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When are we ever gonna use this?

Sometimes, mathematical discoveries come about because people are trying to solve real-world application problems.  Other times, mathematical discoveries come about because people have incredible imagination and insight, but then those discoveries are seemingly useless, for a while.

Quaternions are something that fall into the latter category.  These members of a noncommutative divisional algebra were first discovered by Sir William Rowan Hamilton in 1843.  They were fun for theoretical mathematicians but did not seem to have a practical use until 1985, when computer scientists realized that they can be used in digital animation.  Quaternions are perfect for work involving orienting and rotating objects in 3-D space.  (4)

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