Helly's Theorem

Helly's Theorem is a result in geometry that deals with the intersection of shapes. It states that for a collection of convex shapes (like circles or polygons) in a space, if every group of a certain small number (called the dimension plus one) of these shapes overlaps, then all the shapes together will also have a common intersection point. In simpler terms, if small groups of convex shapes all overlap, then there's a point where they all meet at once. This theorem helps understand how multiple shapes can be guaranteed to share a common point based on simpler overlaps.