Aquatic plants provide an opportunity to characterize the geometrical relationships of leaf patterning. A new polar-coordinate model was used to correlate meristem shape and leaf arrangement in aquatic plants. In aquatic plants, the primary geometrical relationship specifying spiral vs. whorled phyllotaxis is primordial position: primordia arising on the apical dome (as defined by displacement angles θ ≤ 90° during maximal phase) are often positioned in spiral patterns, whereas primordia arising on the subtending axis (as defined by displacement angles of θ ≥ 90° during maximal phase) are arranged in whorled patterns. A secondary geometrical relationship shows an inverse correlation between the primordial size : available space ratio and the magnitude of the Fibonacci numbers in spiral phyllotaxis or the number of leaves per whorl in whorled phyllotaxis. This geometrical analysis provides the morphological context for interpreting phyllotaxis mutants and for constructing realistic models phyllotactic patterns.