Sliding a Ribbon Wrapped around a Rectangle

A ribbon that is wrapped around a box can be removed with out cutting, stretching, or untying it. Try to do so with an actual ribbon on a box. Then model this situation geometrically and explain why it works. It may be easier to explain first with a rectangle.
Remove the ribbon by sliding the green point: Thanks to Walter Whiteley for creating the sketch.

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RibbonSlide2