Fixed spheres again. We are given two spheres that are made of glass and thus are not distortable. They are rigidly fixed in space, one inside the other as illustrated, and they cannot be moved! The middle sphere floats miraculously in midair without any means of support. There is a rubber rope that hangs from the inside ceiling of the big sphere to the roof of the smaller sphere, as shown. The rope has a knot in it. Show that it is possible to unknot the rope without moving or distorting the two spheres. (This quest ion appeared in Section 5.1, Mindscape 38.) Suppose now we add another straight rope as shown. Can you unknot the top rope without introducing a knot in the bottom rope?
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