|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 , 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.