Proportion

A sheet of A4 paper is usually made in the size 21x29,5 cm. And why? In fact, a sheet of this size is the "canon", the proportion of many numbers, open to Leonardo da Vinci. It has an amazing property: if you fold a sheet of paper of the size mentioned above twice, the length will become the width and the proportion will remain the same. And no matter how much you fold this way, the proportion will not be disturbed. And only this proportion has this property.

Proportion (Latin proportio - proportionality, alignment of parts, a certain proportion of parts among themselves), the equality of two relations, that is, an equality of the form a: b = c: d.

In the 4th century BC Ancient Greek mathematician Evdoks generalized the notion of proportion to the case of incommensurable quantities (for example, sides and diagonals of a square). Over time, mathematicians came to the realization that the ratio of quantities is a number, which made it possible to move from proportions with the unknown to equations, and from the transformation of proportions to algebraic transformations.