Rotation

Pronunciation: /roʊˈteɪ ʃən/ ?
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Manipulative 1: Rotation Created with GeoGebra.

A rotation consists of moving an object around a center of rotation. A center of rotation is a point around which a 2-dimensional object is rotated. The angle of rotation is how much the object is rotated. When the direction of rotation is important, rotation is referred to as clockwise or counterclockwise. Click on the blue point in manipulative 1 and drag it to change the figure.

Rotations in 3-Dimensions

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Manipulative 2: 3-Dimensional Rotation. Created with GeoGebra.

A point is insufficient to define a rotation in a 3-dimensional space. While a figure can move around a point, there is nothing to define the direction of movement. In 3-dimensional space, a figure is rotated around a line. The line is the center of rotation. Click on the blue points in manipulative 2 and drag them to change the figure.

Symmetry of Rotation

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Manipulative 3: Rotational symmetry of a circle around the center of the circle. Created with GeoGebra.

Symmetry of rotation refers to geometric figures that, when rotated a certain angle about a center of rotation, are coincidental with the original object. If two objects are coincidental, they are identical in size, shape, and location. Manipulative 3 shows the symmetry of rotation of a circle around the center of the circle. For any angle of rotation, the rotated circle is coincidental with the original circle. The rotated circle always looks just like the original circle.

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Manipulative 4: Rotational symmetry of a square around the center of the square. Created with GeoGebra.

In manipulative 4, the original square (in blue) and the rotated square are coincidental only at three angles of rotation: 90° = π/2 rad, 180° = π rad, and 270° = 3π/2 rad.

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Manipulative 5: Rotational symmetry of a square around one of its corners. Created with GeoGebra.

In manipulative 5, a square is rotated about one of its corners. Notice that the original square and the rotated square are coincidental only with a full circle rotation. So the square does not have rotational symmetry about one of its corners.

References

  1. Rotation. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=rotation&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.

More Information

  • McAdams, David. Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Angle.

Cite this article as:


Rotation. 2009-03-11. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/rotation.html.

Translations

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Revision History


2009-03-11: Clarified a center of rotation applying to 2-dimensional objects. Rewrote definition of symmetry of rotation to be more mathematically correct (McAdams, David.)
2008-11-02: Changed manipulatives to GeoGebra (McAdams, David.)
2008-03-12: Changed see also to match current standard (McAdams, David.)
2008-02-03: Corrected missing manipulative (McAdams, David.)
2007-08-18: Initial version (McAdams, David.)

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