Authors
Yousef Mehrdad Bibalan 1, Behrouz Far 1, Mohammad Moshirpour 2, and Bahareh Ghiyasian 3, 1University of Calgary, Canada, 2University of California, USA, 3Google, USA
Abstract
Quantitative comparisons between the spatial arrangement of major summit points in the Bosnian Valley of the Pyramids and the angular configuration of the Pleiades star cluster (M45) reveal several measurable geometric correspondences. Using LiDAR-derived elevation models for the terrestrial dataset and Gaia DR2 catalog data for the celestial coordinates, the analysis incorporates Golden-ratio evaluation, distance-matrix comparison, angular deviation metrics, Procrustes geometric alignment, and a 100,000-run Monte-Carlo spatial randomization model. Multiple inter-summit distances approximate Golden-ratio proportions within a 2% tolerance, while angular relationships converge within ±2° of the corresponding Pleiades geometry. Procrustes alignment yields a low RMSD, and Monte-Carlo simulations indicate a probability of p = 0.021 that a comparable or stronger match would arise by chance. The combined results point to statistically significant spatial coherence between the terrestrial and celestial configurations, supporting further application of mathematical and geomatic methods in the study of large-scale landscape patterning..
Keywords
Fibonacci ratio; golden ratio; spatial alignment; celestial-terrestrial geometry; Procrustes transformation; Monte-Carlo simulation; Bosnian Valley of the Pyramids; Pleiades star cluster; geomatics; LiDAR