How to Construct an Octagon with a Compass

Step-by-Step Guide

1. 1

   Step 1: Lay the sheet of paper on a flat surface.

   Gather your materials onto your work space.
   
   You should have:
   A mechanical compass with pencil A pencil eraser A ruler A spare pencil (recommended)
2. 2

   Step 2: Draw a horizontal line across the middle of the sheet.

   This line should be about 9 inches across.
   
   For best results, use light markings throughout each step for a finished product. , It should be
   4.5 inches across this line.
   
   Mark it and call it "A." This will be the center. , Measure the width of the pencil tip and the compass needle (the sharp tip of a compass.) Adjust it to 3 inches. ,, Be careful.
   
   The compass needle is sharp. , Label the first intersection on the left end "B" and the second intersection on the right end "C."
   
   ,, Call the uppermost intersection point "D" and the lowermost point "E."
   
   , Call this point "F."
   
   ,, Next place the ruler across the circle, lining it up next to points A and H. ,, Next, align the ruler along points A and G. ,,,, Call this point M. ,, Call this point N. ,, Repeat this step with the following points:
   Points I and M, creating line segment IM Points M and K, creating line segment MK Points K and C, creating line segment KC Points C and J, creating line segment CJ Points J and N, creating line segment JN Points N and L, creating line segment NL Finally points L and B, creating line segment LB , Feel free to erase the extra lines. , You have successfully created an octagon using a compass and a straightedge.
   
   As you can see, this is why its better to use light marks.
   
   Otherwise, your drawing may have this hard-to-erase marks left over.
3. 3

   Step 3: Find the midway point.

4. 4

   Step 4: Place your mechanical compass next to the ruler.

5. 5

   Step 5: Place the compass needle on point A and the pencil tip on the line.

6. 6

   Step 6: Use one hand to hold the compass handle and twist it to create a circle as shown.

7. 7

   Step 7: Find the two different points at which the line and circle intersect.

8. 8

   Step 8: Place the compass needle on point C and the pencil tip on point A.

9. 9

   Step 9: Twist your hand counterclockwise to create an arc intersecting the circle as shown.

10. 10

    Step 10: Find the two points where this arc intersects the circle.

11. 11

    Step 11: Using the pencil and ruler

12. 12

    Step 12: draw a vertical line segment connecting points D and E.

13. 13

    Step 13: Find where the line segment DE intersects the the line from earlier at a single point.

14. 14

    Step 14: Place the compass needle on point F and the pencil on point A.

15. 15

    Step 15: Twist your hand counterclockwise to create an arc that intersects the line segment DE at two points.

16. 16

    Step 16: Label the intersection between points D and F point "G" and the intersection between F and E point "H".

17. 17

    Step 17: Draw a diameter containing points A and H across the circle

18. 18

    Step 18: intersecting the circle at two different points.

19. 19

    Step 19: Label the uppermost intersection point "I" and the lower right intersection point "J."

20. 20

    Step 20: Draw a diameter containing points A and G that intersects the circle at two more points.

21. 21

    Step 21: Label the two new intersections as follows: The upper right most intersection should be called point K. The lower left most intersection should be called point L.

22. 22

    Step 22: Place the compass needle on point K and the pencil tip on point C.

23. 23

    Step 23: Twist your hand clockwise

24. 24

    Step 24: creating an arc that intersects the circle at a new point.

25. 25

    Step 25: Place the compass needle on point J and the pencil tip on point C.

26. 26

    Step 26: Twist your hand counterclockwise

27. 27

    Step 27: creating an arc that intersects the circle at a new point.

28. 28

    Step 28: Pick up the ruler and align it against the points B and I near the upper left of the circle.

29. 29

    Step 29: Connect the two points with a line

30. 30

    Step 30: creating line segment BI.

31. 31

    Step 31: Look for your octagon BIMKCJNL among arcs

32. 32

    Step 32: diameters and line segments.

33. 33

    Step 33: Your octagon should now look like this.

Detailed Guide

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