The intriguing mechanics of a tractrix of cards

Abstract

Figure 1 shows the photograph of a tractrix made of cards. This is a simple yet captivating way to make a tractrix — an arrangement that has recently appeared in some engaging pedagogical resources and literature [1, 2]. When closely spaced cards lean like this, one after another, over a horizontal plane, the contour created is a tractrix — a curve of significance in mathematics, since its revolution around its asymptote produces a pseudosphere: a curved surface with constant negative Gaussian curvature [3, 4].