MATHEMATICS AND ORIGAMI

Mathematics and Origami

7.8 SQUARE ROOT OF A NUMBER

This is a particular case of Point 7.7: it ́s a matter of solving a quadratic equation without lineal

term and having a negative independent term:

x^2 −n= 0

Expressions (5) in Point 7.7 take this form:

− 2 b= 0 ; −n=a() 2 c−a (1)

which transform (6) to:

b= 0 ; 











= − +a

a

n

c

2

1

Let ́s apply this to the following example (fig 1): we wish to find out by means of folding, the

square root of 1.600.

We ́ll take arbitrarily a = 60

As a consequence we have 60 16. 6

60

1600

2

1

=











+

−

c=

After folding A over the OX axis around C, we get as result x=± 40

−n=a() 2 c−a = 255.09(2×41.1 – 255.09) = - 44102.5

n = 44100 (the difference is due to error in screen resolution).

a=60 A(0,60)

c=16.6 C(0,16.6)

-40 (^0) +40 X
1
7.9 SQUARE OF A NUMBER
It ́s the inverse of latter exercise.
Suppose we want to find out the square of 210
(the small side of a DIN A4 rectangle).
We take the lower right-hand side cor-
ner over any point A on left-hand side of paper.
The ordinate of A must be greater than 210 to
enable the construction of point C.
Points A and C are obtained after fold-
ing: taking their respective ordinates a,c into (1)
of Point 7.8, it gives:
A(0,255.09)
C(0,41.1)
O (0,0) (210,0)