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Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry"). More examples may be seen below. The degree of rotational symmetry is how many degrees the shape has to be turned to look the same on a different side or vertex. It can not be the same side or vertex.
Formally, rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore a symmetry group of rotational symmetry is a subgroup of E+(m) (see Euclidean group).
Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homogeneous, and the symmetry group is the whole E(m). With the modified notion of symmetry for vector fields the symmetry group can also be E+(m).
This page contains text from Wikipedia, the Free Encyclopedia -
http://en.wikipedia.org/wiki/Rotational_symmetry
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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- Alternating group
- Ambigram
- Angular momentum
- Axial symmetry
- Bipyramid
- Borromean rings
- Cartesian product
- Circular symmetry
- Crystal system
- Cube
- Cyclic group
- Dihedral group
- Dodecahedron
- Double Pendulum
- Drinking horn
- Duocylinder
- Duoprism
- Euclidean group
- Euclidean space
- Frieze group
- Fundamental domain
- Half-plane
- Hermann Weyl
- Hexagonal
- Hindu
- Icosahedron
- Isle of Man
- Isometry
- Isomorphic
- Isotropy
- Lattice (group)
- Line (mathematics)
- Lorentz symmetry
- Math Is Fun
- Muqarnas
- Noether's theorem
- Octahedron
- Orthogonal group
- Orthogonal matrices
- Parallelogram
- Platonic solid
- Polygon
- Primitive cell
- Prism (geometry)
- Propeller
- Pyramid
- Quadrilateral
- Raelism
- Rectangle
- Recycling symbol
- Reflection symmetry
- Rhombus
- Rotation
- Rotation group SO(3)
- Rotational symmetry
- Roundabout
- Screw axis
- Shogi
- Snoldelev Stone
- Space group
- Square (geometry)
- Swastika
- Symmetric group
- Symmetry
- Symmetry group
- Tetrahedron
- Three hares
- Traffic sign
- Triskelion
- Wallpaper group
- Yin and yang
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http://www.youtube.com/subscription_center?add_user=ehoweducation
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http://www.youtube.com/ehoweducation
The number of degrees of rotational symmetry in a regular hexagon is directly related to a few key things. Find out about the number of degrees in rotational symmetry in a regular hexagon with help from an expert who graduated from the Pforzheimer Honors College at Pace University with a Bachelor's Degree in Mathematics and Adolescent Education in this free video clip.
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Filmmaker: Victor Varnado
Series Description: Certain advanced concepts in mathematics are much easier to understand when they are broken down into their basic parts. Get tips on math solutions with help from an expert who graduated from the Pforzheimer Honors College at Pace University with a Bachelor's Degree in Mathematics and Adolescent Education in this free video series.
http://wn.com/The_Number_of_Degrees_of_Rotational_Symmetry_in_a_Regular_Hexa..._Solutions_to_Your_Math_Problems
Subscribe Now:
http://www.youtube.com/subscription_center?add_user=ehoweducation
Watch More:
http://www.youtube.com/ehoweducation
The number of degrees of rotational symmetry in a regular hexagon is directly related to a few key things. Find out about the number of degrees in rotational symmetry in a regular hexagon with help from an expert who graduated from the Pforzheimer Honors College at Pace University with a Bachelor's Degree in Mathematics and Adolescent Education in this free video clip.
Expert: Marija Kero
Filmmaker: Victor Varnado
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photo: AP / Jae C. Hong
02 Aug 2015
Ronda Rousey flipped her script but kept the timing the same Saturday night. Using her newly developed punching power instead of her famed armbar, Rousey knocked out challenger Bethe Correia 34 seconds into their Ultimate Fighting Championship bantamweight title bout in Brazil. Rousey (12-0) has now won 11 of her 12 fights in the first round, and she has ended her last four in 34 seconds, 14 seconds, 16 seconds and 66 seconds ... RELATED ... ....
photo: Creative Commons / Yathin S Krishnappa
01 Aug 2015
Uncertainty surrounded the fate of another lion from Zimbabwe’s Hwange National Park Saturday after a conservation group reported that Jericho, brother of the lion slain by American dentist Walter Palmer, had also been killed ... “We are absolutely heart broken. We will update you all as soon as we have more details,” the statement added ... Hwange park authorities were unavailable for confirmation ... AFP. ....
photo: AP / Thibault Camus
02 Aug 2015
PARIS. Ending the crisis that has seen thousands of attempts by migrants to reach England from Calais in recent weeks is a "top priority", the interior ministers of France and Britain wrote in a joint statement Sunday ... "Tackling this situation is the top priority for the UK and French governments ... At least 10 migrants have died attempting the dangerous journey since June ... "Our border is secure, and there is no easy way into the UK." ... ....
photo: (AP Photo/Frank Augstein)
02 Aug 2015
• Whistleblower leaks data from 12,000 samples. • Fifty-five Olympic and world golds since 2001 under suspicion ... The blood-doping data, detailing 12,000 tests from 5,000 athletes, was leaked to the Sunday Times and German broadcaster ARD/WRD by a whistleblower at the International Association of Athletics Federations ... ....
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Stockhouse
28 Jul 2015
DesignWare USB-C IP Supports Reversible USB Type-C Connectors and USB 3.1, 3.0 and 2.0 Specifications. MOUNTAIN VIEW, Calif., July 28, 2015 /PRNewswire/ --. Highlights ... Synopsys, Inc ... The new Type-C specification simplifies mechanical USB connectors with reversible cables, rotational symmetry, up to 10 Gbps data rate, bi-directional power delivery, audio multiplexing and alternate modes such as DisplayPort and MHL ... Availability ... MCA, Inc ... ....
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Public Technologies
28 Jul 2015
(Source. Synopsys Inc) DesignWare USB-C IP Supports Reversible USB Type-C Connectors and USB 3.1, 3.0 and 2.0 Specifications. Highlights ... Synopsys, Inc ... The new Type-C specification simplifies mechanical USB connectors with reversible cables, rotational symmetry, up to 10 Gbps data rate, bi-directional power delivery, audio multiplexing and alternate modes such as DisplayPort and MHL ... To view the multimedia news release, please go to....
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The Guardian
06 Jul 2015
Rory Kinnear as Josef K, centre, in The Trial by Franz Kafka at the Young Vic, London, June 2015. Photograph. Tristram Kenton for the Guardian. Letters. Monday 6 July 2015 19.59 BST. When the legal system mirrors the nightmare of Kafka’s Josef K (A man called Y, G2, 6 June), we should ask who is responsible ... • What has happened to the sudoku (G2, 6 July)? Where is the rotational symmetry (of order 2)? ... ....
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Quasicrystal brings about Dirac cone and zero index, by Jianwen Dong in Phys. Rev. Lett. (Sun Yat-Sen University)
noodls06 May 2015
(Source. Sun Yat-Sen University). Last updated .2015-05-06 Source. School of Physics and Engineering. Written by. School of Physics and Engineering. Edited by. Wang Dongmei ... Help has arrived ... The essence of the physics is that conical dispersions require high symmetry to ensure linear bands crossing each other without level repulsion, and quasicrystals provide high enough rotation symmetry to support the cones." ... Rev. Lett ... [Nature Communs....
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Mashable
25 Feb 2015
Symmetry is easy to find in nature, architecture and people ... 17 Photographs That Display Perfect Symmetry. Use a mirror to guarantee perfect symmetry between an object and its reflection, or animate a kaleidoscope to create rotational symmetry....
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The Guardian
04 Feb 2015
How symmetries, and broken symmetries, help physics to be objective and help me to keep my equanimity. Model at Heidelberg University, illustrating spontaneous symmetry breaking in a ferromagnet ... A square is also symmetric, but only under rotations by 90, 180, 270 or 360 degrees ... This breaks the original rotational symmetry into a more limited symmetry - it is only symmetric under rotations by multiples of 60 degrees....
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noodls
28 Jan 2015
(Source. University of Wisconsin-Madison). Veronica Berns, who recently completed her Ph.D ... (.) . Illustrations. Veronica Berns ... Veronica Berns ... Quasicrystals show every indication of having an ordered and organized arrangement of atoms - sometimes including large crystal facets - except that they exhibit rotational symmetries that have long been considered incompatible with such crystalline organization ... Through her whole Ph.D....
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The Examiner
15 Jan 2015
Specifically, she became interested in the origins of quasicrystals, a type of solid material that has rotational symmetry, but ......
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noodls
23 Dec 2014
At the same time, it's symmetric when rotated, like a soccer ball with five-fold and six-fold patches ... While the exotic solid has order and rotational symmetry, it does not have a repeating pattern ... Due to their high symmetry under rotation, they can have a property called a "photonic band gap." A photonic bandgap occurs when the spacing between the particles is similar to that of light....
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Australian Broadcasting Corporation
28 Nov 2014
Does a parallelogram have a line of symmetry? Some shapes do. they have an equal shape on both sides of this line ... Which ones will have at least one line of symmetry (reflective symmetry)? See how you can reflect a shape along its line of symmetry to draw the missing half of the shape. Also find out which shapes have rotational symmetry. See how to describe the degree of rotational symmetry using orders. ....
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The Guardian
21 Nov 2014
Bilateral, mirror or rotational symmetries; Fibonacci spirals; Fermat’s spirals and fractals patterns are all found in nature and can be mapped mathematically in their perfect form. It is necessary for music to contain such patterns otherwise it would be chaotic noise and the structures of both “Verdi Prati” and “Alabama Song” feature symmetry....
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PNAS
22 Aug 2014
Abstract ... Using rotational symmetry, the equations are discretized in the (2D) meridian plane on an adaptive (moving) mesh and is integrated in time with adaptively chosen time steps ... ....
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The Hindu
20 Aug 2014
Professor Sen, who receives this prize for his work on black holes and symmetries of string theory, communicates his thoughts in an e-mail interview with Shubashree Desikan ... Can you explain your work on symmetries of string theory? ... A symmetry refers to a transformation under which an object looks the same. For example a square has 90 degrees rotational symmetry; if we rotate it by 90 degrees about its centre, it looks the same....
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