Mathematics and Origami

We may observe that odd segments succession is a geometric progression with ratio 1 / 2. Same
happens with even segments.
Let ́s calculate the ratio of any two consecutive terms:

2

2

2 1

2

2

1

=

−

−

=

AB

BC

2

2

2

2

2

1

2

= = =

BC

AB

BC

CD

2

2

2

= =

CD

BC

CD

DE

2

2

2

= =

DE

CD

DE

EF

Therefore,

2

2

r=

Let ́s figure out the sum of all the terms of this progression. Applying formula (1) and bearing
in mind that an → 0, we have:

( )

2

1

2

2

2 1

1

(^1) =
−
− −

−
−

r
a
S
Which shows that such sum has equal value than the square`s diagonal, as it should be.
Interlude