MATHEMATICS AND ORIGAMI

Mathematics and Origami

Something similar can be said about lines h and b which determine the other vertices of the
heptagon:

2 2 cos^21

2

=tgβ= = ω

g

t

[]

r

−g

cosπ− 2 ω 1 =

r

g 2 g

2

= ; r = 4

r

g

cos 2 ω 1 =

3 2 cos (^31)
2
=tgγ= = ω
a
t
[]
r
−a
cosπ− 3 ω 1 =
r
a 2 a
2
= ; r = 4
r
a
cos 3 ω 1 =
That is, in the case we are discussing, we always reach 4 for the value of the heptagon
radius.
Therefore, the heptagon folding process will be as follows:
Figure 3

• Begin with a square of paper.


• Set on it the required quadrille centred at O, to get points I (-2,0) and F (1,-2).


• Simultaneously fold over the respective axles: I on the ordinates and F on the ab-
  scissas. And that, in the three possible ways.


• Thus, key points A, B, C are obtained.
  Figure 4


• Get the folds: AH (through A); h (through B); b (through C).


• Fold: V → AH; O → O to get vertex R and its symmetric.


• Same: R → h; O → O to get both vertices on h.


• Fold around O the latter couple of vertices, to lie on b.

I O

F

I

F

O X ́

R A

V

Y ́

a

b

g

h

H

(^34)
A
C
B B
C