Instructions on Drawing Polygons Using a Compass

The compass makes both arcs and circles.

Polygons are two-dimensional figures with three or more sides, such as triangles, diamonds or octagons. A compass commonly makes circles and arcs, but the points where circles and arcs bisect each other become the points of the polygon. Using a circle as the outer boundary of the polygon ensures that the angles are all equidistant from the center of the shape. Bisecting the radius, the distance from the edge of the circle to the center, with the compass creates a perfect pentagon.

Things You'll Need

• Ruler

Instructions

1. Draw a circle with the compass. Place the leg of the compass on the paper. The leg has a slightly pointed end that may puncture the paper if pressed. Touch the pencil on the paper. Keeping the leg stable, as a point of rotation, move the pencil around the leg. The track of the pencil leaves a perfect circle.

2. Measure the radius with the ruler. Find the center point of the radius.

3. Place the leg of the compass on the edge of the circle. Place the pencil of the compass on the center point of the radius. Make another circle.

4. Move the leg of the compass to the point where the edges of the two circles cross. Keeping the distance between the leg and the pencil of the compass steady, make a third circle.

5. Repeat all the way around the larger circle. Always making a new, smaller circle where the line of the previous small circle crosses the line of the larger one. You will draw ten circles around the outside of the larger circle.

6. Mark the points on the edge of the large circle where two smaller circles cross the line of the larger one. There are ten points around the edge where all three lines will come together.

7. Draw straight lines from every other marked point to create a perfect pentagram. Draw lines from each marked point to the next to create a perfect decagon, or ten-sided polygon.

Tips & Warnings

• Other polygons use different measurements. For example, using a quarter of the radial measurement for the diameter of the smaller circles means that you will draw twenty small circles around the outer circle. Using the bisecting arcs as angles results in a twenty sided polygon. Using one and one half times the radius or three quarters of the total diameter results in a perfect equilateral triangle, or a hexagon depending on which bisecting arcs you use as your angles.

• Irregular polygons use different radial measurements for each side and angle.

References

• Hyperflight: Pentagon Construction
• Townsend University: Regular Polygons and the Geometer's Sketchpad