Compass and straightedge construction, also known as ruler and compass construction, is a geometric construction method that uses only two basic tools - a compass and a straightedge - to create various geometric shapes and figures.
The compass is a drawing instrument with two adjustable arms connected by a hinge. It is used to draw circles and arcs of various sizes. The straightedge, typically a ruler or straight piece of wood or metal, is used to draw straight lines and mark distances.
In compass and straightedge construction, specific geometric constructions are made by creating precise relationships between points, lines, and circles using these two tools. A point is marked as the center of a circle or the intersection of lines, and distances are measured with the straightedge.
This construction method is based on the principles of Euclidean geometry and has been used for centuries in fields such as mathematics, architecture, and art. It allows for the precise creation of shapes, angles, and symmetrical figures, and is particularly useful when a high degree of accuracy is required.
Compass and straightedge constructions can be used to perform a wide range of tasks, including drawing equilateral triangles, bisecting angles, constructing perpendicular lines, and finding the midpoint of a line segment. Although this construction method has its limitations, it provides a fundamental and practical approach to creating geometric constructions efficiently and accurately.
