Kvaternioonid

Kvaternioonid, also known as quaternions, are a number system that extends the complex numbers. They were first described by the Irish mathematician William Rowan Hamilton in 1843. A quaternion is typically represented as q = a + bi + cj + dk, where a, b, c, and d are real numbers, and i, j, and k are the fundamental quaternion units. These units satisfy the following multiplication rules: i^2 = j^2 = k^2 = ijk = -1, and ij = k, jk = i, ki = j, ji = -k, kj = -i, ik = -j. Quaternions have several unique properties, including non-commutativity, meaning that the order of multiplication matters (e.g., ij ≠ ji). They are used in various fields such as computer graphics, robotics, and physics, particularly in three-dimensional space. Quaternions can represent rotations in three-dimensional space more efficiently than other methods, such as Euler angles or rotation matrices. This makes them particularly useful in applications where rotations are frequently performed, such as in the control of drones or the animation of characters in video games. Despite their complexity, quaternions provide a powerful tool for mathematical and computational tasks involving three-dimensional rotations.