A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is
In Euclidean geometry the vertices P of those angles ∠AP B of size α 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 straightforward proof could be found. The argument rests on a comparison of the rigid motions that map one of the angles ∠AP B into other ones.fatcat:r45ybumlwjh7vksxvemn7c6f6e