Reconstruction of theHackpen Hill (4) formations of 13-08-2013 (phase 1) and 31-08-2013 (phase 2) | |||||

1. |
Draw a circle. Draw and extend the horizontal and vertical centerlines. | ||||

2. |
Construct the inscribed regular 22-sided polygon of circle 1, pointing up. | ||||

3. |
Construct a "two-points" circle (defined by the two end-points of a centerline) between the top of polygon 2 and its next angular point to the right. | ||||

4. |
Copy circle 3 twenty-two times, to the angular points of polygon 2. | ||||

5. |
Draw twenty-two rays, from the center of circle 1 to the centers of circles 4, and extend these lines up to their outer sides. | ||||

6. |
Construct a circle passing through the intersections of the righthand ray 5 and the righthand circle 4 both just above the horizontal centerline, and passing through the corresponding intersections just below the horizontal centerline. | ||||

7. |
Construct a circle (concentric to circle 1) passing through the outer intersections of circles 4 and (extended) rays 5. | ||||

8. |
Construct a circle concentric to circle 6, tangent to circle 7 at the righthand side. | ||||

9. |
Construct a circle concentric to circle 1, passing through the center of circle 6. | ||||

10. |
Draw twenty-two rays, from the center of circle 1 to its intersections with circles 4, and extend these lines up to circle 7. | ||||

11. |
Copy circles 6 and 8 twenty-one times, to the other intersections of circle 9 and rays 10. | ||||

12. |
Remove all redundant parts from circles 4, 6, 8 and 11, such that the shown pattern remains..This is the reconstruction of the first phase of the Hackpen Hill (4) formation of 13-08-2013High resolution dwf-file | ||||

12a. |
Colour all parts corresponding to standing... High resolution dwf-file | ||||

12b. |
...or to flattened crop. High resolution dwf-file | ||||

12c. |
Courtesy the Crop Circle Connector Photo by: Jim Peyton | The result of the first phase matched with the aerial image. | |||

13. |
Reconstruction of the second phase of Hackpen Hill (4) of 31-08-2013Construct a circle centered at the righthand intersection of circle 6 and the horizontal centerline, tangent to circle 8 at the righthand side. | ||||

14. |
Copy circle 13 to its righthand intersection with the horizontal centerline. | ||||

15. |
Construct two circles concentric to circle 6, tangent to circles 13 and 14 at the righthand sides. | ||||

16. |
Copy circle 6 to the center of circle 1. | ||||

17. |
Copy circle 6 twenty-two times, to the centers of circles 4. | ||||

18. |
Construct a circle centered at the lower intersection of upper circle 17 and the vertical centerline, tangent to upper circle 4 at the lower side. | ||||

19. |
Copy circle 18 to the upper intersection of circle 16 and the vertical centerline. | ||||

20. |
Construct a circle concentric to circle 16, tangent to circle 19 at the upper side. | ||||

21. |
Copy circles 15 twenty-one times, to the centers of circles 11. | ||||

22. |
Remove all redundant parts from circles 15, 17 and 21, such that the shown pattern remains. | ||||

23. |
Copy circle 13 to the upper intersection of circle 20 and the vertical centerline. | ||||

24. |
Copy circle 18 to the upper intersection of circle 23 and the vertical centerline. | ||||

25. |
Construct two circles concentric to circle 16, tangent to circles 23 and 24 at the upper sides. | ||||

26. |
Copy circle 13 to the upper intersection of outer circle 25 and the vertical centerline. | ||||

27. |
Copy circle 18 to the upper intersection of circle 26 and the vertical centerline. | ||||

28. |
Construct two circles concentric to circle 16, tangent to circles 26 and 27 at the upper sides. | ||||

29. |
Copy circle 13 to the upper intersection of outer circle 28 and the vertical centerline. | ||||

30. |
Copy circle 18 to the upper intersection of circle 29 and the vertical centerline. | ||||

31. |
Construct two circles concentric to circle 16, tangent to circles 29 and 30 at the upper sides. | ||||

32. |
Construct the inscribed regular 34-sided polygon of outer circle 25, pointing to the right. | ||||

33. |
Draw the thirty-four rays of polygon 32, from the center to its angular points. | ||||

34. |
Remove all redundant parts from circles 25, and rays 33, such that the shown pattern remains. | ||||

35. |
Construct the inscribed regular 48-sided polygon of outer circle 28, pointing to the right. | ||||

36. |
Draw the forty-eight rays of polygon 35, from the center to its angular points. | ||||

37. |
Remove all redundant parts from circles 28, and rays 36, such that the shown pattern remains. | ||||

38. |
Construct the inscribed regular 58-sided polygon of outer circle 31, pointing to the right. | ||||

39. |
Draw the fifty-eight rays of polygon 38, from the center to its angular points. | ||||

40. |
Remove all redundant parts from circles 31, and rays 39, such that the shown pattern remains. | ||||

41. |
Circles 16 and 20, and patterns 12, 22, 34, 37 and 40, together make up the final reconstruction. High resolution dwf-file | ||||

42. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

43. |
...or to flattened crop, and finish the reconstruction of the second phase of the Hackpen Hill (4) formation of 31-08-2013. High resolution dwf-file | ||||

44. |
Photo copyright: Steve Alexander | The final result, matched with the aerial image. | |||

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Copyright © 2013, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||