Drawing a regular hexagon using just a compass (and a straightedge to connect the points) is a fundamental geometric construction. It relies on the fact that the side length of a regular hexagon inscribed in a circle is equal to the radius of that circle.
Here is a straightforward method based on the provided steps:
Steps to Draw a Hexagon
Follow these simple steps using your compass:
-
Draw a Circle:
- Drawing step: Draw a circle.
- Open your compass to your desired radius (this will be the side length of your hexagon). Place the compass point firmly on your paper and draw a complete circle. Mark the center point.
-
Mark the Top Two Corners:
- Drawing step: Mark the top two corners.
- Without changing the compass width, place the compass point on the very top point of the circle (where a vertical line through the center would intersect the circle). Make a small arc or mark on the circle's circumference to the left and another to the right. These mark two vertices of the hexagon.
-
Repeat and Mark the Bottom Two Corners:
- Drawing step: Repeat and mark the bottom two corners.
- Again, without changing the compass width, place the compass point on the very bottom point of the circle. Make a small arc or mark on the circle's circumference to the left and another to the right. These mark two more vertices.
-
Connect the Marked Points to Draw a Hexagon:
- Drawing step: Connect the marked points to draw a hexagon.
- You now have six marked points on the circle's circumference: the original top point, the original bottom point, and the four points you marked in steps 2 and 3. Use a straightedge to connect these six points in sequence around the circle. This forms your regular hexagon.
Visualizing the Process
You can visualize the process like "stepping off" the radius around the circle. Starting from any point on the circumference, if you place the compass point there and make a mark, then move the point to the new mark and make another mark, and so on, you will step around the circle exactly six times, returning to your starting point. The points you marked are the vertices of the regular hexagon. The method described above uses the top and bottom points as convenient starting points to get four vertices quickly, and then uses the existing top/bottom points for the remaining two.
Why This Method Works
The key principle is that the six triangles formed by connecting the vertices of a regular hexagon to the center of the inscribed circle are all equilateral triangles. Since the sides connecting the center to the circumference are radii (length r), the sides connecting the vertices must also be of length r. By setting your compass to the radius and marking points around the circle, you are essentially measuring out segments of length r along the circumference, which are the sides of the hexagon.
Practical Tips
- Use a sharp pencil for more accurate marking.
- Keep the compass width exactly the same throughout steps 2 and 3.
- Hold the compass point steady when making marks on the circle.
Following these steps allows you to accurately construct a regular hexagon using only a compass and a straightedge.
