Discrete Geometry

The fifteenth general mathematical framework is that of discrete geometry, which is a branch of geometry so named to distinguish it from “continuous geometry.”

For example, two-dimensional continuous geometry allows us to define lines and circles in a Euclidean plane ${ℝ}_2^2$ , such as sets of points with coordinates consisting of pairs of real numbers, whereas discrete geometry deals with sets of points with integer coordinates or with cells (typically squares in two dimensions and cubes in three dimensions) that form what are known as discrete lines or circles.

Discretization (Figure