Preface
The purpose of this book is to examine both the properties and applications of quaternions, and, in particular, to explore visual representations that help to develop our intuition about quaternions and their exploitation. Of all the natural advantages of quaternions, several stand out clearly above all others:
Normalized quaternions are simply Euclidean four-vectors of length one, and thus are points on a unit hypersphere (known to mathematicians as the three-sphere) embedded in four dimensions. Just as the ordinary unit sphere has two degrees of freedom, e.g., latitude and longitude, the unit hypersphere has three degrees of freedom.
There is a relationship between quaternions and three-dimensional rotations that permits the three rotational ...
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