Number of times a curve wraps around a point in the plane
Not to be confused with Map winding number.
This curve has winding number two around the point p.
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In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that the curve travels counterclockwise around the point, i.e., the curve's number of turns. For certain open plane curves, the number of turns may be a non-integer. The winding number depends on the orientation of the curve, and it is negative if the curve travels around the point clockwise.
Winding numbers are fundamental objects of study in algebraic topology, and they play an important role in vector calculus, complex analysis, geometric topology, differential geometry, and physics (such as in string theory).
mathematics, the windingnumber or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that...
a polygon is to compute the given point's windingnumber with respect to the polygon. If the windingnumber is non-zero, the point lies inside the polygon...
of 2π, where N is called the index of the curve or turning number – it is the windingnumber of the unit tangent vector about the origin, or equivalently...
In electrical engineering, coil winding is the manufacture of electromagnetic coils. Coils are used as components of circuits, and to provide the magnetic...
"The Long and Winding Road" is a song by the English rock band the Beatles from their 1970 album Let It Be. It was written by Paul McCartney and credited...
differential equations. The topological quantum number of a solution is sometimes called the windingnumber of the solution, or, more precisely, it is the...
( f , a k ) {\displaystyle \operatorname {Res} (f,a_{k})} and the windingnumber of γ {\displaystyle \gamma } around a k {\displaystyle a_{k}} by I ...
methods such as Liouville's theorem, or topological ones such as the windingnumber, or a proof combining Galois theory and the fact that any real polynomial...
pdf ver 1.3 Michał Misiurewicz (ed.). "Rotation theory". Scholarpedia. Weisstein, Eric W. "Map WindingNumber". From MathWorld--A Wolfram Web Resource....
as the windingnumber, the topological charge (although it is unrelated to 'charge' in the electrical sense), the topological quantum number (although...
cokernel Index of a matrix Index of a real quadratic form Index, the windingnumber of an oriented closed curve on a surface relative to a point on that...
results for the duality between the fermion spectrum and the topological windingnumber of the non-linear sigma model have been obtained by Dan Freed. This...
more times. The number of times the string winds around a circle is called the windingnumber. If a string has momentum p and windingnumber n in one description...
of 2π, where N is called the index of the curve or turning number – it is the windingnumber of the unit tangent vector about the origin, or equivalently...
Degree of a continuous mapping, a generalization of windingnumber Degrees of freedom, the number of parameters of a system that may vary independently...
converges to −1 at the start of the path and to 1 at the end, which has windingnumber 1 around 0, and which does not cross [0, ∞). Fix a branch of log (...
rotor's axis to reduce cogging torque. The armature winding of each phase may be distributed in a number of pole slots. Since the EMF induced in different...
{\displaystyle B(z_{0},r)} , taken with its positive orientation. The windingnumber of f ( γ ) {\displaystyle f(\gamma )} with respect to the point f (...
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