Diversity, Simplicity and Selection of Geometric Constructions: The Case of the n-Section of a Straight Line

This article is a study of geometric constructions. We consider, as an illustration, the methods used for dividing the straight line into n equal parts (n-section). Architects and practicioners of classical Europe had at their disposal a broad range of geometric constructions: ancient ones were edited and translated, whereas new solutions were constantly published. The wide variety and reasons for selection of these geometric constructions are puzzling: the most widespread construction was not the simplest one. This article wonders why so many constructions were used to solve the same problem and why tedious methods were used. It is argued that the practical conditions and scale at which the problem was tackled could account for such diversity.