3. Integral Geometry

The tenth mathematical framework is integral geometry, which applies integral calculus to geometry (in this case, Euclidean geometry), and more specifically deals with geometric measures that are invariant under groups of linear or affine transformations acting on linear or affine subspaces (e.g., lines in two dimensions and lines and planes in three dimensions).

The area of the planar figure shown in blue (Figure 12 ) can be estimated based on the lengths of the line segments formed by the intersections of uniformly distributed affine lines.