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To divide a circle into 12 equal segments without calculating angles, use a compass set to the circle’s radius. Mark the four points where horizontal and vertical diameters meet the circle, then step that unchanged compass setting around the circumference to find the other eight points. Draw lines from the center to each mark if you need wedge-shaped segments.
What you need
- A drawing compass and pencil
- A straightedge for drawing the diameters and, if needed, the segment boundaries
The straightedge can be unmarked; the construction does not require a ruler scale or protractor. The method follows the traditional compass-and-straightedge approach described by Math Is Fun’s guide to geometric constructions.
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Mark 12 equal positions on the circle
- Establish the center. Draw the circle with a compass, or use an existing circle whose center is known. Mark the center clearly.
- Draw two diameters. Through the center, draw one horizontal and one vertical line, extending each to the circumference. These four intersections give you the top, right, bottom, and left starting points.
- Keep the compass at the radius. If you drew the circle with the compass, do not change its opening. Otherwise, set it from the center to the circumference. As WOOD magazine contributor Bob Hunter puts it, “Leave your compass set at the radius for which you drew the circle.”
- Step around the circumference. Place the compass point on a cardinal mark and use the pencil end to mark where the radius-length step meets the circle. Repeat from the four cardinal marks to locate the eight intervening positions. Keep the compass opening fixed as you move it.
- Draw the segments, if needed. For twelve wedge-shaped sectors, use the straightedge to connect the center to every circumference mark. If you only need evenly spaced positions, such as clock-hour locations, the circumference marks are enough.
The compass-only stepping procedure is the practical layout method shown in WOOD magazine’s tutorial, updated July 8, 2025.
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Why the marks are evenly spaced
A chord equal in length to the circle’s radius forms an equilateral triangle with the two radii to its endpoints, creating a 60-degree central angle. The cardinal marks provide halfway positions between those steps, so the full circle is divided into twelve equal 30-degree intervals. Open Text BC’s sheet-metal pattern-development lesson and Nick Doe’s “Divvying up a pie or pizza” construction explain equivalent constructions.
Check the layout before using it
Look for twelve marks distributed evenly around the circumference, with the original top, right, bottom, and left points still easy to identify. Small errors can creep in if the compass slips, its opening changes, or the center is misplaced. The cited construction sources describe ideal geometry, not a measured workshop tolerance; for fabrication, check the layout against the project’s required accuracy.
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When to use a different construction
The radius-stepping approach is quickest when the center and cardinal axes are available and you need either circumference marks or radial sectors. For a more formal straightedge-and-compass explanation, Nick Doe’s construction establishes a six-point, 60-degree framework and bisects the intervals to make twelve parts. Both approaches produce the same division; choose based on whether you want a fast layout or a step-by-step geometric construction.
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