Clock Work Universe

Fig 1.4 A two-dimensional coordinate system can be used to locate the position of any point in terms of its x- and y-coordinates

Figure 1.4 shows the two-dimensional case, with a grid extending over part of the page. The grid is calibrated (in centimetres) so the position of any point can be specified by giving its x- and y- coordinates on the grid. For example, the coordinates of point A are x = 3cm and y = 4cm.

This idea becomes more powerful when we consider lines and geometrical shapes. The straight line shown in Figure 1.5 is characterized by the fact that, at each
point along the line, the y-coordinate is half the -coordinate. Thus, the x- and
y- coordinates of each point on the line obey the equation y = 0.5x, and this is
said to be the equation of the line.



This is the beginning of a branch of mathematics, called coordinate geometry, which represents geometrical shapes by equations, and which establishes geometrical truths by combining and rearranging those equations.