Diffeo·morphisms which satisfy the Beltrami equation with a finite Beltrami coefficient have the “quasi” form of this property. A lesser-known theorem of Liouville states that, in R-n with n greater than two, any function with this property is a composition of (15[1])Mobius transformations. A function with this property that connects the upper half-plane to any simple polygon can be constructed with the Schwarz-Christoffel (15[1])integral. Two subsets of the complex plane have this type of (*) equivalence if there is a bi·holo·morphic (10[1])function connecting them; such equivalence exists between any simply connected open set and the unit disc per the Riemann mapping theorem. For functions with this property, the Jacobian (-5[1])everywhere equals a scalar multiple of a rotation matrix. For 10 points, (-5[1])name this type of function that locally (-5[1])preserves (10[2])angles. ■END■ (10[1]0[7])