A group or set of four people or things.
Used in a Sentence
quaternions
Definitions, parts of speech, synonyms, and sentence examples for quaternions.
Editorial note
The relationship between Quaternions and the 3-dimensional cross-product corresponds to the relationship between the octonions and this 7-dimensional cross-product.
Examples18
Definitions3
Parts of speech1
Quick take
A group or set of four people or things.
Meaning at a glance
The clearest senses and uses of quaternions gathered in one view.
A word of four syllables.
(mathematics) A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.
Definitions
Core meanings and parts of speech for quaternions.
noun
A group or set of four people or things.
noun
A word of four syllables.
noun
(mathematics) A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.
Example sentences
The relationship between Quaternions and the 3-dimensional cross-product corresponds to the relationship between the octonions and this 7-dimensional cross-product.
Any time you are freely rotating a viewpoint or an object in 3D space, you will probably want quaternions.
William Rowan Hamilton, credited as the inventor of quaternions, died of a severe gout precipitated by excessive drinking and overeating.
The pointing data was in satellite frame-of-reference quaternions [1], and the satellite orbited about the axis of the Sun-Earth line, approximately.
You don't want to try to learn something mathematical from the Wikipedia article on it - Quaternions are a great example.
If you look inside any undergrad math textbook, you'll find exact same writing style showcased in the Wikipedia article on quaternions.
Graphics and 3D-modeling programmers will need to know matrices (possibly also quaternions) and vector math.
So quaternions are useful for 3d games, and games are a hot topic for Lua.
In a regular vector based system, we might use vectors and quaternions (2 things) to model rigid bodies.
At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms.
And one could use complex, or quaternions to represent points in order to not have to reinvent the wheels of rotation/translation/computing area/projections/polar to cartesian...
Another fun fact is that the +−−− metric allows relativity to be described in a spinor calculus (which are in turn isomorphic to quaternions).
Quote examples
So when you say "extremely complex" I think quaternions, because i^2 = j^2 = k^2 = ijk = -1.
"In mathematics, the quaternions are a number system that extends the complex numbers." Naturals are a subset of integers.
"So that's quaternions, the magical rotation vectors."
Proper noun examples
Another topic that has confounded me as much as FFTs are Quaternions.
Quaternions are pretty common in 3D graphics.
So to be specific, I've used calculus in a bunch of places, Linear Algebra, Markov Chains, Quaternions, Topology, and Graph Theory is just everywhere.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use quaternions in a sentence?
The relationship between Quaternions and the 3-dimensional cross-product corresponds to the relationship between the octonions and this 7-dimensional cross-product.
What does quaternions mean?
A group or set of four people or things.
What part of speech is quaternions?
quaternions is commonly used as noun.