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)
|
where 
is parameterized by 
for 
along the length of the knot by parameter 
, and the frame 
associated with 
is
 |
(2)
|
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)
|
(Adams 1994, p. 187).
