Carathéodory's theorem

Carathéodory’s theorem states that if you have a set of points in a space with a certain dimension, any point that can be formed as a combination of those points can actually be expressed as a combination of only a limited number of them—specifically, at most one more than the space's dimension. For example, in 3D space, any point inside a set of points can be represented using just four of those points. This theorem helps simplify complex relationships by showing that only a small subset is needed to describe or approximate points within a larger set.