Euler Angles: The Three Numbers That Describe Any Orientation in Space

Euler angles are three numbers that describe how a rigid body is rotated relative to a fixed coordinate system. Introduced by Leonhard Euler in the 18th century, they are the backbone of spacecraft navigation, robotics, video game graphics, and aircraft flight control. This article explains what they are, how they work, the different conventions, and why "gimbal lock" is the problem every engineer must know about.