A quaternion is a mathematical entity that extends complex numbers. It consists of one real part and three imaginary parts, typically represented as q = a + bi + cj + dk , where a, b, c, and d are real numbers, and i, j, k are the fundamental quaternion units. Quaternions are used in various fields, including computer graphics and robotics, to represent rotations in three-dimensional space. Quaternions offer several advantages over traditional rotation methods, such as Euler angles or rotation matrices. They avoid issues like gimbal lock and provide smooth interpolation between orientations, making them ideal for applications in 3D animation, virtual reality, and aerospace engineering. Their unique properties allow for efficient calculations and a compact representation of rotational data.