Part 4/9:
When examining the group of rotations in three dimensions, a cube can act as a visual aid. Every orientation of the cube can be defined by an axis of rotation with a specific rotation amount, which can be represented as a vector. Depending on the axis and angle of rotation, a multitude of different orientations are possible. This representation leads to a discovery that the space of rotations is not simply connected, meaning there are distinct classes of rotations that cannot be continuously transformed into another without cutting.