The Joukovski map, or transform, is the map z = ζ‎ + ζ‎^–1 from the complex plane to itself. The map has the property that a circle in the ζ‎-plane, not centred at zero, is mapped to an aerofoil shape in the z-plane as shown in the figures. The map was instrumental in the early study of flight.

Circle in ζ‎-plane

Aerofoil in z-plane