The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)² + (y/b)² = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|ⁿ +|y/b|ⁿ = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.

叶片的形状表现出相当大的多样性和复杂性，反映了对环境因素的适应，如环境光和降水以及系统遗传。许多叶子似乎是椭圆形的，这可能代表“默认”发育条件。然而，它们的几何形状是否真正符合椭圆方程 (EE)，即 ( x/a ) ²  + ( y/b ) ²  = 1，仍然是猜测。一种替代方案由超椭圆方程 (SE) 描述，它是 EE 的广义版本，即 | x/a | ⁿ  +| y/b | ⁿ  = 1。为了测试 EE 与 SE 描述叶子几何形状的功效，两个含笑的叶子形状物种（即M. cavaleriei var. platypetala和M. maudiae），使用每个物种的 60 片叶子进行了研究。分析表明，大多数叶子（120 片中的 118 片）已将 SE 非线性拟合到叶子几何形状的均方根误差调整为 < 0.05，即从极点到叶子边缘点的平均绝对偏差较小面积等于叶面积的假想圆半径的 5%。这两个物种的n估计值为˂ 2，表明所有采样的叶子都符合 SE 而不是 EE。这项研究证实了叶片中 SE 的存在，将其与其潜在的功能优势联系起来，特别是叶片形状对水力传导的可能影响。