How the line became straight
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How the line became straight book
In algebra, a line is defined by the equation of any two terms, each of which is the product of a constant and the first power of a variable. It might be expressed by the formula ax + by = 0, where a and b are constants, and x and y variables. Plotting the possible values of the two variables by means of Cartesian co-ordinates, the result is a line that is perfectly straight. Other, more complex algebraic functions yield figures of the kind mathematicians call curves. For example, the equation y2 = 4ax generates a parabola. Equations of this kind are called non-linear, even though the curves they specify are composed of lines. It seems as though the quality of straightness has become somehow fundamental to the recognition of lines as lines, not just in the specialized field of mathematics but much more widely. Yet there is no reason, intrinsic to the line itself, why it should be straight. We have already encountered plenty of instances where it is not. Thus our question becomes a historical one: how and why did the line become straight?