Mittelwertfunktionen und Strophoiden

Zur Genese einer Entdeckung durch Axiomatisierung und Visualisierung

Abstract

The Pythagoreans founded the first theory of mean values. In connection with the mean value named after Nicolas Chuquet (1484) it is possible to give axioms for two variable mean value functions including in particular the Pythagorean mean values. Experiments with different visualizations of mean values from Pappus up to now, especially using software tools for kinematic geometry, exhibit an unexpected association between two variable mean value functions and strophoids.