Editing History of geometry (section)

====Geometry of more than 3 dimensions====
{{see also|Euclidean geometry#19th century}}

The 19th century saw the development of the general concept of Euclidean space by [[Ludwig Schläfli]], who extended Euclidean geometry beyond three dimensions. He discovered all the [[Four-dimensional space#Dimensional analogy|higher-dimensional analogues]] of the [[Platonic solids]], finding that there are exactly six such [[Regular 4-polytopes|regular convex polytopes in dimension four]], and three in all higher dimensions.

In 1878 [[William Kingdon Clifford]] introduced what is now termed [[geometric algebra]], unifying [[William Rowan Hamilton]]'s [[quaternions]] with [[Hermann Grassmann]]'s algebra and revealing the geometric nature of these systems, especially in four dimensions. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modeled to new positions.