In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 [1][2] and applied to …

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton.

Aug 20, 2022 · A quaternion contains four components and it is expressed in the form: a+bi+cj+dk, where a, b, c, and d are real numbers, while i, j, and k are unconventional imaginary units (or the …

Jul 25, 2025 · Quaternions are numbers made up of four parts: one real part and three imaginary parts. They can be written in this form: Here, a is the real part, and b, c, and d are the imaginary parts. The …

Nov 12, 2025 · Quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions. Quaternions and rules for operations on them were invented by Irish mathematician Sir …

Aug 4, 2023 · This beginner-friendly guide breaks down quaternions in simple terms, explains their math, and shows how to use them in Unity for game devs.

Quaternions form an interesting algebra where each object contains 4 scalar variables (sometimes known as Euler Parameters not to be confused with Euler angles), these objects can be added and …

Jun 7, 2020 · Quaternions were historically the first example of a hypercomplex system, arising from attempts to find a generalization of complex numbers. Complex numbers are depicted geometrically …

Feb 21, 2022 · Quaternions are based on Euler’s rotation theorem, which states that a relative orientation of two coordinate systems can be described by the rotation about a single rotation axis. …

Sep 8, 2015 · Quaternions are a set of 4-dimensional vectors that are used to represent rotations in computer graphics. They were discovered by William Hamilton as an extension of 2D complex …