Re: Conformal Mapping

*To*: mathgroup at smc.vnet.net*Subject*: [mg128575] Re: Conformal Mapping*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Mon, 5 Nov 2012 18:39:41 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k6t7ut$1ni$1@smc.vnet.net>

Am 01.11.2012 08:22, schrieb MaxJ: > Hi folks, > > I need help finding a Mobius transform such that the region: > > |z-i|< sqrt(2) > && > |z+i|< sqrt(2) > > in z-plane be mapped conformally into a unit circle in w-plane. > > Any help is appreciated very much. The boundaries are two circles with centers at +-i and radius^2 = 2. Consequently the contours are passing through the six points on the squares with vertices +-1, 2i +-1 and +-1 -2i +-1 Consequently the lens shaped area in question is bounded by two symmetric quarter circles with center at +-i intersecting at +-1 with an angle of pi/2. We conclude that the identity w=z is a conformal map of the lens into the inner of the unit circle. The construction of a conformal map onto the unit circle, transforming to straight lines the pi/2 vertices at +-1, needs square roots centered at the vertices +-1. This task could generate homework for up to one day approximately. -- Roland Franzius

**Follow-Ups**:**Re: Conformal Mapping***From:*Andrzej Kozlowski <akozlowski@gmail.com>