MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

8.2.7 ANOTHER CURIOSITY

Right-angled triangle ABC is the result of the two successive folds.

To prove it we ought to see first that points B,E,C are in line. Ang BEC is a straight one as it is

the sum of angles in F and D, pertaining to the square. Besides, AE = AD = AF. Therefore EA

is a unique line perpendicular to BC.

On the other hand, straight angle in A gives:

180 =() 90 −α 2 + 2 γ = 180 − 2 α+ 2 γ ; α=γ

At the end we have that ang EAC= 90 −α= 90 −γ

ang BAC = ang EAC +γ = 90

F

B

D

E

=

=

C

A A

B

C F

A

B

C

45º

60º

=

=

A

C

B

A

C

B F

A

C D

F

E

Interlude