Tell the story of Descartes inventing rectangular coordinate system. Descartes was born into a noble family. Although he is gifted, he has been in poor health since he was a child and often falls ill. One day, he became ill again. Sick Descartes is still thinking about how to combine algebra with geometry. Suddenly, a spider weaving a web in the corner caught his attention. The spider climbed up and down, twitched left and right, and finally made a big net in the corner.
Inspired by the spider web, Descartes found that the spider can be regarded as a point, and every position it moves in space can be represented by a set of definite numbers. Descartes regarded the angle as a point and called it the "origin". The three lines extending from the angle-two horizontal lines and one vertical line-are like three vertical axes.
In this space composed of three orthogonal number axes intersecting at a point, the position of each point can be represented by its values on different number axes, for example, written as P(x, y, z). This is the prototype of Cartesian Cartesian coordinate system. With the help of such mathematical tools, Descartes skillfully combined "number" with "shape", which greatly broadened the field of mathematical research.
Descartes' invention of rectangular coordinate system is closely related to his philosophical thought from another angle. Unlike Bacon's advocacy of scientific induction, Descartes advocated mathematical deduction. He believes that mathematics has the certainty that other disciplines do not have, which is necessary for philosophical research and methodology research; In addition, compared with induction, deduction is inevitable because it strictly follows a certain logical reasoning structure and is not affected by facts.
Geometry is intuitive, algebra is abstract and accurate. If there is a way to combine the two, it would be perfect. Cartesian coordinate system was invented based on this idea; It is precisely because of the rectangular coordinate system that geometry has developed a branch of analytic geometry.