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## quaternion

quaternion (kwətûr´nēən), in mathematics, a type of higher complex number first suggested by Sir William R. Hamilton in 1843. A complex number is a number of the form a+bi when a and b are real numbers and i is the so-called imaginary unit defined by the equation i2=-1. The rules for operating with complex numbers are simply those of operating with the polynomial a+bx except that i2 is replaced by -1 whenever it occurs. A quaternion, an extension of this concept, is a number of the form a+bi+cj+dk when a, b, c, and d are real numbers and i, j, and k are imaginary units defined by the equations i2=j2=k2=ijk=-1. Quaternions, as well as vectors and tensors (later outgrowths of the concept of quaternions), have many important applications in mechanics.

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## quaternion

quaternion group of four XIV; quire of four sheets XVII; (math.) XIX. — late L. quaterniō, -ōn-, f. quaternī four together (see prec.).

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"quaternion." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 22 Aug. 2017 <http://www.encyclopedia.com>.

"quaternion." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. (August 22, 2017). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/quaternion

"quaternion." The Concise Oxford Dictionary of English Etymology. . Retrieved August 22, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/quaternion