Capillarity and the Rectangular Hyperbola

It is generally agreed that making real-world connections in mathematics teaching increases students' motivation and interest and contributes to meaningful and permanent learning. In this paper we propose a simple and fast activity to find a rectangular hyperbola in real life and we show how to operate the data to retrieve a straight line. Since it deals with simple formulas, we believe that it can be useful in a high-school context, either in math or physics class. The activity consists of assembling a wedge with transparent plates (like glass photo frames), dipping it on a liquid and observing the rise of a hyperbola. Instructions are given on how to obtain the coordinates of the liquid/air interface and how to replot them as a straight line, using just a smartphone. For the physics class, an extension is proposed to measure the surface tension of the chosen liquid.