Estimation of π From Statistical Features of Acoustic Time Series Using Optimized Monte Carlo With Grid Search Algorithm

This paper introduces a novel methodology for estimating the mathematical constant π from acoustic time series using grid search optimization of zero-crossing rate (ZCR) statistics. By leveraging Gaussian process theory and exhaustive hyperparameter tuning, we demonstrate that π emerges naturally as a fundamental parameter in oscillatory signals. Our approach ensures global convergence and reproducibility, outperforming traditional Monte Carlo methods in accuracy. Experimental validation on music audio achieves a mean absolute error of 0.0002 while failure on non-Gaussian financial data confirms the theoretical foundations of the method.