When i grows up… | Rob Low

…\(i\) wants to be a quaternion.

We can think of the complex numbers as two dimensional vectors, with a rule for multiplication. This multiplication rule is actually very well behaved, and for some time mathematicians tried and failed to find a similarly well behaved multiplication rule for three dimensional vectors. In fact the failure was not due to any lack of ability: it’s impossible to find such a well-behaved multiplication rule for these vectors. Then William Rowan Hamilton had a flash of inspiration which gave him the insight that although a multiplication rule couldn’t be found…

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