14. Similarity Theorem in CPS Geometry

The source explores the concept of similarity in geometry, arguing that traditional Euclidean geometry’s reliance on the parallel postulate is not the most fundamental approach. Instead, the source proposes a "CPS Geometry" based on the close-packing of spheres, where similarity arises from the inherent patterns and structures within this arrangement. This framework introduces the idea of "quantization" and suggests that the similarity theorem, rather than being a consequence of parallel lines, is a result of the inherent properties of the CPS arrangement.