Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple, closed curve to a double integral over the region enclosed by the curve. It states that the circulation of a vector field around the curve is equal to the sum of the curl of the field over the area inside the curve. This theorem is particularly useful in physics and engineering, as it simplifies the calculation of line integrals by converting them into area integrals. It is named after the mathematician George Green, who formulated the theorem in the 19th century.