Sager G
Anat Anz. 1981;150(4):428-42.
Gaining a mathematical expression for the height development of girls and boys is all the more desirable since acceleration has been observed for some decades. At the first look the height curve is not unsimilar to a simple parabola when considered up to prepuberty age. In fact the relation can be well approximated when applying a power function: W = W0 + ktr; with W0 representing the birth length, t the time, and k and r being coefficients. When reaching about ten years of age, this formula must be modified by a restricting term proposed as: (formula: see text) with tE as time of adolescence whilst WE would be the final height when omitting the puberal growth spurt which can approximately be taken into account by adding the term (formula: see text), where t is the half-spurt time. Calculations mainly based on the height/age tables of Maaser (1974) and using non linear regression show a close agreement with natural development. Graphs with the growth and increase functions for female and male added for better comprehension.
由于几十年来人们观察到了身高增长加速现象，因此获得男孩和女孩身高发育的数学表达式就更加必要了。乍一看，在青春期前阶段，身高曲线与简单的抛物线并无太大差异。实际上，当应用幂函数时，这种关系可以得到很好的近似：W = W0 + ktr；其中W0代表出生时的身长，t代表时间，k和r为系数。当达到大约10岁时，这个公式必须用一个限制项进行修正，该限制项为：（公式：见原文），其中tE为青春期时间，而WE为忽略青春期生长突增后的最终身高，通过添加项（公式：见原文）可以大致考虑青春期生长突增，其中t为突增时间的一半。主要基于Maaser（1974年）的身高/年龄表并使用非线性回归进行的计算表明，其与自然发育情况高度吻合。为便于理解，添加了女性和男性生长及增长函数的图表。
