Peil J, Helwin H
Gegenbaurs Morphol Jahrb. 1976;122(2):162-81.
To compare growth processes of feminine human beings with such one of masculine we have taken as realizations of the growth characteristic the morphological height of face (distance between nasion and gnathion), length of nose (distance between nasion and subnasale) and body length of two spatially and temporally different populations. Measured values of these characteristics for different ages of individuals provide the basis for mathematical evaluation. The parameters of the following three types of mathematical functions were adjusted to the measured time course of the growth characteristics: Gompertz' function, inverse tangent and the generalized logistic growth function. The principal possibilities are explained which a mathematical expression can offer for qualitative and quantitative description of dynamical processes. The results of fitting the 3 competitive function types to the course of the measured values are given and several quantitative conclusions are demonstrated arising from comparisons of corresponding growth processes of feminine and masculine human beings.
为了比较女性和男性的生长过程,我们选取面部形态高度(鼻根点与下颌骨最低点之间的距离)、鼻子长度(鼻根点与鼻下点之间的距离)以及两个在空间和时间上不同的人群的身体长度作为生长特征的体现。针对个体不同年龄阶段这些特征的测量值为数学评估提供了基础。将以下三种类型数学函数的参数调整至生长特征的测量时间进程:冈珀茨函数、反正切函数和广义逻辑斯蒂增长函数。阐述了数学表达式在定性和定量描述动态过程方面所能提供的主要可能性。给出了将这三种竞争函数类型拟合到测量值进程的结果,并展示了从女性和男性相应生长过程比较中得出的若干定量结论。