Quaternions are a four-dimensional number system that extends the complex numbers, with each quaternion written as a plus b i plus c j plus d k for real numbers a, b, c and d and three special units i, j and k satisfying i squared equals j squared equals k squared equals i j k equals minus one. Unlike ordinary numbers or complex numbers, quaternion multiplication is not commutative: the order in which two quaternions are multiplied changes the result. The Irish mathematician William Rowan Hamilton discovered them on October 16, 1843, while walking along Dublin's Royal Canal, and carved the defining formula into the stone of Brougham Bridge on the spot. The quaternions form a division algebra, meaning every nonzero quaternion has a multiplicative inverse, and unit quaternions are widely used today to represent rotations in three-dimensional computer graphics, robotics and spacecraft attitude control.
Facts
Classification
Object KindStructure or Algebraic Object 1 Connections
Attributed To
Source Wikipedia: Quaternion
In Branch
Source Wikipedia: Quaternion
Is Kind Of Object
Sources
1. Wikipedia: Quaternion
History section
The great breakthrough in quaternions finally came on Monday 16 October 1843 in Dublin, when Hamilton was on his way to the Royal Irish Academy to preside at a council meeting.
Lead section
As an abstract mathematical structure, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore a ring, also a division ring and a domain.
Attributed To: William Rowan Hamilton, Lead
Quaternions were introduced by Hamilton in 1843.
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