MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

Fig. 3 is Fig.1 splitted out by translation, in two half-figures. In Fig. 4 those half-figures

appear folded to the final dihedral obtuse angles of 140º in (XO) and (- XO).

The two 3D half-figures of Fig. 4 are moved to fall in coincidence points D and points

E. Fig. 5 is the result.

To pass from Fig. 5 to final Fig. 2 we must revolve the half-figure at left an angle equal

to O ́FO about DE.

Being F the mid-point of DE, angle O ́FO measures the value of dihedral angle deter-

mined by planes O ́DE and ODE.

With the latter revolution O ́ will fall on O, and so we shall get final Fig. 2. Measuring

in said Fig. 2 we get: angle BCN = 113,329º, Ang. DOX = 123,597º, obtuse dihedral angle in

OX = 140º and Ang. O ́FO = 54,4823º. Ang. (–XOX) = 180 – Ang. O ́FO = 125,5177º.

Fig. 6 is Fig.2 led to total flattening.

6

O X

E; D