MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

We must clarify two things: a) Mountain or valley folds in Figs. 16, 17 and 18 not al-

ways are in correspondence with Fig. 15. The formers are represented after the perspective ́s

point of view. b) Dihedral angle values in Fig. 15 do not exhibit any sign: they are supposed to

have the most significant value offered to the point of view.

Fig. 17 helps to get the two α values for those dihedral angles in Fig. 15:

Dihedral angle in OE = Ang. ACD = 2 Ang. BCD

EA = AB = BD = DE = 1 ;

2

1

CD=

∆BCD is right angled in D, and in it:

DC

BD

tgBCD= ; Ang.BCD=Arctg 2

α=Ang.ACD= 2 Arctg 2 = 109. 47 º

Likewise we would obtain the same α value for the dihedral angle in OB.

Dihedral angle in OA = Ang. EAB = 90º, verifiable in Fig. 16 after the data offered by

the drawing and the programs of calculus that complement CAD. In fact, all dihedral angles

have been calculated in this way.

15

90; 90

90; 90

180; 169.1

; 119.5 90; 79.1 ; 119.5

E A B

O

D