How to Construct a Regular Heptagon

Step-by-Step Guide

1. 1

   Step 1: Draw an arbitrary circle

   Keep in mind that you will need some extra space around the circle for construction lines. ,, This circle intersects the first circle at points B{\displaystyle B} and C{\displaystyle C}. , BC{\displaystyle BC} bisects AX{\displaystyle AX} in E{\displaystyle E}. , This circle intersects circle a in D{\displaystyle D}. , BD{\displaystyle BD} is one side of the regular heptagon. , You should end up exactly where you started.
   
   There is an error of about .2% for this method, which is negligible for any heptagon that fits on a regular A4 piece of paper.
   
   If you don't end up exactly where you started, there were probably some inaccuracies with the construction tools (e.g. the thickness of the pencil). ,,
2. 2

   Step 2: centred at a point X{\displaystyle X}.

3. 3

   Step 3: Draw the radius AX{\displaystyle AX}.

4. 4

   Step 4: Draw a circle with radius AX{\displaystyle AX}

5. 5

   Step 5: centred at A{\displaystyle A}.

6. 6

   Step 6: Connect B{\displaystyle B} and C{\displaystyle C}.

7. 7

   Step 7: Draw a third circle with radius BE{\displaystyle BE}

8. 8

   Step 8: centred at B{\displaystyle B}.

9. 9

   Step 9: Connect B{\displaystyle B} and D{\displaystyle D}.

10. 10

    Step 10: Use your compass to trace the distance BD around the circle.

11. 11

    Step 11: Connect adjacent vertices.

12. 12

    Step 12: Erase the construction lines if needed.

Detailed Guide

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