rotációkat

Rotációkat refers to rotations, a fundamental geometric transformation. In two dimensions, a rotation is a rigid motion that turns a figure around a fixed point called the center of rotation. The amount of turn is measured by an angle. Rotations are often described by the angle of rotation and the direction (clockwise or counterclockwise). A positive angle typically signifies a counterclockwise rotation, while a negative angle indicates a clockwise rotation.

In three dimensions, rotations are also rigid transformations, but they occur around an axis of rotation. The angle of rotation defines the extent of the turn around this axis. Rotations preserve distances and angles between points, meaning that the shape and size of an object remain unchanged after a rotation. They are crucial in various fields, including geometry, physics, computer graphics, and engineering, for describing the orientation and movement of objects.

Mathematical representations of rotations often involve matrices. In two dimensions, a 2x2 rotation matrix can transform the coordinates of a point. In three dimensions, a 3x3 rotation matrix or a quaternion can be used. The composition of rotations is also a rotation, but the order of composition matters, meaning rotations are not generally commutative. Understanding rotations is key to comprehending many physical phenomena and geometric properties.