Definition

1. Noun:
   • A set or group of four: "quaternion" can refer to a group or set consisting of four parts, people, or things.
   • The cardinal number four: In a more specific mathematical or formal sense, "quaternion" denotes the cardinal number that is the sum of three and one.
   • A mathematical concept: In advanced mathematics, particularly algebra, a "quaternion" is a type of number system that extends the complex numbers, typically represented as a + bi + cj + dk, where a, b, c, d are real numbers and i, j, k are fundamental quaternion units.

Usage Examples

• Noun (Group of four):
  • The ancient text described the universe as being composed of a quaternion of elements: earth, air, fire, and water.
  • They formed a quaternion to tackle the project, each member responsible for a different quarter.
• Noun (The number four):
  • The quaternion is an even number that follows three.
• Noun (Mathematical concept):
  • Quaternions are used in computer graphics and physics to represent rotations in three-dimensional space.

Advanced Usage

• "Quaternion algebra": A branch of mathematics dealing with the structure and properties of quaternions.
  • He specialized in quaternion algebra during his graduate studies.
• "Quaternion group": In group theory, a specific non-abelian group of order eight, often denoted Q₈, which can be represented using quaternion units.
  • The properties of the quaternion group are fundamental in abstract algebra.

Variants and Related Words

• Quatern (noun, archaic): A group or set of four.
  • The soldiers marched in a quatern.
• Quaternate (adjective): Composed of, arranged in, or divided into four parts.
  • The leaf had a quaternate structure.

Synonyms

• Four: The cardinal number.
• Tetrad: A group or set of four.
• Quadruplet: A set of four, especially four born at one birth.
• Quartet: A group of four people or things, especially musicians.

Related Phrases

(Note: "Quaternion" itself is not commonly used in phrasal verbs. The following are related descriptive phrases.) - Quaternion of forces: A conceptual grouping. - The theory proposed a quaternion of fundamental forces. - In quaternion: Arranged in a set of four. - The data was presented in quaternion for clarity.

Related Idioms

(Note: There are no common idioms centered on the word "quaternion" due to its technical nature.)

Noun

1. the cardinal number that is the sum of three and one