An application of the golden ratio and fibonacci numbers to analyses of canopy structure of forage plants

This study was designed to conduct analyses of canopy structure of forage plants by applying the golden ratio and the Fibonacci sequence to the infinite series of exponential function with base e used for analyses of production structures in forage plants. The results obtained were as follows. (1) The product of light extinction coefficient (K) and leaf area index (F) in the plant canopy took the value of golden ratio, where K and F were in inverse proportion. (2) The combination of large K and low F suggested the canopy leaves showing a horizontal inclination. (3) The small K and high F suggested the canopy leaves showing a vertical inclination. (4) These phenomena depended on the leaf inclination angle with which upper leaves shaded lower leaves, provided that other factors were the same. Therefore, the case (3) might give the canopy structure that was higher in the production of forage plants compared with the case (2). It was suggested that the golden ratio and the Fibonacci sequence, which appeared in the infinite series of exponential function with base e, were related to the analysis of canopy structure of forage plants.