Straightedge

A straightedge or straight edge is a tool used for drawing straight lines, or checking their straightness. If it has equally spaced markings along its length, it is usually called a ruler. Straightedges are used in the automotive service and machining industry to check the flatness of machined mating surfaces. They are also used in the decorating industry for cutting and hanging wallpaper. True straightness can in some cases be checked by using a laser line level as an optical straightedge: it can illuminate an accurately straight line on a flat surface such as the edge of a plank or shelf. A pair of straightedges called winding sticks are used in woodworking to make warping easier to perceive in pieces of wood. Three straight edges can be used to test and calibrate themselves to a certain extent, however this procedure does not control twist. For accurate calibration of a straight edge, a surface plate must be used. Compass and straightedge An idealized straightedge is used in compass-and-straightedge constructions in plane geometry. It may be used: Given two points, to draw the line connecting them Given a point and a circle, to draw either tangent Given two circles, to draw any of their common tangents Or any of the other numerous geometric constructions The idealized straightedge is: Infinitely long Infinitesimally thin (i.e. point width) Always assumed to be without graduations or marks, or the ability to mark Able to be aligned to two points with infinite precision to draw a line through them It may not be marked or used together with the compass so as to transfer the length of one segment to another. It is possible to do all compass and straightedge constructions without the straightedge. That is, it is possible, using only a compass, to find the intersection of two lines given two points on each, and to find the tangent points to circles. It is not, however, possible to do all constructions using only a straightedge. It is possible to do them with straightedge alone given a circle and its center.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (4)

Related lectures (2)

Introduction to Euclidean Elements

Introduces the fundamental concepts of Euclidean geometry and the Elements of Euclid, exploring historical background, key propositions, and postulates.

Constructing Polygons: Euclidean Geometry

Explores algebraic divisions, geometric constructions, Luca Pacioli's contributions, and the constructibility of regular polygons.

Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass. In 1837, Pierre Wantzel proved that the problem, as stated, is impossible to solve for arbitrary angles. However, some special angles can be trisected: for example, it is trivial to trisect a right angle (that is, to construct an angle of 30 degrees).

In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances.