Plane (or Euclidean) geometry is the branch of mathematics that studies figures (such as points, lines, and angles) constructed only with the use of the straightedge and the compass. It is primarily concerned with such problems as determining the areas and diameters of two-dimensional figures. To determine geometric designs four important tools of geometry—compass, straightedge, protractor, and ruler—are used. Technically a true geometric construction with Euclidian tools, originally used by the ancient Greeks, uses only a compass or a straightedge. The ruler and protractor were later inventions. Today, the study of geometry is an essential part of the training of such professionals as mathematicians, engineers, physicists, architects, and draftspersons.

As early as 2000 B.C.E. geometers were concerned with such problems as measuring the sizes of fields and irrigation systems, and laying out accurate right angles for corners of buildings and monuments...