Conformal mapping from polygon with circle segments

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The discussion centers on finding a conformal map from a polygon with circular segments to the upper half-plane, specifically using examples like quadrilaterals with circular arcs. The Schwarz-Christoffel mapping is mentioned as a related concept, but the user seeks additional resources or tips on this specific mapping type. There is a suggestion to explore the topic of circular arc polygons, which may yield useful references. Forum members are encouraged to share insights or clarify any found references. The conversation highlights the complexity of conformal mappings involving circular segments.
Kurret
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I am looking for a conformal map from a "polygon" to eg the upper half plane, which consists of circle segments instead of lines. So for example, it could be a quadrilateral ABCD, but where AB is a circle segment. The closest I can find is the Schwarz-Christoffel mapping.

Anyone has any tips?
 
I don't know about this subject, but I notice that you can find numerous hits by searching for the topic of conformal mapping and "circular arc polygons". (For example: http://en.wikipedia.org/wiki/Schwarzian_derivative mentions circular arc polygons.)

If you find a reference that seems to do what you want and have a specific question about it, there are probably forum members who can explain it.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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