rotated a fixed number of degrees about a central point before it is repeated.
		For example, crystals of the holomorphic class of the isometric system possess inversion symmetry, three 4-fold axes of rotational symmetry, the characteristic set of four 3-fold axes of rotational symmetry which is indicative of the isometric crystal system, six 2-fold axes of rotational symmetry, and nine different mirror planes.
		It is thus apparent that the characteristic symmetry element of the isometric crystal system is the possession of four 3-fold axes of rotational symmetry, while the characteristic symmetry element of the rhombohedral division of the hexagonal crystal system is the possession of a single 3-fold axis of rotational symmetry.
	dave.ucsc.edu /myrtreia/crystal.html (4278 words)

	Rotational Symmetry Answer (Site not responding. Last check: 2007-10-16)
		Answer: When a shape is rotated about its centre, if it comes to rest in a position and looks exactly like the original, then it has rotational symmetry.
		Following from this, then a square, which is a regular polygon, has 4 sides, 4 lines of symmetry and an order of rotational symmetry of 4.
		When there is point symmetry and also rotational symmetry, the order of the latter is even.
	www.zephyrus.co.uk /rotationalsymmetryanswer.html (334 words)

	Activity 5
		A figure has rotational symmetry if there is a point called the center of rotation around which the figure can be rotated so that it aligns with itself in less than one complete rotation of 360°.
		The order of rotational symmetry is the number of small rotations that must be made to return to the original orientation.
		Rotational symmetry can be investigated by tracing the figure on paper, and rotating the tracing paper until the figures are aligned.
	homepage.mac.com /efithian/Geometry/Activity-05.html (589 words)

	Exploiting symmetry in Meep - AbInitio
		In particular, the symmetry of the currents/fields will typically require you to specify phase factors associated with the symmetry operations—for example, a mirror plane can either be used for even sources/fields (phase +1) or for odd sources/fields (phase −1).
		Technically, the symmetry operations that preserve the structure form the symmetry group (in particular, this is a point group or, if you include translations, the space group of the structure).
		One subtlety that arises in specifying the symmetry of the system is that you have to transform the fields appropriately according to their vector nature.
	ab-initio.mit.edu /wiki/index.php/Exploiting_symmetry_in_Meep (1055 words)

	Advances in the Philosophy of Technology
		There are objects that possess both types of symmetry as the Hargittais note in one of their beautiful books on symmetry (Hargittais, 1994): "Rotational symmetry, as we have seen, may appear alone, without reflection.
		Michael Leyton claims that the movement between symmetry and asymmetry is always bidirectional from the former to the latter and that cognition consists of the determination of past changes in shape (Leyton, 1992):
		The symmetry of stability of the spin of the nuclei of atoms was perturbed by a large magnetic field tuned to a radiofrequency range moving the nuclei into instability (asymmetric to their normal movement).
	scholar.lib.vt.edu /ejournals/SPT/v4n2/MACCORMA.html (4443 words)

	Rotational symmetry of the C ring and a mechanism for the flagellar rotary motor -- Thomas et al. 96 (18): 10134 -- ...
		Rotational symmetry of the C ring and a mechanism for the flagellar rotary motor -- Thomas et al.
		Rotational symmetry of the C ring and a mechanism for the flagellar rotary motor
		of subunits of FliM, and hence the rotational symmetry of the
	www.pnas.org /cgi/content/full/96/18/10134 (5678 words)

	Symmetry Lesson Plan for Fifth Grade
		Tell students that a circle has an infinite number of lines of reflectional symmetry, but it is still possible to have a line in a circle that does not show reflectional symmetry.
		Write on the board and tell students: "Rotational symmetry is when an object spins around an axis and the object appears to look the same two or more times.
		Rotate your snowflake so that it is not at a point of rotational symmetry.
	www.bsu.edu /web/jmkocher/symmetrylesson.htm (2200 words)

	Geometry Session 7, Part B: Rotation Symmetry
		If you can rotate (or turn) a figure around a center point by fewer than 360° and the figure appears unchanged, then the figure has rotation symmetry.
		The point around which you rotate is called the center of rotation, and the smallest angle you need to turn is called the angle of rotation.
		As you will see in the next section, in order to have rotation symmetry, the center of rotation does not have to be the center of the figure.
	www.learner.org /channel/courses/learningmath/geometry/session7/part_b/index.html (296 words)

	[No title]
		The point group or symmetry group is the name given to the collection of symmetry elements possessed by a molecule.
		The symmetry that is the least talked about is point symmetry even though it can be spotted everywhere in the world around you....
		An image has Rotational Symmetry if there is a center point where an object is turned a certain number of degrees and still look the same.
	www.lycos.com /info/symmetry--rotational-symmetry.html (301 words)

	Circle Symmetry
		As you’ll discover, rotational symmetry is more circular, and with a bit of practise it can start to feel natural.
		Examples of rotational symmetry are everywhere (flowers, logos, games), and the study of symmetry serves as a wonderful bridge between the sciences and the arts: the same ideas that appear in geometry, graphing and chemistry also appear in architecture, art and dance.
		One way of thinking of rotational symmetry is that each person is doing the exact same shape and facing toward the center of the circle.
	www.scottkim.com /dance/circlesymmetry/circlesymmetry.html (1135 words)

	Design Tips for Rapid Injection Molding
		We’re all familiar with bilateral symmetry, in which the left and right halves of an object are mirror images of one another.
		Rotational symmetry, on the other hand, may not be as obvious to the eye, but it involves halves (or thirds, quarters, etc., depending on the degree of symmetry) that are identical.
		Rotate a king, queen, or jack 180° and the image is the same as the one you started with.
	www.protomold.com /designtips/2005/2005-06_designtips (700 words)

	An Intuitive Notion of Rotations
		The leaf on this plant illustrates the concept of a rotation.
		The center of rotation is the point where the leaf is attached to the stem.
		The concept of rotations can be seen in wallpaper designs and art work.
	regentsprep.org /Regents/math/rotate/Lrotate.htm (112 words)

	Logo License
		The underlying theme is of reflective and rotational symmetry, though there is some reference to translation symmetry.
		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 (1759 words)

	Illuminations: Symmetries I
		Now that you have found out how to describe rotations of a figure, you can predict the effect of a rotation through a given angle and even the effect of two or more rotations performed one after the other.
		In this part, you will investigate the relationship between rotations and the symmetry you recognize in a figure or a design.
		The figure rotates, but the figure does not appear to have moved.
	illuminations.nctm.org /index_o.aspx?id=138 (373 words)

	Math Forum - Ask Dr. Math Archives: High School Symmetry/Tessellations
		The four rotational symmetries of the square satisfy the four requirements for a group, and so they are called a subgroup of the full symmetry group.
		Use three isometries (translation, rotation, and reflection) in composition with each other and deduce the net result of the two transformations.
		Prove that the group of symmetries of a cube is isomorphic to S_4.
	mathforum.org /library/drmath/sets/high_symmetry.html (793 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)

	TeachNet -- Symmetry All Around You - Rotational Symmetry
		Another way of thinking of rotational symmetry is seeing an image arranged in rays diverging from a single point.
		The point in the middle of the pinwheel is the center of rotation.
		These symmetry pages have been brought to you by Nancy Powell, a TeachNet Web Mentor from Bloomington High School, Bloomington, IL.
	teachersnetwork.org /dcs/math/symmetry/rotational (243 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.
		Assessments: The Symmetry of Various Geometric Shapes will be collected and reviewed by the teacher to ensure that each student can accurately draw multiple lines of symmetry and rotational symmetry among various geometric shapes.
	www.europa.com /~paulg/edug55x/GeomUnit.doc (1906 words)

	Introduction To Symmetry
		A glide-reflection symmetry is a combination of reflection symmetry and translation symmetry.
		Glide-reflection symmetry are commonly found on the decorative patterns on vases or the edges of carpets.
		For example, there are translational symmetries, because if you move the pattern up 2 squares or to the right 2 squares, the whole thing becomes itself again.
	xahlee.org /Wallpaper_dir/symmetry.html (739 words)

	Symmetry
		Symmetry n 1: (mathematics) an attribute of a shape; exact correspondence of form on opposite sides of a dividing line or plane [syn: symmetricalness, correspondence, balance] [ant: asymmetry] 2: balance among the parts of something [syn: proportion] [ant: disproportion]
		I will circulate in the classroom as the students are exploring the symmetry of shapes, and check to see who is and is not getting it.
		They will use a string to demonstrate the bi-lateral symmetry of their own face as they look in the hand held mirror, and observe the similarities and differences in exact symmetry and the approximate symmetry of a human face.
	eprentice.sdsu.edu /S03X1/asanders/Aimee/symmetry.htm (1142 words)

	Symmetry and Point Groups
		Symmetry elements are geometric entities that are used to minipulate molecules so as to transform them from one spatial orientation into another, indistinguishable, orientation.
		Mirror planes are further classified as vertical (subscript 'v') or horizontal (subscript 'h') according to whether they contain the principal rotational axis of the molecule or are perpendicular to it.
		It also is the symmetry (approximately) possesed by most of us critters who go about on the surface of the earth.
	chemistry.umeche.maine.edu /Modeling/symmetry.html (1161 words)

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