On the generating motions and the convexity of a well-known curve in hyperbolic geometry - Dieter Ruoff In Euclidean geometry the vertices P of those angles APB of size alpha that pass through the endpoints A, B of a given segment trace the arc of a circle. In hyperbolic geometry on the other hand a set of equivalently defined points P determines a different kind of curve. In this paper the most basic property of the curve, its convexity, is established. No straight-forward proof could be found. The argument rests on a comparison of the rigid motions that map one of the angles APB into other ones. ✪ ✪ ✪ ✪ ✪ Link tải tài liệu: LINK TẢI TÀI LIỆU Theo LTTK Education
