Apollonian packing

Apollonian packing is a fascinating way of arranging circles within a larger circle. It begins with three touching circles, and then additional smaller circles fit perfectly into the gaps between them, creating a complex, never-ending pattern. This process can continue indefinitely, adding smaller circles that touch the previous ones. The result is a densely packed arrangement of circles, showcasing mathematical beauty and symmetry. Apollonian packing connects to geometry, number theory, and even art, providing insights into how shapes can fill space harmoniously.