Knowing how to construct polygons accurately is very important in geometry and is also simple. If you have always wondered how to build a regular polygon from a circle, you are reading the right article.
Steps
Method 1 of 2: Using the Protractor
Step 1. Draw a straight line using the protractor
It will be the diameter of the circle (which divides it into two semicircles).
Step 2. Align the protractor with 0 ° and 180 ° on the ends of the line you have drawn and mark the center point
Step 3. Trace the semicircle following the edge of the protractor from 0 ° to 180 °
Step 4. Put the protractor on the other side of the diameter and again position 0 ° and 180 ° on the ends
Step 5. Complete the circle by tracing the outline of the protractor
Step 6. Calculate the angle between the adjacent vertices, α
Since the circle has 360 °, divide 360 ° by, the number of vertices (or sides) to find α.
- α = 360 ° / n
- α is the angle between two lines connecting the center of the circle to adjacent vertices (rays).
- For a dodecagon, = 12. A dodecagon has 12 sides and 12 vertices, so 360 ° divided by 12 = 30 ° and therefore α = 30 °.
Step 7. Mark a point for each subsequent corner
With the protractor, mark the multiples of the angle α calculated in the previous step.
Step 8. Join the points marked on the circumference with segments
For a dodecagon there must be 12 points and 12 sides, since it has 12 vertices.
If the points are outside the circle, simply mark another point on the circumference on the same line that marks the corners. Do it for all the points and then merge them
Step 9. Check that the sides are all the same length
If they are, you can clear the circle.
Step 10. Done
Method 2 of 2: Using Compass, Ruler and Calculator
Step 1. Draw a circle with the desired radius measurement, r
Set the compass to measure the radius, r, and draw the circle.
Step 2. Calculate the length ℓ of each side of the regular polygon of n sides.
- ℓ = 2 * r * sin (180 / n)
- 180 / n is in degrees, so make sure your calculator is set to degrees, not radians.
Step 3. Set the compass to length ℓ
Be very accurate and double-check the measurement several times to make sure it is as accurate as possible.
Step 4. Start anywhere on the circumference and mark a point with a dash
Do not change the opening of the compass.
Step 5. Pointing the compass at the mark you just made, mark another point
Continue like this until you find a point that coincides with the first one you marked.
Make sure the compass does not open or close
Step 6. Connect the dots using the ruler
- Check that the sides are all the same length.
- If they are, you are done. Erase the lines used for construction.
Advice
- For the final result, mark all the points with a fine-tipped black pen, then place a piece of tracing paper on top of them, attaching it to the sheet with a paper clip and trace the perimeter carefully in pen or pencil.
- If you are using a mechanical pencil (or mechanical pencil), slowly rotate the pencil as you draw the segments. This will produce more pronounced lines. Otherwise the mine will wear out and the lines will be too thick.
