Use a compass to step the circle’s radius around its circumference six times, then connect the marks: neighboring points make a regular hexagon; alternating points make a six-point star. You need only a compass and a straightedge or ruler—no angle calculations or separately measured sides.
What you need
- A compass
- A straightedge or ruler
- A pencil and paper or another surface suitable for drawing
A basic compass-and-ruler set is sufficient for this construction. The method uses the radius of one circle as the repeated spacing, rather than measuring six sides individually.
Mark six equally spaced points on a circle
- Draw a circle large enough for your finished figure. Choose and mark a starting point on its circumference.
- Place the compass point on the starting mark and set the pencil end to the circle’s radius—the distance from the circle’s center to its circumference.
- Without changing the compass span, place its point on the starting mark and make a mark where the arc meets the circumference.
- Move the compass point to the new mark and repeat, stepping around the circle until you have six points in all. Keep the span unchanged so the marks stay equally spaced.
The spacing works because the side of a regular hexagon inscribed in a circle is equal to the circle’s radius. Math Open Reference explains this compass-and-straightedge construction in its regular hexagon construction guide.
Draw a regular hexagon
Use a ruler or straightedge to join each point to the next one around the circumference, then connect the last point back to the starting point. The six consecutive segments form the hexagon’s sides.
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Draw a six-point star
Use the same six marks, but connect every other point rather than neighboring points. Draw one triangle through the first alternating set, then a second triangle through the three points left over. The two overlapping triangles create the six-point star. WOOD magazine’s video description puts the goal this way: “Learn how to draw a perfect 6 pointed star or hexagon without having to use math.”
Choose which construction lines to keep
- Show the method: Leave the circle and stepping marks visible as construction guides.
- Show only the finished figure: Once the outline is complete, erase the circle and guides if you want a clean presentation.
The construction marks and tools are the same for both figures; the difference is which points you connect. Teachoo’s six-point star construction steps also describe connecting alternating points to form the two triangles.
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