three dimensional space

History

In the 19th century, developments of the geometry of three-dimensional space came with William Rowan Hamilton's development of the quaternions, a hypercomplex number system. For this purpose, Hamilton coined the terms scalar and vector, and they were first defined in the three dimensional sense within his geometric framework for quaternions. Three dimensional space could then be described by quaternions ${\displaystyle q=a+ui+vj+wk}$ which had a vanishing scalar component, that is, ${\displaystyle a=0}$.