quaternion

[ kwuh-tur-nee-uhn ]

noun

1. a group or set of four persons or things.
2. Bookbinding. four gathered sheets folded in two for binding together.
3. Mathematics.
   1. an expression of the form a + bi + cj + dk, where a, b, c, and d are real numbers; i 2 = j 2 = k 2 = −1; and ij = −ji = k, jk = −kj = i, and ki = −ik = j.
   2. a quantity or operator expressed as the sum of a real number and three complex numbers, equivalent to the quotient of two vectors. The field of quaternions is not commutative under multiplication.

quaternion

/ kwəˈtɜːnɪən /

noun

1. maths a generalized complex number consisting of four components, x = x 0 + x 1 i + x 2 j + x 3 k, where x , x 0 … x 3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc
2. another word for quaternary

quaternion

/ kwə-tûr′nē-ən /

1. 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 that multiplication is not commutative.

Word History and Origins

Origin of quaternion¹

1350–1400; Middle English quaternioun < Late Latin quaterniōn- (stem of quaterniō ), equivalent to Latin quatern ( ī ) four at a time + -iōn- -ion

Word History and Origins

Origin of quaternion¹

C14: from Late Latin quaterniōn, from Latin quaternī four at a time

Example Sentences

Halfway through the episode, Urmson is describing the mathematical model his company chose: quaternions.

From The Verge

In his 1865 treatise 'A dynamical theory of the electromagnetic field', Maxwell laid out 20 equations using esoteric mathematical expressions known as quaternions.

From Nature

But science is full of them - my favorite being William Hamilton using his pocketknife to carve quaternion equations on a bridge abutment after inspiration hit when he had no paper or pencil.

From Washington Times

In particular he explained the principle of least action, first advanced by P. L. M. de Maupertuis, and developed by Sir W. R. Hamilton, of quaternion fame.

From Project Gutenberg

Every pulse pushes nature's quaternion along life's currents recreating us afresh; the morn feeding the morn, Memnon's music issuing from every stop, as if the Orient itself had sung.

From Project Gutenberg