Straightedge and compass construction

Drawing a pentadecagon

Straightedge and compass construction, also known as ruler-and-compass construction, is drawing of lengths, angles or shapes using only a ruler and compass.

Ruler and compass

Some things cannot be drawn this way. For example, there are only 32 regular polygons with an uneven number of sides which are known to be constructible. It has been proven that a square with the same area as the area of a circle cannot be constructed. This is called "Squaring the circle".

Straightedge And Compass Construction Media

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  Creating a regular hexagon with a straightedge and compass

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  ruler-and-compass

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  CyrkielRB

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  Basic ruler-compass construction demonstration. From left to right:* * Line through two points * Circle through center and perimeter points * Intersection between two lines * Intersection(s) between a circle and a line * Intersection(s) between two circles

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  x = a·b   (intercept theorem)

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  x = a/b   (intercept theorem)

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  x=√a   (geometric mean theorem)

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  Construction of a regular pentagon

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  Trisection of a straight edge procedure.