MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

18.8.2 The CUBE of the sum of two numbers

We know that the square of a binomial r + s (Fig. 1) is (see Point 7.2.1):

()()()r s r s r s r^2 s^22 rs

2

+ = + + = + +

I.e., the sum of two different squares and two equal rectangles.

Let ́s see now, as an analogy, what is the value of the cube of binomial a + b.

Let the cube of side a (Fig.2), and the cube of side b (Fig. 3).

Algebraically we know that

()()()()a b a b a b a b a^3 b^3 a^2 b b^2 a

3

+ = + + + = + + 3 + 3

that is, the cube of side a + b (Fig. 4) may be considered as made up by both cubes of

Figs. 2 and 3, three parallelepipeds same as Fig. 5 and another three like that of Fig. 6.

rs

1 r

s