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Winding Number Illustrator

The winding number of a curve around a point p in the plane measures the numbers of times on net that the curves winds around the point in a counter clockwise direction.

The idea of a winding number and its applications in math and science can be described in intuitive terms, and in mathematical terms.

One of the most interesting things about the winding number is that it can be calculated by the following amazing formula:

The winding number of a curve doesn't change no matter how we deform it, provided the curve never crosses over the point p. In mathematical terms, the mechanism for deforming one curve into an equivalent one is called a homotopy.

Part of the reason the winding number formula is so surprising is that the value of the integral doesn't change as we deform the the path provided we avoid crossing p

The ideas of the winding number and a homotopy are beautifully illustrated by a special family of curves in the plane:

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Created: Fri Sep 8 11:39:00 1995 --- Last modified: Wed Apr 17 17:09:58 1996