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Dieter Ruoff - Solution of a non-Euclidean convexity problem

DIETER RUOFF, Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan  S4S 0A2, Canada
Solution of a non-Euclidean convexity problem

The curve that will be investigated is made up from the vertices of the angles which have size $\alpha$, share the common chord AB and lie in one and the same halfplane with respect to the line through AB. It is a well-known fact that in Euclidean geometry these points form an arc of a circle. Also, it is clear that any one of the given angles can be moved into any other by a rotation. In non-Euclidean geometry all this does not hold. A sketch of a convexity proof for this latter setting will be provided.


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