MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

! AD = 2

L = 0,7071067 L is the side of square ADBF.

! Triangles BCD, ADC and ABD are isosceles, congruent and right-angled (Point 18.2.1.2);

their three sides are given: hypotenuse CA = L, and both legs AD = 2

L .

! Triangles CDG and GFE are similar: all their angles are, respectively, equal:

FE

GF DG

CD = ; DG = GF ; 4

2

4

2 2 L L

L CD

DG FE= = = = 0,3535533 L

! Triangles BFE and AFE and properly defined: the former is right angled in F; BF = 2

L ;

4

2 FE=L , hence 4

10 4

2 2

2 2 L L L BE  = 

   

  + 

  

 = = 0,7905694 L

! With all that information we can draw Fig. 3 which is the folding diagram of the cube emerging through the dihedral of side AB.

C

A

B

E

F

D

B

3