The most common and straightforward way to draw an equilateral hexagon is by drawing a regular hexagon. A regular hexagon is a polygon with six equal sides (making it equilateral) and six equal interior angles (making it equiangular). The provided reference describes a method that aligns perfectly with drawing a regular hexagon using a compass and ruler.
Drawing a Regular (Equilateral) Hexagon Step-by-Step
Drawing a regular hexagon is simple using a compass and a straight edge (ruler). Here's how:
- Draw a Circle: Start by using a compass to draw a circle of your desired size. The size of this circle will determine the size of your hexagon. Keep the compass set to this radius. Mark the center of the circle.
- Mark a Starting Point: Draw a horizontal diameter or just pick a point on the circle's circumference to serve as your starting point.
- Divide the Circle: With your compass point placed on the starting point you just marked on the circumference, draw an arc that intersects the circle at two points.
- Continue Marking Points: Move the compass point to one of the new intersection points on the circle and draw another arc that intersects the circle. Continue this process, moving the compass point to each new intersection point along the circumference, until you have marked six equally spaced points around the entire circle. As mentioned in the reference, this process effectively "divided into six equal parts" along the circle's edge.
- Connect the Points: Use your ruler to drawing a straight line between neighboring points along the circle. Connect the first marked point to the second, the second to the third, and so on, until all six points are connected.
Once all six adjacent points on the circle's circumference are connected, you will have successfully drawn a regular hexagon.
Understanding the Method (Based on Reference)
The method described above, and echoed in the reference, works because the side length of a regular hexagon is exactly equal to the radius of the circle it is inscribed within. By using the compass set to the radius to mark points along the circumference, you are effectively stepping off six segments, each equal to the radius, which naturally fall into place as the six vertices of a regular hexagon.
The reference mentions "Turn each section into a triangle by drawing a straight line between neighboring points along the circle." This can be interpreted in a couple of ways, but the key action for drawing the hexagon is drawing the straight line between neighboring points. When you connect adjacent points on the circle that were marked using the radius, you are creating the sides of the hexagon. If you were also to draw lines from the center of the circle to these points, you would form six equilateral triangles, each with sides equal to the radius (and the side length of the hexagon).
Why This Works
Connecting six points on a circle that are spaced apart by the circle's radius creates a polygon with six equal sides. Because these points are equally spaced on the circumference, the shape is also symmetrical, resulting in equal interior angles. Therefore, this method reliably produces a regular hexagon, which is always an equilateral hexagon.
By following these steps, you can easily draw an equilateral hexagon using basic geometric tools.
