<![CDATA[The claim that the golden ratio appears in nature is frequently used as a context for mathematics learning; however, such claims require rigorous examination through precise variable definitions and appropriate analysis. This study critically examined whether internode-distance patterns in water spinach (Ipomoea aquatica) approximate the golden ratio. The objectives were to: (1) describe the pattern of five consecutive internode distances across 30 water spinach stems, (2) examine the closeness of adjacent-distance ratios to φ = 1.618, and (3) translate the findings into an inquiry-STEM activity for ratio learning. The data comprised 150 distance measurements and 120 adjacent paired ratios collected using AR Meter, a smartphone-based augmented reality measurement application. The analysis retained directional ratios to identify positional changes and used symmetric ratios, defined as the longer distance divided by the shorter distance, to evaluate proximity to φ. Differences among the five positions were tested using the Friedman test, while stem-level geometric means were compared with φ using the Wilcoxon signed-rank test. The results showed significant differences in internode distance by position, χ²(4) = 22.744, p < 0.001, Kendall’s W = 0.190. The arithmetic mean of the 120 symmetric ratios was 1.629, which appeared close to φ but was influenced by two extreme ratios, 11.25 and 11.67. Only 11 of the 120 ratios (9.17%) fell within a 5% tolerance of φ. Therefore, the data did not support a consistent golden-ratio pattern in water spinach internode distances. The educational value of this study lies in using an unconfirmed popular claim as a context for teaching measurement, reciprocal ratios, robust statistics, and evidence-based argumentation through inquiry-STEM.]]>
Copyrights © 2026
