QUATERNIONS Meaning and
Definition
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Quaternions are a mathematical concept and a specialized type of number system that extends the complex numbers. They are used in mathematics, physics, computer graphics, and robotics for their ability to represent rotations in a three-dimensional space. Developed by Irish mathematician William Rowan Hamilton in 1843, quaternions are a four-dimensional number system that consist of one real component and three imaginary components.
In quaternions, the real component is denoted by "a" and the imaginary components by "bi + cj + dk," where "i," "j," and "k" are the basis elements and represent three perpendicular axes in a three-dimensional space. The imaginary components can be multiplied, divided, and added together just like complex numbers, but quaternions also introduce the concept of quaternion conjugation, where the signs of the imaginary components are switched.
Quaternions have several advantageous properties that make them useful in applications such as 3D computer graphics and robotics. Unlike other rotation representations like Euler angles or rotation matrices, quaternions avoid the problem of "gimbal lock," where a certain combination of rotations can result in a loss of the degree of freedom. Quaternions also have efficient computational properties for combining or interpolating rotations.
In summary, quaternions are a mathematical concept that extends complex numbers to four dimensions and are used to represent rotations in a three-dimensional space, offering advantages in efficiency and avoiding certain limitations found in other rotation representations.
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In math., the metagraphic relation which exists between any two right lines having definite lengths and directions in space.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
Common Misspellings for QUATERNIONS
- 1uaternions
- 2uaternions
- wuaternions
- auaternions
- qyaternions
- qhaternions
- qjaternions
- qiaternions
- q8aternions
- q7aternions
- quzternions
- qusternions
- quwternions
- quqternions
- quarernions
- quafernions
- quagernions
- quayernions
- qua6ernions
- qua5ernions
Etymology of QUATERNIONS
The word "quaternions" is derived from the Latin word "quaterni", meaning "four each". It was coined by the Irish mathematician William Rowan Hamilton in 1843. Hamilton introduced the concept of quaternions as a four-dimensional extension of complex numbers, focusing on the algebraic properties of these mathematical entities. Quaternions are an essential component of modern mathematics, particularly in the fields of vector analysis and three-dimensional rotation calculations.
Similar spelling words for QUATERNIONS
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