(untitled) (mathematica didactica, 2005)
This article retells the early history of curve design and optimization from Galilei’s „discorsi” to Joh. Bernoulli’s solution of the brachistochrone problem, the famous origin of the calculus of variations. The didactical intent is threefold: Firstly, it is a beautiful story, which should please and inspire Hans Schupp (and many others) to continue the promotion of curves as a tool of mathematical education. Secondly, it should serve as an outstanding example of the historical creation process of analysis on the grounds of Galilei’s law of falling and gliding bodies and of Fermat’s fundamental speed optimization principle. And last but not least it points out how a creative mistake has become fruitful because the error producer was not condemned but taken seriously.