Dirac Belt Trick

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Dirac Belt Trick.
The animation shows how one can twist and untwist a belt by rotating the end of the belt always in the same direction. The demo was invented by the physicist Paul Dirac to explain a topological property of the rotation group.
Observe that the middle section of the belt stays paralllel to the screen and keeps rotating in the SAME direction. This called “The waiters cup trick”.
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dirac belt anaglyph
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The movement of the frames (no rotation at both ends of the belt) can be interpreted as a homotopy ( = deformation) in the group SO(3) of rotations of R^3.
Air On The Dirac Strings.
This remarkable 1993 animation shows all three classic visualizations of the fact that the fundamental group of SO(3) is cyclic of order two, namely the Dirac Belt Trick, the Phillipine Wine Glass Trick, and Orientation Entanglement. It was designed by George Francis, Louis Kauffman, and Daniel Sandin, and the computer graphics were implemented by Chris Hartman and John Hart.

See also: Professor Bob Palais demonstrating the Belt Trick and the Plate Trick, at http://www.math.utah.edu/~palais/links.html

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