Encyclopedia > Straightedge

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This article is about the tool used in geometry. For information on the subculture of the same name, you may want Straight edge instead.
A straightedge is a tool similar to a ruler, but without markings.

An straightedge is used in ruler-and-compass constructions. It may be used to:

  • Given two points, draw the line connecting them.
  • Given a point and a circle, draw either tangent.
  • Given two circles, draw any of their common tangents.
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 straightedge-and-compass 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 by drawing one circle and its center, then using only the straightedge.

Making a straightedge

A real-world straightedge is a practical tool that approximates the idealized mathematical object described above.

Making a practical straightedge without access to a pre-existing straightedge or modern machine tools is an interesting problem in mechanical engineering. One way of doing this is to make a high-quality flat surface first, engineer's blue and polishing techniques, then to shape the straightedge so as to lie flat along the flat surface.

The method of producing accurate flat surfaces using three trial surfaces was invented by Sir Joseph Whitworth in 1830.

Another way of doing this is described in the link at the end of the article.


  • Wayne R. Moore, Foundations of Mechanical Accuracy, Moore Special Tool Company, Bridgeport, CT (1970)

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