MATHEMATICS AND ORIGAMI

Mathematics and Origami

Process is the inverse if we want to get the square root of b:

• Start with points C (-1, 0) and B (b,0).


• Fold: C → y ́; B → B
  Fold AB gives point A(0,a) such that:
  b× 1 =a^2 ; a= b

This process reminds orthogonal billiards, just because of orthogonality, but with the addition

of this nuance: When ball C hits the tableside OY, a virtual reflection AB is produced outside

the table.

7.14.2 CUBES AND CUBIC ROOTS (H.H.)
Iterating the former process we can find out the cube of a (Fig. 1).

• To start with points C (-1,0); A (0,a) to get B (a^2 ,0).


• To draw x ́ such that OA ́= OA.


• To fold: A → x ́; B → B.


• Folding line BD produces OD = a^3.

Justification:

∆ABD is a rectangled one, and therefore:

OB^2 =AO×OD ; ()a =a^4 =a×OD

2 2

; OD=a^3

By working the opposite way as we did in former Point for the square root, we ́ll reach the con-

clusion that OA=^3 OD.

= =

1

C(-1,0)

O

A(0,a)

B(a ,0)

2

y

x

y ́

C(-1,0)

O

1

y

x

y ́

A

D B

A ́ x ́