THEORY OF IDEAL DIMENSIONS OF THE KUKULCÁN PYRAMID (CHICHEN ITZA): MODULAR GEOMETRY, PYTHAGOREAN TRIPLETS, AND THE VIGESIMAL HARMONIC CANON

Abstract

The architectural composition of the Kukulcán Pyramid (El Castillo) at Chichén Itzá is traditionally interpreted in the literature through the lens of a 365-day solar calendar, relying on an approximate division of 91 steps per flight plus the shared summit platform. This study presents an exact geometric, metrological, and stochastic deconstruction of the pyramid based on field measurements and architectural surveys. It is proven that the monument’s architectural corpus is not grounded in uncoordinated anthropometric measures, but in a rigorous geometric canon governed by two primitive Pythagorean triples: (dictating the macro-slope of the stepped flank at ) and (regulating the batter profile of the nine terrace tiers at and enabling the mechanics of the equinoctial shadow). Furthermore, the vertical profile deconstruction documents the physical existence of exactly 90 constructed steps per staircase flight ( elements), directly materializing the canonical Maya Tun calendar cycle of 360 days, while the summit platform with the temple forms a unified geometric monad. Through the application of the modular unit and its rational transition to the Maya Zapal (, in the ratio ), the base dimensions, terrace heights, staircase width, and summit temple resolve into rational and integer modules. Finally, a Monte Carlo permutation test () establishes the joint probability of concurrently embodying these geometric canons at , categorically rejecting the null hypothesis of accidental construction.