Mathematical Correspondence Between the Bosnian Valley of the Pyramids and the Pleiades Star Cluster: A Fibonacci-Ratio and Spatial-Alignment Study

Abstract

Advances in geomatics and computational astronomy enable rigorous quantitative analysis of potential terrestrial–celestial spatial correspondences. This study investigates whether summit- point distributions in the Bosnian Valley of the Pyramids exhibit statistically meaningful geometric similarities with the angular configuration of the Pleiades star cluster (M45). Using LiDAR-derived elevation models, geodetic summit coordinates, and astronomical catalog data, we construct normalized distance matrices and evaluate rotational similarity, Fibonacci-ratio proportions, and angular-alignment tolerances under formal geometric and statistical criteria. Primary analytical metrics include: (1) Fibonacci proportional relationships di/dj≈1.618d_i/d_j approx 1.618di/dj≈1.618, (2) rotation-invariant angular convergence with tolerance below 2∘2^circ2∘, and (3) scale-adjusted shape correspondence using Procrustes transformation. A Monte-Carlo random spatial simulation of 100,000 iterations establishes a null model for alignment probability. Results demonstrate multiple spatial intervals and triangular configurations whose proportional ratios deviate less than 2% from Fibonacci sequence expectations, alongside star–summit alignments exceeding random distribution thresholds. No causal inference or cultural interpretation is asserted; rather, this contribution presents a reproducible mathematical methodology for evaluating celestial-terrestrial pattern comparisons. Findings support the viability of Fibonacci-based geomatic analysis and rotational alignment testing as tools for examining structural spatial coherence. Future work will extend these methods to broader stellar frameworks and integrate Bayesian modeling to refine probability estimates for non-random spatial patterning.