Chapter 01. The Discovery of Quaternions

Hamilton’s Walk

Quaternions arose historically from Sir William Rowan Hamilton’s attempts in the midnineteenth century to generalize complex numbers in some way that would be applicable to three-dimensional (3D) space. Because complex numbers (which we will discuss in detail later) have two parts, one part that is an ordinary real number and one part that is “imaginary,” Hamilton first conjectured that he needed one additional “imaginary” component. He struggled for years attempting to make sense of an unsuccessful algebraic system containing one real and two “imaginary” parts. In 1843, at the age of 38, Hamilton (see Figure 1.1) had a brilliant stroke of imagination, and invented in a single instant the ...

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