Download Article
Download Article
Constructing regular polygons accurately is very significant in geometry and is easy to do. If you have ever wondered about how to construct regular polygons from a circle, you’re reading the right article.
Steps
-
Draw a straight line using the protractor. This will be the center line of your circle (dividing it into semi-circles).
-
Align the protractor so that both 0° and 180° lie on the center line. Mark the center point.Advertisement
-
Trace the semicircle along the protractor from 0 ° to 180°.
-
Put the protractor on the other side of the center line, again with both the 0°and 180° marks on the center line. [1] X Research source
-
Complete the circle by tracing along the protractor.
-
Calculate the angle between adjacent vertices, α . Since a circle has 360°, divide 360° by n , the number of vertices (or sides) to get α . [2] X Research source
- α=360°/n
- α is the measured angle between lines drawn from the center of the circle to adjacent vertices.
- For a dodecagon, n =12. A dodecagon has 12 sides and 12 vertices, so 360° divided by 12 is 30°, and α=30°.
-
Mark a point for each of the successive angles. Using the protractor, mark on the circumference of the circle all the multiples of angle α calculated above. [3] X Research source
-
Join the points marked on the circle with a line segment. [4] X Research source For a dodecagon there should be 12 marks and 12 sides, because it has 12 vertices. Don’t overlap the line segments.
- If your points are outside of the circle, then simply mark another point along the radial line from the center onto the circle for each point and then join them.
-
Check to see that the sides are the same length. If they are, you can erase the circumscribed circle.
-
Finished.
Advertisement
-
Draw a circle of the desired radius, r . Set your compass to the radius, r , and draw a circle. [5] X Research source
-
Calculate the length, â„“ , of each side of the regular polygon of n sides.
- â„“=2*r*sin(180/n) [6] X Research source
- 180/n is in degrees, so make sure your calculator is set for degrees, not radians.
-
Set your compass to this length, â„“ . Be ultra-accurate and triple-check the measurement to ensure that it is as accurate as possible.
-
Start from any point on the circle and mark an arc or line. Don't change the radius of your compass.
-
Mark another arc or line on the circle. Continue the process until the arc or line touches the first point.
- Make sure your compass doesn't move!
-
Join the lines/arcs accurately using a ruler.
- Check to see that the sides are identical in length.
- If they are, then you're finished. Erase the construction guide lines.
Advertisement
Community Q&A
Search
-
QuestionHow can I obtain angle 32.75 on a protractor?DonaganTop AnswererWith a normal protractor, all you can do is measure extremely carefully.
-
QuestionIf it is a pentagon, can I still use the compass method?DonaganTop AnswererYes.
-
QuestionHow do I construct an eleven-sided pologonDonaganTop AnswererUse Method 1 above, except that the central angles used would not be 30°, they would be 360° divided by 11, or 32¾°.
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
Advertisement
Tips
- If you use a mechanical pencil, rotate the pencil slightly as you draw. This will produce a strong, consistent line. Otherwise, the lead wears and the line increases in boldness/width.Thanks
- For the final construction, do all of the marks in fine-line black pen, then paperclip a piece of tracing paper to your ink drawing and do the tracing carefully in pen or pencil.Thanks
Submit a Tip
All tip submissions are carefully reviewed before being published
Thanks for submitting a tip for review!
Advertisement
Things You’ll Need
Method One
- Protractor
- Calculator (optional, but may be necessary depending on the number of sides)
- Paper
- Tracing paper (optional)
- Pencil
- Pen - black, fine point (optional)
- Eraser
Method Two
- Compass
- Ruler
- Calculator
- Paper
- Tracing paper (optional)
- Pencil
- Pen - black, fine point (optional)
- Eraser
References
- ↑ https://chestofbooks.com/crafts/metal/Metal-Pattern/The-Construction-Of-Regular-Polygons-III-By-Means-Of-The-Protractor.html
- ↑ https://www.mathalino.com/reviewer/plane-geometry/regular-polygon
- ↑ https://arts.onehowto.com/article/how-to-draw-a-perfect-pentagon-9425.html
- ↑ https://arts.onehowto.com/article/how-to-draw-a-perfect-pentagon-9425.html
- ↑ https://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm
- ↑ https://www.purebasic.com/documentation/reference/formulas.html
About This Article
Thanks to all authors for creating a page that has been read 174,605 times.
Advertisement
