Rotation (geometry)

A rotation is a transformation that turns an object around a fixed point or axis, preserving distances and angles. Unlike translation, which slides an object, rotation spins it in place.

In 2D, rotating a shape means spinning it around a center point by a specified angle, measured in degrees or radians. A 90-degree rotation of a square around its center produces a visually identical square—but rotated coordinates reveal the mathematical transformation. In 3D, rotations occur around an axis, and the mathematics becomes richer: group theory shows that 3D rotations form a continuous structure called SO(3).

Rotations are isometries—they preserve distances and areas. This makes them essential in Design, Engineering, Physics, and Computer Graphics. They're used to reorient maps, animate objects in video games, describe planetary motion around the Sun, and solve puzzles like the Rubik's cube.

The concept appears everywhere: a spinning wheel, Earth's rotation, the twirl of a dancer, or how a gyroscope maintains orientation. Understanding rotations deepens intuition about spatial relationships and symmetry.

Related

Symmetry (geometry), Transformation (geometry), Vector (mathematics), Complex numbers, Angle, Axis (geometry)