MATHEMATICS AND ORIGAMI

Mathematics and Origami

Another manner to indicate the revolving angle, is to denote on the folding line the

value of the dihedral angle to build (T. Kawasaki). By so doing, the process data are completed:

Fig. 12 shows a pair of angles on each of the hinges; the set of the first is used in Fig. 13,

whereas the second is for Fig.14 (only approximate values in this case).

It is pertinent to clarify certain things about the three latter figures.

It is evident that in node O of Fig. 12 not all the conditions of Point 8.2.8.5 to flat fold-

ing are fulfilled. The fact is that there is not such a flat folding anymore: what we have pro-

duced is, actually, a 3D form.

We said before that dihedral angles in Fig. 14 have an approximate value. There is not

other alternative: the quadrilaterals of Fig. 12 that are kept as they are in Fig. 13, have, on the

contrary in Fig. 14, their vertices subjected to compound revolutions in such a way that the

former plane figures, are not such any more. Only paper docility allows that manipulation.

The case of Fig. 15 (also by T. Kawasaki) is different though two pair of values are

shown in the hinges: first set for Fig. 16 and second for Fig. 18.

✁

= ✁ = ✁ =

= =

=

=

7

8

75º

A

B

9

A

B

10

A

B

A

11

B

12

180; 30

90; 161

90; 144

90; 169

90; 159

180; 135

180; 127

90; 153

90; 71

90; 165

O