Quantitative Validation of Fibonacci Patterning in Pineapple Phyllotaxis

Grade XII, Jumeirah English Speaking School, United Arab Emirates

Abstract

This study provides a quantitative, reproducible analysis of the Fibonacci structures alongside the Golden ratio within Ananas Comosus (Pineapple) using calibrated ImageJ measurements and a Python program alongside it. Three mature pineapples of different sizes were photographed under controlled conditions, and their interscale distances alongside the number of visible spirals have been calculated. We then compared these measurements to the theoretical expectations derived from the golden ratio and evaluated the proximity of both the Fibonacci and Lucas sequences. Our results support the hypothesis that pineapple scale arrangements tend towards Fibonacci structures, with occasional anomalies toward Lucas numbers. We discuss the biological mechanisms that form these regularities, and we outline the limitations of our methodology for further work.