How Did Rene Descartes Build Cartesian Coordinates

René Descartes created Cartesian coordinates in order to study geometry algebraically. This form of math involves a plane with a horizontal axis and a vertical axis, named X and Y. As in geometry, both axes, as well as the plane, go on into infinity. Along the axes, points are numbered so that with only two numbers (for example -5, 7) one can know exactly where on the chart to look. This is very useful in computer programming because a computer screen is set up similarly to the Cartesian coordinate plane. Cartesian coordinates can also be used in determining the best places for a fire station in a town. In addition, latitude and longitude lines are based off Cartesian coordinates, and thus are helpful in finding an exact location on a globe.

This system uses a plane and two perpendicular axes, named X and Y. Points along the axes are numbered through infinity in every direction, starting at zero where the axes cross, which is called the origin. Using this system, any point on the plane can be described with only two numbers: the position on the X axis, followed by the position on the Y axis. So -5, 7 would be five to the left of the Y axis, and seven above the X axis. Through equations, lines and shapes can be found as well. Y=mX+b is the equation for a straight line, thus Y=1X+0, shortened to Y=X, is when a line evenly bisects the origin, rising as it gets further to the right.

A computer screen, which is two-dimensional, much like a plane, is the most obvious use for Cartesian coordinates. On a computer screen, the corner is the origin so that all numbers are positive. Each pixel is a point, and is given a number. For computer links, a rectangle is set up using the points of the four corners. Everything inside these four points is part of what is called a hot spot over the word linking one page to another. When somewhere on the hot spot is clicked, a command is sent through the computer to go to the specified

The equator (0˚ latitude) and the prime meridian (0˚ longitude) are given the roles of the X and Y axes. For example, Boston is located at about 42˚N 71˚W. If one wanted to know how far a flight would be to Los Angeles (34˚N 118˚W), the equation d=3963arccos[sin(latitude1)sin(latitude2)+cos(latitude1)cos(latitude2)cos(longitude2-longitude1)] would be used. This equation is different from the one used for the fire station because this brings into account the curvature of the earth. In this example, Boston would be latitude1 and longitude1, and Los Angeles would be latitude2 and longitude2. Both locations would be expressed in radians. Thus, before putting them into to equation, each coordinate should be multiplied by2π/360 to convert the latitude and longitude