[Mathematical formulation of human height growth (author's transl)].

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.