Before the end of the European Renaissance, math was cleanly divided into the two separate subjects of geometry and algebra. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. Then, around 1637, a French guy named René Descartes (pronounced "ray-NAY day-CART") came up with a way to put these two subjects together.
Rene Descartes was born on March 31, 1596, in Touraine, France. He was entered into Jesuit College at the age of eight, where he studied for about eight years. Although he studied the classics, logic and philosophy, Descartes only found mathematics to be satisfactory in reaching the truth of the science of nature. He then received a law ...view middle of the document...
This is known as the Cartesian Plane.
Now let’s explore:
You learned about the basic (counting) number line back in elementary school:
Later on, you were introduced to zero and negatives, which completed the number line:
Descartes' breakthrough was in taking a second number line, standing it up on its end, and crossing the first number line at zero:
The Cartesian plane consists of two directed lines that perpendicularly intersect their respective zero points. The horizontal line is called the x-axis and the vertical line is called the y-axis. The point of intersection of the x-axis and the y-axis is called the origin and is denoted by the letter O. The arrows at the ends of the axes indicate the direction in which the numbers are getting larger. Therefore, only the axes should have arrows. The whole flat expanse, top to bottom, side to side, bursting outside, (see below), and stretching off to infinity in all directions, is called the "plane". When you put the two axes in the plane, it is then called the "Cartesian" ("carr-TEE-zhun") plane.
The position of any point on the Cartesian plane is described by using two numbers: (x, y). The first number, x, is the horizontal position of the point from the origin. It is called the x-coordinate. The second number, y, is the vertical position of the point from the origin. It is called the y-coordinate. Since a specific order is used to represent the coordinates, they are called...