Part 5/9:
Different types of loops exist in this rotational space, characterized as “wiggles” (minimal rotations) or full rotations (360 degrees). Remarkably, two distinct classes emerge; one involves continuous rotations around an axis, and the other presents properties involving teleportation or crossing boundaries that illustrate a profound mathematical relationship.
Algebraic Representation: SU(2) and SO(3)
As we move into algebra, the relationships between these concepts illuminate the role of SU(2) and SO(3) matrices. The SO(3) group describes rotations in three-dimensional space, while SU(2) serves as its double cover—every rotation in SO(3) corresponds to two transformations in SU(2). This connection extends the understanding of spinners further, revealing their algebraic properties.