Rotation

Pronunciation: /roʊˈteɪ.ʃən/ Explain
Click on the green point on the slider and drag it to rotate the object. Click on the blue points and drag them to change the figure.

At what angles of rotation is the rotated object exactly on top of the original object?
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.

Rotations in 3-Dimensions

Click on the blue points and drag them to change the figure.

Manipulative 2 - Rotation about a Line 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.

Symmetry of Rotation

Click on the blue points and drag them to change the figure.

Are there any angles of rotation about the center of the circle such that the image is not on top of the pre-image?
Manipulative 3 - Rotational Symmetry Created with GeoGebra.

Symmetry of rotation refers to geometric figures that, when rotated a certain angle about the center of the object, 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.

Click on the blue points and drag them to change the figure.

At what angles of rotation does the image lay on top of the pre-image?
Manipulative 4 - Rotation of a Square about its Center 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.

Click on the blue points and drag them to change the figure.

At what angles does the image lie on top of the pre-image?
Manipulative 5 - Rotation of a Square about a Corner 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.

More Information

  • McAdams, David E.. Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/a/angle.html.

Cite this article as:

McAdams, David E. Rotation. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/rotation.html.

Image Credits

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
3/11/2009: Clarified a center of rotation applying to 2-dimensional objects. Rewrote definition of symmetry of rotation to be more mathematically correct (McAdams, David E.)
11/2/2008: Changed manipulatives to GeoGebra. (McAdams, David E.)
3/12/2008: Changed see also to match current standard. (McAdams, David E.)
2/3/2008: Corrected missing manipulative. (McAdams, David E.)
8/18/2007: Initial version. (McAdams, David E.)

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