Quaternion

Quaternion multiplication table

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Cayley Q8 graph showing the 6 cycles of multiplication by Template:Red, Template:Green and Template:Blue. Template:Nowrap hover over or click a cycle to highlight it.)

In mathematics, the quaternion number system (represented using the symbol $ℍ$) extends the complex numbers into four dimensions. They were first described by Irish mathematician William Rowan Hamilton in 1843. They are often used in computer graphics to compute 3-dimensional rotations.

The eight-dimensional octonions come after the quaternions.

Other websites

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• Paulson, Lawrence C. Quaternions (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)
• Quaternions – Visualisation