"Everybody knows" that quaternions are not used for the purposes for which they were originally intended. They are, however, used in computer graphics, and perhaps in astrogation.
Besides that, what are the current uses of quaternions?
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3Well, not exactly an answer, but one use is to extract €1.79 from tourists for yet another 'app' http://ingeniousireland.ie/podcast-audio-tours/quaternions-by-the-royal-canal/. Supposedly, in an early act of vandalism, Hamilton carved the basic quaternion equations on a stone in Broom Bridge over the Royal Canal in Dublin. – copper.hat Sep 15 '13 at 06:35
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@copper.hat If only he then robbed a liquor store, stole a carriage, filled it with prostitutes and rode it to Mexico, he would be a mathematician that many of today's young people could identify with. – rschwieb Sep 19 '13 at 14:07
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El Quaternion strikes again... – copper.hat Sep 19 '13 at 14:50