Samose Seminar Series : A talk on 'Quaternions'

Speaker : David Farris

Date : Friday, 16th September 2016

Topic : A talk on 'Quaternions'


Complex numbers a+bi may be viewed as a "two-dimensional" number system.They give a elegant way to describe plane geometry, which sparked an intensive search in the 19th century to find an analogous system of three-dimensional numbers to understand the geometry of three-dimensional space.  But it turns out there is no such system! However, William Rowan Hamilton discovered a beautiful and totally unexpected *four-dimensional* number system, the quaternions, which can be used to describe three-dimensional geometry (and many other things).  I'll begin by telling you about using complex numbers to describe rotations in the plane, and to easily derive all those complicated trigonometric identities you had to memorize in 10th standard.  Then I'll introduce the quaternions and their remarkable properties, and show how they describe rotations of three-dimensional space.

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