Dirac string trick
Take a cardboard square and tie the four corners to another larger square by loose string. Rotate the small square by 360° about a vertical axis, that is, in a horizontal plane. The strings will become somewhat tangled, and it is not possible to untangle them without rotating the square. Turn the square through another 360°, for a total of 720°. Contrary to all expectations, it is now possible to untangle the string, without further rotation of the square, simply by allowing enough space for the strings to be looped over the top of the square!
Another version of the Dirac string trick has been called the Philippine wineglass trick. A glass of water held in the hand can be rotated continuously through 720° without spilling any water. Surprisingly, these geometrical demonstrations are related to the physical fact that an electron has spin ½. A particle with spin ½ is something like a ball attached to its surroundings with string. Its amplitude changes under a 360° (2π) rotation and is restored on rotation to 720° (4π).