Contour Winding Number
المؤلف:
Krantz, S. G.
المصدر:
"The Index or Winding Number of a Curve about a Point." §4.4.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser
الجزء والصفحة:
pp. 49-50
17-11-2018
1050
Contour Winding Number
The winding number of a contour 
about a point 
, denoted 
, is defined by
and gives the number of times 
curve passes (counterclockwise) around a point. Counterclockwise winding is assigned a positive winding number, while clockwise winding is assigned a negative winding number. The winding number is also called the index, and denoted 
.
The contour winding number was part of the inspiration for the idea of the Brouwer degree between two compact, oriented manifolds of the same dimension. In the language of the degree of a map, if ![gamma:[0,1]->C](http://mathworld.wolfram.com/images/equations/ContourWindingNumber/Inline6.gif)
is a closed curve (i.e., 
), then it can be considered as a function from 
to 
. In that context, the winding number of 
around a point 
in 
is given by the degree of the map
from the circle to the circle.
REFERENCES:
Krantz, S. G. "The Index or Winding Number of a Curve about a Point." §4.4.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 49-50, 1999.
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