Quaternion

Cayley Q8 graph showing the 6 cycles of multiplication by i, j and k. (In the SVG file, hover over or click a cycle to highlight it.)

In mathematics, the quaternion number system (represented using the symbol <math>\mathbb H</math>) extends the complex numbers into four dimensions. They were first described by Irish mathematician William Rowan Hamilton in 1843.^[1]^[2] They are often used in computer graphics to compute 3-dimensional rotations.

The eight-dimensional octonions come after the quaternions.

References[change]

↑ "On Quaternions; or on a new System of Imaginaries in Algebra". Letter to John T. Graves. 17 October 1843.
↑ Rozenfelʹd, Boris Abramovich (1988). The history of non-euclidean geometry: Evolution of the concept of a geometric space. Springer. p. 385. ISBN 9780387964584.

File:Xy icon.svg This short article about mathematics can be made longer. You can help Wikipedia by adding to it.

v t e Number systems
Commonly used systems	Natural numbers (<math>\mathbb N</math>) Integers (<math>\mathbb Z</math>) Rational numbers (<math>\mathbb Q</math>) Real numbers (<math>\mathbb R</math>) Complex numbers (<math>\mathbb C</math>)
Hypercomplex numbers	Quaternions (<math>\mathbb H</math>) Octonions (<math>\mathbb O</math>) Sedenions (<math>\mathbb S</math>) Pathions (<math>\mathbb P</math>) Chingons (<math>\mathbb X</math>) Routons (<math>\mathbb U</math>) Voudons (<math>\mathbb V</math>)