Reconstruction of theIvinghoe Beacon 26-07-2002 formation |
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1. |
Draw a circle. Draw the horizontal and vertical centerlines. | ||||

2. |
Construct the inscribed nonagon (regular 9-sided polygon) of circle 1, pointing up. | ||||

3. |
Construct the inscribed circle of nonagon 2. | ||||

4. |
Construct a circle centered at the lower intersection of the vertical centerline and circle 1, passing through both nearest angular points of nonagon 2. | ||||

5. |
Copy circle 4 to the center of circle 1. | ||||

6. |
Construct a circle concentric to circle 1, tangent to circle 4 at the near side. | ||||

7. |
Draw two connecting lines between the center of circle 1 and both angular points of nonagon 2 just below the horizontal centerline. | ||||

8. |
Copy circle 4 to the intersection of right hand line 7 and circle 6. | ||||

9. |
Copy circle 4 another two times, to the intersections of circle 6 with left hand line 7 and with the upper half of the vertical centerline. | ||||

10. |
Copy circle 6 to the intersection of right hand line 7 and circle 5. | ||||

11. |
Copy circle 6 another two times, to the intersections of circle 5 with left hand line 7 and with the upper half of the vertical centerline. Note, that circles 10 and 11 pass through the intersections of circle 5 and circles 8 and 9. This is far from trivial and will be explained in "Non ruler-and-compass constructions". | ||||

12. |
Copy circle 1 to the upper intersection of circle 3 and the vertical centerline. | ||||

13. |
Construct a circle concentric to circle 1, tangent to circle 12 at the upper side. | ||||

14. |
Construct a line tangent to both circle 5 and circle 8 at the lower sides. Extend this line down right up to circle 13. | ||||

15. |
Draw the connecting line between the center of circle 1 and the intersection of line 14 and circle 13. | ||||

16. |
Copy circles 1 and 3 to the intersection of line 15 and circle 3. | ||||

17. |
Copy circles 16 two times, and distribute the three sets of circles in total evenly around the center of circle 1. | ||||

18. |
Construct a circle concentric to circle 10, tangent to circle 3 at the near side. | ||||

19. |
Construct a second circle concentric to circle 10, tangent to circles 9 at the near sides. | ||||

20. |
Copy circles 18 and 19 to the intersection of inner circle 16 and line 14. | ||||

21. |
Extend line 14 down right up to outer circle 20. | ||||

22. |
Construct a circle concentric to circle 8, tangent to circle 3 at the near side. | ||||

23. |
Copy circles 8 and 22 to the intersection of line 21 and inner circle 20. | ||||

24. |
Construct a circle passing through the outer intersections of outer circle 16 and both outer circles 17, tangent to inner circle 23 at the far side. | ||||

25. |
Construct a circle concentric to circle 24, tangent to outer circle 23 at the far side. | ||||

26. |
Copy circles 20, 23, 24 and 25 two times and distribute the three sets of circles in total evenly around the center of circle 1. | ||||

27. |
Circles 1, 5, 8, 9, 10, 11, 16, 17, 20, 23, 24, 25 and 26 are all that is necessary for the reconstruction. | ||||

28. |
Leaving out all parts not visible in the formation itself... High resolution dwf-file | ||||

29. |
...and colouring green all areas corresponding to standing crop... High resolution dwf-file | ||||

30. |
...or to flattened crop, finishes the reconstruction of the 2002 Ivinghoe Beacon formation. High resolution dwf-file | ||||

31. |
courtesy the Crop Circle Connector photo by: Andrew King | The final result matches fairly well with the aerial image, but not precisely everywhere. | |||

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Copyright © 2002, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||

Since 1-Februari-2005 |