# Cartesian coordinates

**Cartesian coordinates** did not appear by accident. Occupying a place in the theater, "according to the tickets bought," we do not even suspect who and when suggested the method of numbering armchairs in rows and places that has become common in our life. It turns out that this idea dawned on the famous philosopher, mathematician and naturalist Rene Descartes (1596-1650) - the very one whose name is given to rectangular Cartesian coordinates. Visiting the Parisian theaters, he never tired of marveling at the confusion, squabbles, and sometimes challenges to the duel, caused by the lack of an elementary order of distribution of the audience in the auditorium.

The Cartesian coordinates he proposed, in which each place received the number of the series and the serial number from the edge, immediately took off all the grounds for discord and made a real sensation in the Parisian high society. The aristocratic theatergoers did not cease to besiege the king with requests to reward the scientist for such a remarkable invention. However, the king persisted, and for this reason: "You say that even the English have no such thing? Yes, Cartesian coordinates are wonderful, yes, this discovery is worthy of the order! But give it to the philosopher? No, that's too much!"

R. Descartes was considered the largest at that time mathematician in Europe. The results of philosophical reflection and natural science experiments Descartes set out in a number of works that brought him wide fame. His Cartesian coordinates quickly spread across Europe, having a profound effect on the minds of his contemporaries.

Each Cartesian coordinate axis is considered as a numerical line, that is, it has a positive direction, and the negative values of the coordinate are assigned to the points on the negative ray (the distance is taken with the minus sign). All Cartesian coordinates in three-dimensional space are divided into two classes - right and left. Usually, by default, the right coordinate systems are tried, and if they are graphically displayed, they also have them, if possible, in one of several usual positions. The figure shows the right coordinate system.

The Cartesian coordinates are also described by a set of unit vectors co-ordinated with the coordinate axes. The number of units is equal to the dimension of the coordinate system and they are all perpendicular to each other. Such units form the basis. In the three-dimensional case such orthes are usually denoted by *i*, *j*, *k* (see the figure).