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...

a polygon is to compute the given point's winding number with respect to the polygon. If the winding number is non-zero, the point lies inside the polygon...

1: 167–244. Michał Misiurewicz (ed.). "Rotation theory". Scholarpedia. Weisstein, Eric W. "Map Winding Number". From MathWorld--A Wolfram Web Resource....

differential equations. The topological quantum number of a solution is sometimes called the winding number of the solution, or, more precisely, it is the...

point has negative winding number. Therefore, the winding number of a curve may be any integer. The pictures above show curves with winding numbers between...

viewed from P) add 1. If the total winding number is zero, P is outside C; otherwise, it is inside. The winding number is effectively a count of how many...

results for the duality between the fermion spectrum and the topological winding number of the non-linear sigma model have been obtained by Dan Freed. This...

Danish filmmaker Romain Winding (born 1951), French cinematographer Victor Winding (1929–2014), British actor Other uses: Winding number, an integer representing...

physical consequences of having different winding number become more apparent for a finite chain with an even number of N {\displaystyle N} lattice sites....

G} , then the winding number of γ {\displaystyle \gamma } about w {\displaystyle w} is 2 n {\displaystyle 2^{n}} times the winding number of f n ∘ γ {\displaystyle...

equal to 2πN for an integer N called the turning number or index of the curve. N is the winding number about the origin of the hodograph of the curve parametrized...

hand, using the Cauchy integral formula for the winding number, it can be seen that the winding number is constant on connected components of the complement...

electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Divisions of a turn include the half-turn and quarter-turn...

methods such as Liouville's theorem, or topological ones such as the winding number, or a proof combining Galois theory and the fact that any real polynomial...

transformations which preserve the winding number are called small gauge transformations while ones that change the winding number are called large gauge transformations...

immersions of the circle in the plane are classified by the winding number, which is also the number of double points counted algebraically (i.e. with signs)...

⁡ ( f , a k ) {\displaystyle \operatorname {Res} (f,a_{k})} and the winding number of γ {\displaystyle \gamma } around a k {\displaystyle a_{k}} by I ⁡...

"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...

of 2π, where N is called the index of the curve or turning number – it is the winding number of the unit tangent vector about the origin, or equivalently...

contractible to a point inside Ω. For each point z ∈ Ω, let n(C,z) be the winding number of C around z. Then 1 2 π i ∮ C f ′ ( z ) f ( z ) d z = ∑ a n ( C ,...

In electrical engineering, coil winding is the manufacture of electromagnetic coils. Coils are used as components of circuits, and to provide the magnetic...

as the winding number, the topological charge (although it is unrelated to 'charge' in the electrical sense), the topological quantum number (although...

Instead, a more robust approach is the Generalized Winding Number. Inspired by the 2D winding number, this approach uses the solid angle at q {\displaystyle...

current of one ampere flowing in a single-turn loop. Turns refers to the winding number of an electrical conductor composing an electromagnetic coil. For example...

{\displaystyle B(z_{0},r)} , taken with its positive orientation. The winding number of f ( γ ) {\displaystyle f(\gamma )} with respect to the point f (...

more times. The number of times the string winds around a circle is called the winding number. If a string has momentum p and winding number n in one description...

_{f\circ C}{\frac {dz}{z}}=\mathrm {Ind} _{f\circ C}(0),} i.e., the winding number of the closed curve f ∘ C {\displaystyle f\circ C} around the origin;...

homomorphism to H1(2πiZ|U) gives the winding number for each loop. So this homomorphism is therefore a generalized winding number and measures the failure of U...

where I ⁡ ( C , a k ) {\displaystyle \operatorname {I} (C,a_{k})} , the winding number, is 1 {\displaystyle 1} if a k {\displaystyle a_{k}} is in the interior...

using a formula involving the winding number of the polygon around each integer point as well as its total winding number. The Reeve tetrahedra in three...