How to Construct Octagons With a Compass
Eight-sided polygons, called octagons, are often constructed inside a circle using a compass and a straight edge. The points created by equally spaced diameters create the octagon's vertices, which you can then connect to form its sides. The compass not only serves to create the circle that defines the vertices, but also to create the arcs that define the lines that bisect each angle. Therefore, although an octagon has no curves, the compass remains your most important construction tool.
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Instructions
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Draw a line segment the length you want the widest point of the octagon to become. Label one end of the line as "A" and the other as "B."
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Adjust the width of the compass to the length of line, from point A to point B.
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Anchor the compass on point A and draw an arc above and below the line.
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Anchor the compass on point B and draw an arc above and below the line. These two arcs should intersect with the arcs created from point A.
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Draw a straight line through the points of intersection between the arcs with a straight edge. This is the perpendicular bisector of line AB. Label the point of bisection "C."
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Adjust the width of the compass to the length of line AC.
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Anchor the compass on point C and draw a circle. It should run through points A and B, so that C is the midpoint of the circle and line AB is the diameter. Name it circle C.
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Label the points at which the perpendicular bisector crosses the circle "D" and "E."
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Anchor the compass on point B and create an arc between points B and D.
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Anchor the compass on point D and create an arc between points B and D.
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Draw a line through the point of intersection between the arcs using a straight edge. It should pass through both sides of the circle and bisect the angle between line AB and the perpendicular bisector.
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Label the points where the line intersects the circle "F" and "G."
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Anchor the compass on point A and create an arc between points A and D.
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Anchor the compass on point D and create an arc between points A and D.
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Draw a line through the points of intersection between the arcs using a straight edge. It should pass through both sides of the circle and bisect the angle between line AB and the perpendicular bisector.
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Label the points where the line intersects the circle "H" and "I."
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Connect the eight points on the line using a straight edge. This creates an octagon.
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Erase the circle.
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References
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