this post was submitted on 03 Jul 2023
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Because the tire is topographically a radially flattened torus, when you turn it half inside out, it becomes a 2D möbius strip. At this point it effectively has only one side. When you push such construct horizontally against a solid, because the z-axis perpendicular to the strip has no negative values (it only has one side), if that coincides with the orientation of the ∇Np of the solid, the z vector wraps around the solid. When the tire snaps to its rest state (inside in), it's easy to see why it ends up around the pillar.
This 3D animation demonstrates the concept:
https://youtu.be/xvFZjo5PgG0
:(