A regular hexagon, also called a perfect hexagon, has six equal sides and six equal angles. The following steps allow you to draw a perfect hexagon. For an explanation for how this works geometrically, see this tips section.
Step 1
Draw a circle to start the process:
- Widen the compass to about an inch/inch-and-a-half (or whatever seems like an appropriate radius for your circle).
- Tighten the compass so it won't slip.
- Choose a good spot on the paper and poke in the compass point.
- Sweep the compass around in a circle. Sometimes it's easier to do a half-circle in one direction, then come back and do another half-circle in the other direction.
Step 2
Without changing the settings on the compass, move the compass point to the edge of the circle.
Step 3
Poke the compass point into the edge of the circle, and use the pencil end to make a small mark on the edge of the circle.
- Remember, do not change how wide the compass is set.
Step 4
Move the compass point where the mark you just made crosses the edge of the circle.
Step 5
Use the pencil to make another little mark on the edge of the circle.
Step 6
Move the compass point to where this new mark crosses the circle, and make another mark again.
Step 7
Repeat this process until you have six marks.
- By now you should have come back to where the you originally put the point of the compass through the circle's edge.
Step 8
Complete it. The six places where your marks cross the edge of the circle are the six points of your hexagon. Use your ruler and a pencil to draw a straight line segment that connects each one with its immediate neighbors.
Tips
- The point of the pencil on the pair of compasses needs to be kept sharp in order to minimize errors from marks that are too wide.
- If you connect every other mark, instead of all six marks, you will end up with an equilateral triangle.
- A compass (of the sort used for drawing circles) is technically referred to as a pair of compasses, as opposed to a navigator's compass.
Why this works
This method works to create a perfect hexagon by forming 6 equilateral triangles with the radius as the length of all of the sides. The six radii drawn are all of the same length, and the six chords drawn to create the hexagon are each of same length as the radius because the compass width was not changed. Because the six triangles are all equilateral, the angles between the vertices are each 60°.
Warnings
- It is absolutely vital that the compass setting stays the same from the moment you draw the circle through to the end of the process.
- A compass is a sharp instrument; please handle with care to prevent injury.
Things You'll Need
- A circle-drawing pair of compasses (not the magnetic North/South kind used for navigation, but the kind with a pencil on one side and a point on the other)
- Paper
- Something to put under the paper so that the compass point doesn't slip
- Pencil
- Ruler
