(Winding number) Let C be a piecewise smooth curve in the xy
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(Winding number) Let C be a piecewise smooth curve in the xy-plane that does not pass through the origin. Let D .x; y/ b
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(Winding number) Let C be a piecewise smooth curve in the xy-plane that does not pass through the origin. Let D .x; y/ be the polar angle coordinate of the point P D .x; y/ on C, not restricted to an interval of length 2 , but varying continuously as P moves from one end of C to the other. As in Example 5 of Section 15.2, it happens that r D ? y x2 C y2 i C x x2 C y2 j: If, in addition, C is a closed curve, show that w.C/ D 1 2 I C x dy ? y dx x2 C y2 has an integer value. w is called the winding number of C about the origin.
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