# Study Vector Bundle in a Relatively Harder Way - Definition

MotivationDirection is a considerable thing. For example take a look at this picture (by David Gunderman):The position of the red ball and black ball shows that this triple of balls turns upside down every time they finish one round. This wouldn’t happen if this triple were on a normal band, which can be denoted by $S^1 \times (0,1)$. What would happen if we try to describe their velocity on the Möbius band, both locally and globally? There must be some significant difference from a normal band....