Books XI to XIII of Euclid's Elements dealt with three-dimensional geometry. Book XI develops notions of orthogonality and parallelism of lines and planes, and defines solids including … 展开

Gradient, divergence and curl
In a rectangular coordinate system, the gradient of a (differentiable) function $${\displaystyle f:\mathbb {R} ^{3}\rightarrow \mathbb {R} }$$ is given by
and in 展开

Many ideas of dimension can be tested with finite geometry. The simplest instance is PG(3,2), which has Fano planes as its 2-dimensional subspaces. … 展开

Coordinate systems
In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three … 展开

Another way of viewing three-dimensional space is found in linear algebra, where the idea of independence is crucial. Space has three dimensions because the length of a box is independent of its width or breadth. In the technical language of linear algebra, space is three … 展开

Three-dimensional space has a number of topological properties that distinguish it from spaces of other dimension numbers. For example, at least three dimensions are required to tie a knot in a piece of string.
In differential geometry the generic three-dimensional spaces are 展开

• 3D rotation
• Dimensional analysis
• Distance from a point to a plane
• Four-dimensional space
• Skew lines § Distance 展开