Conics constructions by pins and string: tangential and physical properties

Pietro Milici, Massimo Salvi

We introduce conic sections' construction by pins and string, without rigid linear components. In addition to well-known methods (as gardener's ellipse), we analyze some recent constructions based on tangent properties and, as an original contribution, extend these constructions to all kinds of conics. In this setting, the physical analysis of the string's tension permits us to smoothly analyze these constructions since the first years of high school. From a didactical perspective, we think that such ideas can be fruitfully adopted in laboratory activities to deepen the tangential properties of conics by a rich interaction between mathematics and physics. Furthermore, the simplicity of the required materials allows the introduction of these manipulative activities in distance learning.