THE TREASURY OF ATREUS ‘RELIEVING’ TRIANGLE: INSIGHTS FROM HYPERBOLIC GEOMETRY

Author: Stavroula Patsiomitou

ABSTRACT

In the Treasury of Atreus, also known as the Tomb of Clytemnestra, the visitor’s attention is immediately captured by the relieving triangle positioned above the entrance. Although this architectural element was created thousands of years prior to the official emergence of hyperbolic geometry, its form closely resembles a hyperbolic triangle, comparable to those generated within the Poincaré Disk through the use of dynamic geometry software. Here, the Mycenaeans’ empirical understanding and intuitive mastery of structural stability intersect/ converge with ideas that would later be formulated by Bolyai and Lobachevsky, thereby creating an intriguing connection between ancient times and contemporary geometry. In the current study, I present my thoughts in conjunction with earlier research on the topic. To investigate this hypothesis, I utilize the Poincaré Disk, which facilitates a comprehensive visualization and examination of the geometric characteristics of the relieving triangle. Within this framework, the relieving triangle stands out not only as an extraordinary architectural element but also as a mathematical symbol of continuity, illustrating the persistent human endeavor to understand space and balance through the tools and knowledge available throughout various historical periods. Based on the existing literature, it seems that no previous study has explicitly linked the relieving triangle to hyperbolic geometry.

Keywords: Treasury of Atreus, the ‘relieving’ triangle, hyperbolic geometry, Poincaré Disk

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