Carathéodory

Carathéodory’s theorem is a concept in mathematics that deals with representing points in space. It states that any point inside a shape formed by adding up smaller parts in n-dimensional space can be expressed as a combination of no more than (n+1) of those parts. For example, in 3D space, any point inside a complex shape can be reconstructed using at most four points from its boundary. This theorem helps simplify complex problems by reducing the number of key points needed to describe or analyze a shape or distribution.