(2) Using the image properties of the function, various problems can be handled conveniently and intuitively.
Plane rectangular coordinate system was invented by French mathematician Descartes.
Before Descartes, geometry and algebra were two different research fields in mathematics. Descartes stood at the height of methodology and natural philosophy, and thought that Greek geometry relied too much on graphics, which bound people's imagination. For algebra, which was popular at that time, he felt that it was completely subordinate to laws and formulas and could not be a science to improve intelligence. Therefore, he proposed that we must combine the advantages of geometry and algebra to establish a "real mathematics".
The core of Descartes' thought is to reduce geometric problems to algebraic problems, calculate and prove them by algebraic methods, and finally solve geometric problems. According to this idea, he founded what we now call analytic geometry.
1637, Descartes published geometry and founded the plane rectangular coordinate system. He uses the distance from a point on a plane to two fixed straight lines to determine the position of the point, and uses coordinates to describe the point in space. He further founded analytic geometry, showing that geometric problems can not only be reduced to algebraic form, but also be discovered and proved through algebraic transformation.
The appearance of analytic geometry has changed the trend of separation between algebra and geometry since ancient Greece, unified the "number" and "shape" which are opposite to each other, and combined geometric curves with algebraic equations. Descartes' invention laid the foundation for the establishment of calculus, thus opening up a broad field of variable mathematics. The most valuable thing is that Descartes regards the curve as the trajectory of a point from the point of view of motion, and not only establishes the corresponding relationship between a point and a real number. Moreover, the shape (including point, line and surface) and "number" are unified, and the corresponding relationship between curve and equation is established. The establishment of this correspondence not only marks the germination of the concept of function, but also marks the entry of variables into mathematics, which makes a major turning point in the mathematical thinking method-from constant mathematics to variable mathematics.