The twist of a ribbon measures how much it twists around its axis and is defined as the integral of the incremental twist around the ribbon. A formula for the twist is given by
(1)
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where is parameterized by for along the length of the knot by parameter , and the frame associated with is
(2)
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where is a small parameter and is a unit vector field normal to the curve at (Kaul 1999).
Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then the calugareanu theorem states that
(3)
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(Adams 1994, p. 187).