This article explores how a mathematical tool called SU(2)/SO(2) helps us understand the behavior of Cooper pairs, tiny electron couples responsible for superconductivity. Copper pairs consist of two electrons with opposite spins bound together by vibrations in the material. The article explains how SU(2)/SO(2) describes the electron spins and their spatial arrangement within the pairs. It shows how this tool helps predict their distribution, formation process, and magnetic properties. Ultimately, this allows us to understand superconductivity better and design new superconducting materials.