Geometry - Constructions

Another lasting influence of Euclid's Elements is the emphasis which is placed on constructions. Three of the five postulates on which Euclid based his geometry describe simple drawings and the conditions under which they can be made. One such drawing (construction) is the circle. It can be drawn if one knows where its center and one point on it are. Another construction is drawing a line segment between two given points. A third is extending a given line segment. These are the so-called ruler-and-compass constructions upon which Euclidean geometry is based.

Modern courses in geometry are frequently based on other postulates. Some, for example, permit one to use a protractor to draw and measure angles; some allow the use of a scale to measure distances. Even so, the traditional limitations which the Euclidean postulates placed on constructions are often observed. Protractors, scales, and other drawing tools which would be easier and more accurate to use are forbidden. Constructions become puzzles, intriguing but separate from the logical structure of the course, and not overly practical.