PTOLEMAIC SPACES AND CAT(0)

We consider Ptolemy's inequality in a metric space setting. It is not hard to see that CAT(0) spaces satisfy this inequality. Although the converse is not true in full generality, we show that if our Ptolemaic space is either a Riemannian or Finsler manifold, then it must also be CAT(0). Ptolemy's inequality is closely related to inversions of metric spaces. We exploit this link to establish a new characterization of Euclidean space amongst all Riemannian manifolds.

The Ptolemaic ruler as a religious figure in Cyrenaica

This article examines the particularities of Ptolemaic power outside Egypt through the religious activities of the Ptolemies in Cyrenaica. Since evidence is scarce on the direct administration of this Ptolemaic possession between 321 and 96 BC, the study of the royal cult and the relations between the Ptolemies and traditional cults of the city provides valuable insight on the nature of the dialogue between the king and the cities. It is clear from the available evidence that cult structures already existing in Egypt strongly included Cyrenaica in the Ptolemaic space. But the participation of the city in the royal cult and the flexibility of the royal language of power show that imperialistic views fail to fully explain both the longevity of Ptolemaic power in Cyrenaica and the necessity for the Ptolemies to legitimise their power even in a territory under direct administration.