MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

7 GEOMETRY IN THE PLANE. CARTESIAN PLANE. ALGEBRA.
7.1 AREA OF A RECTANGLE.

That area is expressed by the amount of unit squares contained within its surface. If the linear

unit is contained exactly an integer number of times in both sides of the rectangle, it is evident

that the area amounts to b×a= 4 ×2 = 8 unit squares.

If we consider the small side of the rectangle as the linear unit, the area of the small rectangle

left aside is equivalent to the fraction of unit square expressing the decimal part of the big side.

Therefore, in all cases the product of its base times the height defines the area of a rectangle.

7.2.1 BINOMIAL PRODUCT

()() 4 x+a× 2 x+b = 8 x^2 + 2 xa+ 4 xb+ab

Once the paper is folded to get the figure, we can see that the second member of the expression

above relates to the sum of areas of the four correspondent rectangles.

1

b

1 a 1 1 X X X b

a