The Cartesian Coordinate System
The Cartesian coordinate system was invented by Descartes during his studies, and it is vital to the development of modern mathematics. The Cartesian coordinate system is a plane in which you can graph a specific set of numbers as ordered pairs. These points are based off the x and y axes, which separate the graph into four quadrants (shown left). Shapes, curves, and lines can be graphed using the formulas and equations developed by Descartes. Descartes also developed a 3D system in which 3D figures such as cubes and prisms can be graphed. It is important to graphing figures to find their equations and analyze how they are graphed.
Importance of the System
Descartes invention of the Cartesian coordinate system is important to modern math in many ways. It is a bridge between algebra and geometry, and it can help mathematicians better understand how more than one mathematics are connected. The system helped Descartes invent analytic geometry as well.
Analytic Geometry
Analytic geometry is the study of geometry using the Cartesian coordinate system and thinking about how it connects to other fields of math, like algebra and analysis. Descartes is accredited to being the "Father of Analytic Geometry" because of his major advancements. Using this system, Descartes could examine how algebra was connected to graphing, and how that is translated into other fields of mathematics. He drew lines, curves, and shapes in the plane, found their equations, and extracted numerical information to better understand how these ideas worked the way they did. Descartes goes more in depth on this concept in his essay La Geometrie, which is introduced by one of his most revered works Discourse on the Method.
Discourse on the Method and Its Content
One of René Descartes many works, Discourse on the Method is a philosophical autobiography that was published in 1637. The novel is about Descartes’ ideas on philosophy, mathematics, and skepticism. In it, he doubts any previous theories so he can develop his own ideas. The book is an introduction to La Géométrie, which contains the first explanation of the Cartesian coordinate system. This novel was one of his most important because it states most of the concepts used in modern philosophy.
In this book, Descartes first uses the quote "I think, therefore I am," which is still widely used today as well.
In this book, Descartes first uses the quote "I think, therefore I am," which is still widely used today as well.