MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

Taking base GH as reference, the other four sides are congruent to each other and have

a length of 103,52 % of the base.

10.1.5 KNOT TYPE PENTAGON
Start with a paper strip long at least six times its width h. The pentagon is obtained just
producing a knot centred on the strip (1): as it was a string, but adequately adjusting the folds.
Do not flatten till the vertices are properly fastened. The result is a perfect convex regular pen-
tagon as we are going to see (2).

First, note in (3), the three quadrilaterals

AXDE ; ABYE ; ABCZ

The three of them are parallelograms: They are determined by overlapping of two por-

tions of the strip, obviously, of the same width. If we recall Point1.3.2 fig.1, we ́ll see that those

parallelograms have congruent opposite sides and also congruent adjacent sides.

Therefore, if ABCZ has an area S, it is:

S = BC × h = AB × h that is BC = AB

Consequently, the three parallelograms are congruent rhombs with all their respective

sides and angles also congruent.

As these three rhombs display some common sides, we are able to mark in pentagon (4)

sides and angles congruency:

CB = BA = AE = ED = l ; Ang. B = Ang. A = Ang. E

A

B

C

X

Y

Z

D

E

h

1 2

3

F

A

O

C

(^5) D
E
11.25º
B V
J ́
G
H
C