Movement of a figure about a fixed point, at a given angle, often expressed in degrees. The angle is called the angle of rotation.
Transformation of a plane defined by a fixed point O, called the “centre of rotation”, and a real number α, called the “angle of rotation”. This transformation maps a point P to a point P’ so that segments OP and OP’ are congruent and the measure of the angle formed by rays OP and OP’ is the absolute value of α.
- A rotation is defined by a fixed point called the centre of rotation and a angle of rotation.
- Rotations may be used to create frieze patterns and tessellations.
- A rotation in a clockwise direction is a negative rotation.
- A rotation in a counterclockwise direction is a positive rotation.
The invariants under a rotation of the plane are the following :
- the perimeter and area of plane figures;
- the measures of angles;
- the alignment of the points;
- the orientation of the plane, since a rotation is a direct isometry.
A rotation does not preserve parallelism between a segment and its image.