Jesús de la Peña Hernández
respect to the vertical. I leave to the ingenious paper-folders the task of getting a pa-
per hyperboloid containing both, u and v generatrices.- All the u generatrices cross to each other; the same happens to the v ones. A genera-
trix u is parallel to the diametrically opposite v as can be easily imagined looking at
the paper constructed hyperboloid. - Any straight-line v intersects all the lines u it comes across between its two ends.
- As any two lines u / v intersect in one point, this point will belong to the hyperboloid
and also to the plane formed by those two lines. In consequence, that plane will be
tangent to the hyperboloid in the afore-said u / v intersection point. - That plane of tangency (Fig. 12), paradoxically does intersect the hyperboloid. It is
nothing extraordinary, though. Fig. 13 shows an antecedent: the tangent to a curve in
one of its inflexion points, cuts the curve, too.
13
Interlude