Duplicating the cube with GeoGebra

Abstract

In this work, we present dynamic experiments addressing the two strategies proposed by the Greek mathematician Menaecmo to duplicate the cube through conic sections, thus relating analytical geometry and the history of mathematics. These strategies allow us to determine the edge measurement of the duplicate cube using two parabolas or a parabola and a hyperbola. In dynamic activities, organized with GeoGebra and accessed via external links, we employ sliders to establish/vary the parameters that satisfy Menaecmo's two conditions. The activities were designed to contextualize the study of conic sections in the analytical geometry courses of the Mathematics-Teaching Degree and the Professional Master's Degree in Mathematics on a National Network – PROFMAT. The activities can also be adapted for High School. We conclude that GeoGebra is the ideal tool to represent cube duplication dynamically.