If domain elements correspond to only one range element, and range elements correspond to only one domain element, domain and range elements have one-to-one correspondence {mapping, function}. Functions and their inverse functions map.
Two functions can map {conformal map} in an ordered sequence, with no overlaps or gaps. Angles are the same as in Euclidean space. Shapes stay the same, but sizes change.
Complex-plane closed region, bounded by closed loop that has no intersections, can holomorphically map onto complex-plane unit disc {Riemann mapping theorem}. Two simply connected planes can conformally map one-to-one. One inner and one boundary point of one plane are in other plane. Transformations on unit circles through z = -1 makes airfoil shapes {Zhoukowski airfoil transformation} {Joukowski airfoil transformation}.
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Date Modified: 2022.0225