Petiole length in Boerhavia (Nyctaginaceae) approximates the golden ratio phi

  • Justin K. Williams Department of Biological Sciences, Sam Houston State University
Keywords: Boerhavia, Nyctaginaceae, Anisophylly, Anisoclady, C4, Golden Ratio, phi


The leaves of Boerhavia exhibit anisophylly. It is here hypothesized that the scale of the uneven leaves exhibits a determined pattern, rather than an arbitrary difference in size. To test for this, the opposite petioles of Boerhavia diffusa and B. erecta from both regional and local populations were measured, and the ratio of the measurements were compared to the Golden Ratio. One-paired t-tests for a critical mean indicate that the ratios of paired petioles for both species are not statically different from the value 1.6180339887…. These tests indicate that petiole length in Boerhavia approximates the Golden Ratio. The significance of this observation is that the Golden Ratio is here expressed as a line segment rather than as a spiral, which is how the Golden Ratio has been previously observed and reported in plant growth.


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How to Cite
Williams, J. K. (2018). Petiole length in Boerhavia (Nyctaginaceae) approximates the golden ratio phi. Journal of the Botanical Research Institute of Texas, 12(2), 667-682. Retrieved from