The gardener's hyperbolas

Pietro Milici (1) , Frédérique Plantevin (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We propose two new simple constructions of hyperbolas with a string passing through two fixed points (the foci): because of the similarities to the ellipse case, we call such constructions "gardener's." The first construction defines the curve by posing some constraints on the position of the tracing point, the second by the solution of certain tangent conditions. We also study a vertical transposition of the previous horizontal constructions.

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Mathématiques générales [math.GM]

Pietro Milici, Frédérique Plantevin. The gardener's hyperbolas. 2020. ⟨hal-02889469⟩