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I am not entirely sure about the details but thought I would share...

Link to Press Release:

http://www.eurekalert.org/pub_releases/2008-03/icl-1yo030308.php

A problem, the Schwarz-Christoffel formula which has defeated mathematicians for almost 140 years has been solved by a researcher at Imperial College London.

More detail:

he Schwarz-Christoffel mapping maps a suitably "nice" (such as the interior of the unit circle, or the upper half plane) region of the complex plane (numbers of the form x+iy, mapped as (x,y) in cartesian coords, where i^2 = -1) to the interior of a general polygon (in the complex plane) in a conformal manner (angles are preserved). However, the polygon must be "simply connected" (any loop can be smoothly shrunk to a point, without getting "caught" around a hole); a few "multiply connected" polygons were possible, but not in the general case. Now it appears the formula can be extended to include polygons that include such a hole (such as perhaps the area outside a small square, but inside a larger one), to be mapped to some member well-described family of regions like the exterior of several unit disks

http://sinews.siam.org/old-issues/2008/januaryfebruary-2008/breakthrough-in-conformal-mapping [Broken]

Link to Press Release:

http://www.eurekalert.org/pub_releases/2008-03/icl-1yo030308.php

A problem, the Schwarz-Christoffel formula which has defeated mathematicians for almost 140 years has been solved by a researcher at Imperial College London.

More detail:

he Schwarz-Christoffel mapping maps a suitably "nice" (such as the interior of the unit circle, or the upper half plane) region of the complex plane (numbers of the form x+iy, mapped as (x,y) in cartesian coords, where i^2 = -1) to the interior of a general polygon (in the complex plane) in a conformal manner (angles are preserved). However, the polygon must be "simply connected" (any loop can be smoothly shrunk to a point, without getting "caught" around a hole); a few "multiply connected" polygons were possible, but not in the general case. Now it appears the formula can be extended to include polygons that include such a hole (such as perhaps the area outside a small square, but inside a larger one), to be mapped to some member well-described family of regions like the exterior of several unit disks

http://sinews.siam.org/old-issues/2008/januaryfebruary-2008/breakthrough-in-conformal-mapping [Broken]

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