The Cartesian Coordinate System Research Paper Example | Topics and Well Written Essays - 1250 words

The Cartesian Coordinate System - Research Paper Example The Cartesian Coordinate System does not merely point reference to the graphical means of finding link between variables, rather, it gives Mathematics the desired image of identity in visible shapes and forms by which a learner can gain appreciation of the course as an interesting field of study. The Cartesian Coordinate System Prior to the concept of a two-dimensional system, the discovery of a coordinate system with one dimension had already enabled demonstration of the relative magnitudes of numbers in a graphical manner and had even shown how a distance between two points in the number line may be represented by the magnitude of their differences. The overall advantage, however, of a one-dimensional coordinate system is limited and is unable to extend its applicability to the relation or dependence of two sets of numbers quite significant in the mathematical studies of corresponding values wherein a set constituted by an ordered pair of numbers may be held in association to another or a couple other sets in a planar system of coordinates (Vance, p. 75). Importance of the Cartesian Coordinate System In 1637 Rene Descartes, a French mathematician and philosopher, used the Rectangular Cartesian System of Coordinates or a method of associating points with numbers, and by doing so. , associated a curve with its equation. Great progress in mathematics and the application of mathematics in science followed after this unification of algebra and geometry (Smoller). By definition of the Cartesian product of two sets, the case of interest is X ? Y where X and Y are both the set of real numbers R is symbolically denoted R x R ? { (x, y) | x ? R and y ? R }. Each member of the set is an ordered pair (x, y) and through the Cartesian coordinate system, it is possible to set up an association between this set of all ordered pairs (x, y) of R x R and the set of all points in the plane. Hence, the two-dimensional coordinate system becomes important in relating a point in a plane and a pair of real numbers which may be constructed using two perpendicular straight lines, vertical and horizontal, commonly known as the coordinate axes. With the point of intersection being the origin O, one may establish on each line a one-dimensional system which bears the same unit of length f or both axes where, normally, the horizontal line refers to the x-axis or axis of the values of ‘x’ or abscissa whereas the vertical line pertains to the y-axis along which lie the values of ‘y’ called the ordinates. Once the axes are drawn, one can begin to plot a data of points (x, y) and in determining a point corresponding to an ordered pair of values, it helps to draw lines parallel to the axes through the point (x1, 0) on the x-axis and the point (0, y1) on the y-axis (Vance, 76). These lines intersect at a point P, a distance x1 from the y-axis (to the right or left, depending upon whether x1 is positive or negative) and a distance y1 from the x-axis (above or below, depending upon whether y1 is positive or negative). These distances can be called directed distances and the point P, determined by the ordered pair of values x1 and y1, is denoted by the ordered pair, expressed as (x1, y1), where x1 and y1 are called coordinates of P. The two coordinate axes divide the plane into four parts, called the first, second, third, and fourth quadrants. It is useful to verify that the coordinates of points located in the different quadrants have the signs shown in the table. Quadrants Abscissa Ordinate I + + II _ + III _ _ IV + _ Since every other point may be plotted on the xy-plane, the line or curve connecting the