Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun A set of four persons or items.
 noun Mathematics Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i^{2} = j^{2} = −1, and ij = −ji. Under addition and multiplication, quaternions have all the properties of a field, except multiplication is not commutative.
from The Century Dictionary.
 To divide into quaternions, files, or companies.
 noun A set, group, or body of four: applied to persons or things.
 noun A word of four syllables; a quadrisyllable.
 noun A fourfold quantity capable of being expressed in the form xi +
yj +zk +w , where x, y, z, w are scalars, or real numbers, while i, j, k are vectors, or quantities whose squares are negative scalars. The calculus of such quantities is termed quaternions.  noun In bookmaking, a set or ‘gathering’ of four sheets of paper or parchment folded in two.
from the GNU version of the Collaborative International Dictionary of English.
 transitive verb To divide into quaternions, files, or companies.
 noun Poetic The number four.
 noun A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
 noun A word of four syllables; a quadrisyllable.
 noun (Math.) The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun the cardinal number that is the sum of three and one
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Outside the quaternion were the dancing Pauppukkeewis, the Whirlwind, and the fierce and shifty hero, Monobozho, the NorthWest

But we would maintain, nevertheless, that it is the identical book, and explain this variation in the description by the circumstance that the library having, in the space of nearly two centuries, been materially enriched, numerous works, consisting in many cases only of a single "quaternion," were inserted in the volumes already existing.

In [[mathematics]], a '' 'quaternion' '' is a fourdimensional [[object]] important in

Go to the use of a better (higher group symmetry) modern electrodynamics model (such as quaternion electrodynamics, very close to Maxwell's original theory), and the operation of such asymmetric systems now is included (as it was and is in Maxwell's original 20 quaternionlike equations in 20 unknowns).

It happens we both suffer from quaternion headaches, though his remedy, cold beet, was one I have not yet tried.

It happens we both suffer from quaternion headaches, though his remedy, cold beet, was one I have not yet tried.

Whence it appears that in the structure of the universe the motions of living creatures are generally effected by a quaternion of limbs or of bendings.

Farther he avers the virtue of ten consists in the quaternion; the reason whereof is this, — if any person start from one, and add numbers so as to take in the quaternary, he shall complete the number ten; if he passes the four, he shall go beyond the ten; for one, two, three, and four being added up together make ten.

Bacon's biquaternion theory necessarily refers to the sublunary as well as to the superlunary world.

The quaternion theory functions in Bacon's thought as a constructive element for constituting his own theory of planetary movement and a general theory of physics.
sionnach commented on the word quaternion
Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i2 = j2 = 1, and ij = ji. Under addition and multiplication, quaternions have all the properties of a field, except that multiplication is not commutative.
Introduced by my compatriot, the mathematician Sir William Rowan Hamilton in 1843.
In modern language, quaternions form a 4dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton). It can also be given the Clifford algebra classifications Cℓ0,2(R) = Cℓ03,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only three finitedimensional division rings containing the real numbers as a subring.
December 7, 2007
vanishedone commented on the word quaternion
So is WeirdNet just plain wrong, or can quaternion also mean four?
October 27, 2008
sionnach commented on the word quaternion
Some dictionaries (mainly Webster's, or those that borrow from Webster's) do include four as one of the definitions, though "a set of four objects" seems to make more sense.
Quaternions apparently provide a useful parameterization of the space of threedimensional rotations, one which avoids the potential problem of gimbal lock. As I understand it, the obvious method of specifying a rotation through its three Euler angles is problematic because this parameterization is degenerate at some points on the relevant hypersphere, leading to gimbal lock. This degeneracy is an unavoidable consequence of the socalled hairy ball theorem of algebraic topology, and is analogous to the breakdown of lines of latitude and longitude at the poles.
October 27, 2008
knitandpurl commented on the word quaternion
""Yes! Russell and Whitehead. It's like this: when mathematicians began fooling around with things like the square root of negative one, and quaternions, then they were no longer dealing with things that you could translate into sticks and bottlecaps. And yet they were still getting sound results."
Cryptonomicon by Neal Stephenson, p 18 of the Avon Books paperback edition
January 21, 2013