The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of 3-dimensional real space, extending the way that the complex numbers capture the alg...The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of 3-dimensional real space, extending the way that the complex numbers capture the algebra of rotations of 2-dimensional real space.
Euclidean geometry is the geometry of our experience in three dimensions. Planes look like infinite tabletops, lines in space are Euclidean straight lines. Any planar slice of 3-space inherits two-dim...Euclidean geometry is the geometry of our experience in three dimensions. Planes look like infinite tabletops, lines in space are Euclidean straight lines. Any planar slice of 3-space inherits two-dimensional Euclidean geometry. The Poincaré disk model of hyperbolic geometry may also be extended to three dimensions. Three-dimensional elliptic geometry is derived from the fact that the 3-sphere consists of all points in 4-dimensional space one unit from the origin.
