Vol. 34, No. 3, 1970

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An analogue of Ptolemy’s theorem and its converse in hyperbolic geometry

Joseph Earl Valentine

Vol. 34 (1970), No. 3, 817–825
Abstract

The purpose of this paper is to give a complete answer to the question: what relations between the mutual distances of n(n 3) points in the hyperbolic plane are necessary and sufficient to insure that those points lie on a line, circle, horocycle, or one branch of an equidistant curve, respectively ?

Mathematical Subject Classification
Primary: 50.40
Milestones
Received: 4 August 1969
Published: 1 September 1970
Authors
Joseph Earl Valentine