Jesús de la Peña Hernández
21.4.2 PAPER-FOLDED VERSION
To start with a square of paper, pleat-folded to Fig. 1. The result is a collapsed flat fig-
ure in which the square ́s diagonals end up in coincidence with its sides.The unfolding of this figure yields a complete hyperbolic paraboloid with equal pa-
rabolas both, generatrix and directrix, though in each case their parameters differ depending on
the degree of unfolding (Fig. 2).Because of its shape, the hyperbolic paraboloid is familiarly called the saddle. If we
suppose it set on horseback (Fig. 3) and cut by planes, we get the following conics (remind that
the horse also has bilateral symmetry):
Parabolas:- The planes parallel to the symmetry plane of the horse.
- The vertical planes that in turn are perpendicular to the aforesaid horse plane.
Hyperbolas: - The planes parallel to the ground. This circumstance determines the adjective “hy-
perbolic” added to the noun paraboloid.
1
2