Abstract
Hamilton's quaternions are introduced in the usual abstract algebra course as simply an example of a division algebra that is not a field. This paper is designed to supplement this deficiency by showing how the quaternions are used in navigation to indicate the position of an aircraft or a surface craft on the earth. The treatment here has examples throughout to illustrate the development of the Quaternions from a vector space, of which the real numbers and the complex numbers are subsets, to the navigation quaternions, which are used in navigation.
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