Crossword clues for quaternion
The Collaborative International Dictionary
Quaternion \Qua*ter"ni*on\, v. t.
To divide into quaternions, files, or companies.
--Milton.
Quaternion \Qua*ter"ni*on\, n. [L. quaternio, fr. quaterni four each. See Quaternary.]
The number four. [Poetic]
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A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
Delivered him to four quaternions of soldiers.
--Acts xii. 4.Ye elements, the eldest birth Of Nature's womb, that in quaternion run.
--Milton.The triads and quaternions with which he loaded his sentences. -- Sir W. Scott.
A word of four syllables; a quadrisyllable.
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(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.
Note: The science or calculus of quaternions is a new mathematical method, in which the conception of a quaternion is unfolded and symbolically expressed, and is applied to various classes of algebraical, geometrical, and physical questions, so as to discover theorems, and to arrive at the solution of problems.
--Sir W. R. Hamilton.
Wiktionary
n. 1 A group or set of four people or things. 2 A word of four syllables. 3 (context mathematics English) A four-dimensional hypercomplex number that consists of a real dimension and 3 imaginary ones (''i'', ''j'', ''k'') that are each a square root of -1. They are commonly used in vector mathematics and in calculating the rotation of three-dimensional objects.
WordNet
n. the cardinal number that is the sum of three and one [syn: four, 4, IV, tetrad, quatern, quaternary, quaternity, quartet, quadruplet, foursome, Little Joe]
Wikipedia
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In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors.
Quaternions are generally represented in the form:
a + bi + cj + dkwhere a, b, c, and d are real numbers, and i, j, and k are the fundamental quaternion units.
Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics, computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application.
In modern mathematical language, quaternions form a four- dimensional associative normed division algebra over the real numbers, and therefore also a domain. In fact, the quaternions were the first noncommutative division algebra to be discovered. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by $\mathbb H$ ( Unicode U+210D, ℍ). It can also be given by the Clifford algebra classifications . The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only two finite-dimensional division rings containing the real numbers as a proper subring, the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which quaternions are the largest associative algebra.
The unit quaternions can be thought of as a choice of a group structure on the 3-sphere S that gives the group Spin(3), which is isomorphic to SU(2) and also to the universal cover of SO(3).
In mathematics:
- The quaternion number system, a generalization of complex numbers.
- The quaternion group, a non-abelian group of order 8.
Quaternion may also refer to:
- In bookbinding, a set of four sheets of folded paper
- Quaternion (poetry), a style of poetry with four parts
- In the Armorial of the Holy Roman Empire, the Quaternion Eagle
- A group of four soldiers in the Roman Army
Quaternion is a poetry style in which the theme is divided into four parts.
Usage examples of "quaternion".
Bob Beech found that his admiration of the mysterious quaternion had run out.
Beech sat down in front of the screen again the quaternion turned towards him.
Of bipedal travelers and their accompanying quaternion of talkative trees, there was no sign save for some splintered branches and a mighty axe that, in the absence of its owner, lay useless and forlorn amid the settling debris.
The quaternion, the book containing five sections of pages, would be sent with Sister Agnes to the abbess in the morning.
There is in these Aztec legends a quaternion besides this of the first men, one that bears marks of a profound contemplation on the course of nature, one that answers to the former as the heavenly phase of the earthly conception.
Outside the quaternion were the dancing Pauppukkeewis, the Whirlwind, and the fierce and shifty hero, Monobozho, the North-West Wind.
The multitudinous philosophies may thus be reduced to a single quaternion, and the reputed inaugurator of a new philosophy is like to be a charlatan.
No one, I repeatno onehas used Hamiltonian quaternions since 1915 when tensor analysis was invented.
When I should have been looking after my quaternions, I was doing something else, something not so useful to one who would be a mathematician, but perhaps more useful to a writer who had already learnt enough to count the words in an article and to estimate the number of guineas due to him.
With the previous examples before our eyes, it asks no vivid fancy to see in these quaternions once more the four winds, the bringers of rain, so swift and so slippery.
Think of the advancement man has made since the time when he was a cannibal cave dweller, shivering out of the glacial epoch, and contending with wild beasts for a foothold on the earth, till now that he enjoys the idealism of Berkeley, wields the quaternions of Hamilton, uses the lightnings for his red sandaled messengers, holds his spectroscope to a star and tells what elements compose it, or to an outskirting nebula and declares it a mass of incandescent hydrogen.
The gatherings, originally quaternions or quires, became different, and those who undertake to examine MSS.
At home, I was free to read books and web pages about molecular biology and particle physics, quaternions and galactic evolution, and to write my own Byzantine computer games and convoluted abstract animations.
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 there can be nae fear but, atween you and me, and the Michty at the back o' 's, we s' get breid eneuch for the quaternion o' 's!