A Note on Geometric Construction

The whole of plane geometry is based on two figures,the straight line and the circle. Both these figures are defined by two points, say A and B. For drawing these figures, two instruments are available: (i) an unmarked straight edge for drawing a straight line joining A and B and, if necessary, extending the straight line beyond the segment AB on both sides; (ii) a compass for drawing a circle with one of the points A (or B) as centre and passing through the other point B (or A). Attention is drawn to the fact that in Euclid’s original text, the compass is regarded as “collapsible.” This implies that both ends of the compass—the needle and the pencil—must always be in contact with the drawing plane. The compass ‘collapses’ as soon as one of the ends is lifted. This, in turn, means that we cannot transfer distances by using the compass or divider in the manner routinely used in schools. It is necessary to emphasize that neither the straight edge nor the compass can be used for measurement. As Borovik and Gardiner [1] say: “Measuring is an approximate physical action, rather than an exact “mental construction,” and so is not really part of mathematics.” The emphasis is necessary especially in view of our school geometric box instrument set which consists of a marked ruler and a divider. The job of the divider, as said earlier, is routinely carried out in school by using the “real compass” which does not collapse like Euclid’s compass. Such a compass is generally referred to as a “rusty compass.” Note that the use of these instruments for measurement is perfectly acceptable for engineering drawings