MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

17.2 VIRTUAL SURFACES

Let ́s start with Fig. 9 (Point 17.1) to get Fig.1 of present Point 17.2. Thus we have

eliminated both spiroids of Fig. 11 (Point 17.1) to facilitate folding of central part of said Fig.

9.

Present Fig. 1 may be folded flat as shown in Fig.2. But it also

A

O

A

1

O

✁ B B ́

B

B ́

O

2

can be left free-folded in the space producing an elastic form (recall

Figs. 1 and 2, Point 15), due to alternate mountain and valley folds.

That ́s why it is feasible to get a form like that of Fig. 3. In it, all

mountain generatrices are parallel to the horizontal plane (what does

not mean that they will be parallel between them).

Those generatrices in turn, rest on either open polygonals that

tend to the helicoidal spiral curves already seen in Point 17.1.

Fig. 4 shows that pair of curves in such a manner that the

virtual ruled surface determinated by those mountain fold horizontal

generatrices, is a quasi-conoid