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.
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Présente les concepts fondamentaux de la géométrie euclidienne et les éléments d'Euclid, explorant le contexte historique, les propositions clés et les postulats.
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.
La trisection de l'angle est un problème classique de mathématiques. C'est un problème géométrique, faisant partie des trois grands problèmes de l'Antiquité, avec la quadrature du cercle et la duplication du cube. Ce problème consiste à diviser un angle en trois parties égales, à l'aide d'une règle et d'un compas. Sous cette forme, le problème (comme les deux autres) n'a pas de solution, ce qui fut démontré par Pierre-Laurent Wantzel en 1837.
Euclide a fondé sa géométrie sur un système d'axiomes qui assure en particulier qu'il est toujours possible de tracer une droite passant par deux points donnés et qu'il est toujours possible de tracer un cercle de centre donné et passant par un point donné. La géométrie euclidienne est donc la géométrie des droites et des cercles, donc de la règle (non graduée) et du compas. L'intuition d'Euclide était que tout nombre pouvait être construit, ou « obtenu », à l'aide de ces deux instruments.