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The winding numbers of the curve around two points in the same region are equal. The winding number around (any point in) the unbounded region is zero. Finally, the winding numbers for any two adjacent regions differ by exactly 1; the region with the larger winding number appears on the left side of the curve (with respect to motion down the ...
The winding number of an oriented curve in the x-y plane is equal to its linking number with the z-axis (thinking of the z-axis as a closed curve in the 3-sphere). More generally, if either of the curves is simple, then the first homology group of its complement is isomorphic to Z. In this case, the linking number is determined by the homology ...
A curve (top) is filled according to two rules: the even-odd rule (left), and the non-zero winding rule (right). In each case an arrow shows a ray from a point P heading out of the curve. In the even-odd case, the ray is intersected by two lines, an even number; therefore P is concluded to be 'outside' the curve.
This curve has total curvature 6 π, and index/turning number 3, though it only has winding number 2 about p.. In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length:
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This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), ...
A Möbius strip made with paper and adhesive tape. In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist.
Sofía Vergara hid her bombshell looks to transform into the cartel leader Griselda Blanco.. In an interview with Variety, published on Wednesday, Aug. 14, the actress, 52, opened up about the ...