Definition:Rotation (Geometry)/Angle

Definition

Let $r_\theta$ be a rotation in the Euclidean Space $\Gamma = \R^n$.

Let $\map {r_\theta} P = P'$ about a point $O$ on the axis of rotation of $r_\theta$.

The number $\theta$ which defines the angle $POP'$ is called the rotation angle or angle of rotation of $r_\theta$.

Positive

$\theta$ is defined as being positive if and only if the rotation it measures is in the anticlockwise direction.

Negative

$\theta$ is defined as being negative if and only if the rotation it measures is in the clockwise direction.

Also see

• Results about rotation angles can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angle