Rotation

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.

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 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.

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.

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.