Twist
المؤلف:
Adams, C. C.
المصدر:
The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, 1994.
الجزء والصفحة:
...
15-6-2021
1777
Twist
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).
REFERENCES:
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, 1994.
Kaul, R. K. "Topological Quantum Field Theories--A Meeting Ground for Physicists and Mathematicians." 15 Jul 1999. https://arxiv.org/abs/hep-th/9907119.
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