A new characteristic of Möbius transformations by use of Apollonius points of triangles (Q1916693)
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scientific article; zbMATH DE number 902422
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new characteristic of Möbius transformations by use of Apollonius points of triangles |
scientific article; zbMATH DE number 902422 |
Statements
A new characteristic of Möbius transformations by use of Apollonius points of triangles (English)
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10 March 1997
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In the authors' definition the distance of the Apollonius point from each vertex of a triangle multiplied by the length of the side opposite to that vertex is the same for all three vertices. They offer a proof that among the functions nonconstant and meromorphic on the whole open complex plane exactly the Möbius (linear rational) functions preserve the Apollonius point of every nondegenerate triangle in the plane.
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Möbius transformations
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Apollonius points of triangles
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functional equations
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meromorphic functions
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univalent functions
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analytic functions
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Möbius linear rational functions
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0.9481201
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0.9475261
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0.92923284
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0.92223525
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0.9130769
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0.90356416
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