Geometric constructions use only a compass and ruler to draw accurate figures without measuring angles or lines. They are used in engineering and education, and can create various shapes. Architects and engineers need to know this for precise drawings, and it is still taught despite CAD systems.
Geometric constructions, also called Euclidean constructions after the ancient Greek mathematician Euclid, are geometrically correct figures that are drawn using only a compass and ruler. In creating a geometric construction, no angle and line measurements are taken, and no rulers are used except as rulers. This method can be used in technical design writing in engineering and as a way to teach students the fundamentals of geometric theory.
A drawing compass is a tool used to draw arcs and circles. It consists of two legs connected by an adjustable central hinge, with one leg ending in a spike and the other with a lead at its end. The device is used by attaching the pointed end to paper and inscribing an arc or circle by rotating the pencil end around this fixed centre. Different sized circles and arcs can be drawn by adjusting the center hinge to a wider or narrower angle.
Rulers are used in geometric construction to draw lines and can be any object with a perfectly straight edge. Rulers are often used, although the markings should be ignored in creating the construction. Drawing triangles, which are flat right triangles of plastic or metal used in engineering drawing, are another popular choice for a ruler, although the angles of the triangle shouldn’t be used to create the construction.
Many different geometric figures can be constructed using just the two tools mentioned above. For example, to construct an equilateral triangle, a line segment is first drawn using the ruler. Suppose this line has endpoints A and B. The compass is fixed at point A and extended so that the lead of the pencil touches B. An arc is drawn through B to a point above AB.
Next, the compass is fixed at point B and another arc is drawn using the same radius, so that the points intersect above line AB. Using the ruler, a line is drawn from this intersection point to point A and another to point B. The three lines that have been created now form a perfect equilateral triangle.
Geometric constructions are useful for teaching how geometric figures are related, but are also used in non-academic contexts. Architects and engineers need to know the elements of geometric constructions in order to create precise engineering drawings for machinery or building designs. Although automated computer-aided design (CAD) systems have replaced manual drafting in most engineering contexts, geometric constructions are still widely taught as background information for understanding design principles.
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