Geometry: Instrument Epicycle

This lecture explores the invention of instruments by artists like Albrecht Dürer to draw complex curves and lines, including twisted columns, not achievable with a ruler. It delves into the historical significance of Dürer's treatise on geometry, focusing on the modeling of instruments described in his work. The lecture discusses the use of mechanical instruments for drawing architectural elements and solving mathematical problems, such as duplicating the cube. It also covers the concept of epicyclic curves, their periodicity, and their role in ancient astronomy. The presentation includes demonstrations of the spider instrument and the anatomical use of epicyclic curves. The lecture concludes with a discussion on the commensurability of epicycle and deferent arms, periodicity criteria, and the distinction between closed and open curves.