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

Of course, each player also does his best to stop his opponent from forming his quaternion or file of four.

From Project Gutenberg

Keep forming threes as long as you can so as to force your opponent to stop the threatened quaternion.

From Project Gutenberg

His days are thus described: from dawn to the third hour he copied rapidly, filling a (quaternion) each day.

From Project Gutenberg

Even then the captain of the gate was replying to a question from the quaternion.

From Project Gutenberg

Should neither player be able to form a quaternion, then the game is drawn.

From Project Gutenberg