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What is a quaternion?

What is a quaternion? Here are some definitions.

Noun
  1. A group or set of four people or things.
  2. A word of four syllables.
  3. (mathematics) A four-dimensional hypercomplex number that consists of a real dimension and 3 imaginary ones (i, j, k) that are each a square root of -1. They are commonly used in vector mathematics and in calculating the rotation of three-dimensional objects.
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Examples
Even then the captain of the gate was replying to a question from the quaternion.
I am not likely to attempt your quaternion of colour very soon.
William Hare, the second of our quaternion, was also a native of Ireland, having been born in the neighbourhood of Londonderry.
Next, to assign the distinction between the first and the second quaternion in propositions tertii adjacentis.
The two figural miniatures and all the canon tables are contained on a separate gathering, a quaternion, physically joined together.
There was no sound of trumpet at the sun's rising, but a quaternion of legionaries came and the guard was changed.

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