quaternion love

# quaternion

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. A set of four persons or items.
• n. Mathematics 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 multiplication is not commutative.

### from the GNU version of the Collaborative International Dictionary of English

• n. The number four.
• n. A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
• n. A word of four syllables; a quadrisyllable.
• n. 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.
• transitive v. To divide into quaternions, files, or companies.

### from The Century Dictionary and Cyclopedia

• n. A set, group, or body of four: applied to persons or things.
• n. A word of four syllables; a quadrisyllable.
• n. 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.
• To divide into quaternions, files, or companies.
• n. In book-making, a set or ‘gathering’ of four sheets of paper or parchment folded in two.

• n. the cardinal number that is the sum of three and one

## Etymologies

Middle English quaternioun, from Late Latin quaterniō, quaterniōn-, from Latin quaternī, by fours, from quater, four times.
(American Heritage® Dictionary of the English Language, Fourth Edition)
From Middle English quaternioun, from Late Latin quaterniō, from quaternī (ablative form of quater, “four times”) + -iōn, “-ion”.[2][3] (Wiktionary)

• ""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

• 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 three-dimensional 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 so-called hairy ball theorem of algebraic topology, and is analogous to the breakdown of lines of latitude and longitude at the poles.

October 27, 2008

• So is WeirdNet just plain wrong, or can quaternion also mean four?

October 27, 2008

• 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 4-dimensional 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 finite-dimensional division rings containing the real numbers as a subring.

December 7, 2007