MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

10.3.2 HEPTAGON: A QUASI-PERFECT SOLUTION

After the analysis of five different solutions, the one that is presented now is, no doubt,

the best.

The last but one figure shows the obtained heptagon; from the last one we can figure out

the value of the angles of said heptagon (the side of the given square equals 1).

Isosceles ∆BAP has Ang. B = 22,5º

0 , 270598

4 cos 22 , 5

1

PA= =

In ∆APO:

PA = 0,270598 ; Ang. A = 22,5º ;

2

1

AO=

P

AO

O

PA

sen sen

=

O

PA

A

PO

sen sen

=

A+O+P= 180

Solving the system:

Ang. POA = 12,764389º

C

A

F

O

B

D P

A

F

C

B

D

B

F F

A

B P

D

E

O F O

O

A

P

O

P

P

C

B

D

F

A

E

O

P

D

O

F

E

B A

C