The Parthenon and the Temple of Zeus at Olympia: A Four-Part Synchronous System of Measures, Sacred Geometry, and the Geodetic Canon of Doric Architecture

This paper presents an analytical, empirical, and comparative deconstruction of the metric-geometric canon applied in the design of 5th-century BCE monumental Doric architecture. Challenging the prevailing paradigm in historical metrology — which regards ancient Greek units of length solely as local, anthropometric derivations devoid of geodetic standardization — this study demonstrates the existence of a unified, four-part synchronous system of linear measures. The system comprises: the ideal Attic foot (AF = 25/81 m approx 0.308642... m), the Olympic foot (OF = 25/90 = 5/18 m} approx 0.277778... m), the piki (P = 5 AF approx 1.543210... m), and the tetrapodia (TP = 4 AF = 1.23456789... m), all derived from a harmonic sexagesimal-decimal division of the ideal Earth circumference (C = 40,000... km). Empirical verification was conducted on the Athenian Parthenon (Ictinus, Callicrates, Phidias) and comparatively evaluated against the Temple of Zeus at Olympia (architect Libon of Elis). The comparative analysis reveals that both temples constitute complementary "hekatompedons": the Parthenon with a stylobate width of 100 AF = 30.864... m (30.880... m in situ), and the Temple of Zeus with a width of 100 OF = 90 AF = 27.778... m (27.68 m in situ). As conclusive proof of direct canon transmission and the central role of the sculptor Phidias, it is shown that the exterior peristyle columns of both temples share an identical canonical height of 10.432... m (33.8... AF at the Parthenon and 37.555... OF = 33.8 AF at the Temple of Zeus), exhibiting a field discrepancy of less than 1 cm. Statistical null-hypothesis (H_0) testing via stochastic Monte Carlo simulations confirms that the observed geometric alignment, integration of the constants 1,618033... and 3,1415..., and modular roof grids cannot be the product of random coincidence (p < 1.0 × 10^-6).