Compass and straightedge refer to classical construction tools used in Euclidean geometry, allowing for the creation of precise geometric shapes and constructions. The compass is a drawing instrument with two pointed legs joined at a hinge, which can be adjusted to different distances, enabling the drawing of circles and arcs of a particular radius. It is typically used in combination with the straightedge, a ruler with a straight edge, to create straight lines and measure distances.
These tools are fundamental in classical geometric constructions, where precise geometric shapes are created using only these instruments and without the use of measurements or modern technology. Compass and straightedge constructions rely on the properties of Euclidean geometry, such as the ability to bisect a line, to find the midpoint of a line, to construct perpendiculars, and so on.
The compass and straightedge are essential in Euclidean geometry, primarily because they enable the construction of complex geometric figures, such as triangles, quadrilaterals, and circles. They can also be used to solve geometric problems, including angle trisection, the duplication of a cube, and the construction of certain regular polygons.
By using the compass and straightedge, mathematicians and geometers have been able to create and explore a vast array of geometric constructions and proofs throughout history. While modern technology has made mathematical constructions easier and more precise, the compass and straightedge remain fundamental tools in teaching and understanding Euclidean geometry.
