MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

so, it will be

9. 2

1. 111 1

2. 2458 1. 111 1. 4742

=

−

× −

S=

on the other hand, if we add up the 5 terms of the progression we also have:

9. 2

5

1

∑ =

=

=

i

i

ai

Now we shall construct, by folding, a decreasing geometric progression (r < 1). See Fig. 2.

We can get straight away points B and C (C is the center of the square): Process to get succes-

sive points is as follows:
Fold Is got
O → BD
O → CE
O → DF
O → EG
..........................
Now we are going to see that segments AB, BC, CD, DE, EF, ....... are the terms of a decreas-
ing geometric progression.
If we assume that side of the square is one unit, then:
OA= 2 ; OB= 1 ;
2

1

BD= ;

4

1

DF= ..............

therefore, the respective segments will measure:

AB= 2 − 1

2

2

1

2

2

BC= −AB= −

2

1

2

2

2

1

CD= 2 − −BC−AB= −

4

2

2

1

4

2

DE= −CD= −

4

1

4

2

4

1

EF= −DE= − ...........................................

O

A

B

C

D

E

F

2 G