Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Technical Report

Publication Date



William Rowan Hamilton invented the quaternions in 1843, in his effort to construct hypercomplex numbers, or higher dimensional generalizations of the complex numbers. Failing to construct a generalization in three dimensions (involving triplets) in such a way that division would be possible, he considered systems with four complex units and arrived at the quaternions. He realized that, just as multiplication by i is a rotation by 90o in the complex plane, each one of his complex units could also be associated with a rotation in space. Vectors were introduced by Hamilton for the first time as pure quaternions and Vector Calculus was at first developed as part of this theory. Maxwell\'s Electromagnetism was first written using quaternions.'


Sandia National Laboraties

Publication Title

Sandia Technical Report

Language (ISO)



Sandia Technical Report;SAND2004-0153

Article author is part of the Main Campus Math Department.

Included in

Mathematics Commons