The origin of the planar Cartesian coordinate system, what is the origin of the planar Cartesian coo

The idea of coordinates was created by the French mathematician and philosopher Descartes.

Legend: One day, Descartes (1596-1650, French philosopher, mathematician, physicist) was sick and bedridden, but his mind never rested, and he was repeatedly thinking about a question: geometric figures are intuitive, while algebraic equations are more abstract, can the equations be represented by geometric figures?

Here, the key is how to link the points that make up the geometry to each set of "numbers" that satisfy the equation. He pondered it desperately. What kind of method can be used to connect "points" and "numbers"?

Suddenly, he saw a spider in the corner of the roof, pulling the silk and hanging down, and after a while, the spider climbed up the silk again, pulling the silk left and right. The spider's "performance" made Descartes' thinking suddenly clear. He thought, you can think of the spider as a point, it can move up, down, left and right in the room, can you use a set of numbers to determine the position of the spider?

He also thought that if the corners of the walls on the ground were taken as the starting point, and the three lines handed over were the three number lines, wouldn't the position of any point in the space be represented by the three sequential numbers found on the three number lines? Conversely, arbitrarily given a set of three ordered numbers, such as , can also be represented by a point p in space. Similarly, a set of numbers (a, b) can be used to represent a point on a plane, and a point on a plane can be represented by a set of two ordered numbers.

So under the inspiration of the spider, Descartes created the Cartesian coordinate system.

References.

The planar Cartesian coordinate system was invented by Descartes, and the coordinate system cleverly linked shapes and numbers.

Two number axes perpendicular to each other on the same plane with a common origin.

It constitutes a planar Cartesian coordinate system, referred to as rectangular coordinate system.

In general, the two number axes are placed in the horizontal and vertical positions, and the orientation to the right and up is the positive direction of the two number axes, respectively.

The horizontal number axis is called the x-axis or horizontal axis, the vertical number axis is called the y-axis or vertical axis, and the x-axis and y-axis are collectively called the coordinate axis.

Their common origin o is called the origin of the Cartesian coordinate system.

The planar Cartesian coordinate system with the point o as the origin is denoted as the planar Cartesian coordinate system xoy.

Draw two number axes that are perpendicular to each other and have a common origin in the plane "two-dimensional", referred to as a Cartesian coordinate system. The Cartesian coordinate system has two axes, of which the horizontal axis is the x-axis.

The orientation to the right is positive; The vertical axis is the y-axis, and the orientation is the positive direction. The plane where the coordinate system is located is called the coordinate plane, and the common origin of the two coordinate axes is called the origin of the planar Cartesian coordinate system.

The x-axis y-axis divides the coordinate plane into four quadrants, and the upper right part is called the first quadrant.

The other three parts are called the second quadrant in a counterclockwise direction.

Quadrant 3 and 4.

The quadrants are bounded by the number axis, and the points and origins on the horizontal and vertical axes are not in any one quadrant. In general, the x-axis and y-axis take the same unit length plane right-angle sitting base starvation system, but in special cases, different unit lengths can also be taken.

There are two axes.

The horizontal axis is the x-axis, and the orientation to the right is the positive direction; The vertical axis is the y-axis, and the orientation is the positive direction.

The planar Cartesian coordinate system is also called the Cartesian coordinate system.

The Descartes and Cartesian coordinate system is said to have been sick and bedridden one day by the Chinese philosopher and mathematician Descartes, who was very ill, but he also repeatedly pondered a question: geometric figures are intuitive, and algebraic equations are relatively abstract, can we combine geometric figures with or attack algebraic equations, in order to achieve this purpose, the key is how to hook the points that make up geometric figures with each set of numbers that satisfy the equations, he pondered and pondered, what way to connect points and numbers. Suddenly, he saw a spider on the corner of the roof, pulling the silk and hanging down, and after a while, the spider climbed up the silk again, pulling the silk left and right.

The spider's performance opened Descartes' train of thought. He thought that the spider could be regarded as a point, and the position of the spider could be determined, and if the corner of the wall on the ground was taken as the starting point, and the three lines handed over were the three number lines, then the position of any point in space could be used to find the three numbers in order on the three number lines. In the same way, a set of numbers xy can represent a point on a plane, and a point on a plane can also be represented by a set of two sequential numbers, which is the prototype of a coordinate system.