Do hypercomplex numbers have some use in Science ?

Question

Do hypercomplex numbers have some use in Science ?

Answer 1

Quaternion

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For other senses of this word, see quaternion (disambiguation).

In mathematics, the quaternions are a non-commutative extension of the complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. At first, the quaternions were regarded as pathological, because they disobeyed the commutative law ab = ba. Although they have been superseded in most applications by vectors, they still find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.



In modern language, the quaternions form a 4-dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by

Answer 2

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Answer 3

According to the Wikipedia article,



"Quaternions are often used in computer graphics (and associated geometric analysis) to represent rotations (see quaternions and spatial rotation) and orientations of objects in three-dimensional space.

...

Quaternions also see use in control theory, signal processing, attitude control, physics, and orbital mechanics, mainly for representing rotations/orientations in three dimensions."