A vector field in the plane is a continuous assignment of a vector to each point in some plane region. To a topologist, a vector field that is nowhere zero in some disk "looks like" a constant non-zero field. If a vector field is zero at one point of a disk, there is an integer invariant, called the index, that counts "how many times the value turns" along the boundary circle of the disk. Vector fields having absolute index between one and four are shown. The blue arrows indicate where the field is rightward-pointing along the boundary circle, signifying that the value has made one full rotation.
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