Reconstruction of theWindmill Hill 25-05-2009 formation | |||||

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

2. |
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Construct a circle centered at the lefthand intersection, and passing through the righthand intersection of circle 1, both with the horizontal centerline. | |||||

3. |
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Construct a circle centered at the righthand intersection, and passing through the lefthand intersection of circle 1, both with the horizontal centerline. | |||||

4. |
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Construct a "two-points" circle (defined by the end-points of a centerline), between the lefthand intersections of circles 2 and 3 with the horizontal centerline. | |||||

5. |
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Construct a "two-points" circle between the righthand intersections of circles 2 and 3 with the horizontal centerline. | |||||

6. |
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Construct the inscribed equilateral triangle of circle 4, pointing to the left. | |||||

7. |
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Construct a circle, passing through the righthand intersection of circle 4 and the horizontal centerline, tangent to the upper and lower (lefthand) sides of triangle 6. | |||||

8. |
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Copy circle 7 to its lefthand intersection with the horizontal centerline. | |||||

9. |
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Copy circle 7 to the righthand intersection of circle 1 and the horizontal centerline. | |||||

10. |
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Copy circle 7 two times, to the righthand intersection of circle 9 and the horizontal centerline and to the corresponding intersection of this copied circle itself. | |||||

11. |
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Construct a "two-points" circle between the lefthand intersections of circles 7 and 8 with the horizontal centerline. | |||||

12. |
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Construct a "two-points" circle between the lefthand intersection of circle 7 and the righthand intersection of circle 8 with the horizontal centerline. | |||||

13. |
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Construct a "two-points" circle between the righthand intersections of circles 7 and 8 with the horizontal centerline. | |||||

14. |
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Copy circles 11, 12 and 13 to the corresponding positions with respect to circles 10, as shown. | |||||

15. |
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Draw the connecting line between the righthand intersections of circle 11 and the upper and lower (lefthand) sides of triangle 6. | |||||

16. |
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Construct a circle concentric to circle 11, tangent to line 15. | |||||

17. |
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Copy circle 16 to the center of circle 12. | |||||

18. |
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Copy circle 16 to the center of circle 13. | |||||

19.
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Copy circle 16 three times, to the centers of circles 14. | |||||

20. |
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Construct the inscribed equilateral triangle of circle 1, pointing up. | |||||

21. |
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Construct the inscribed circle of triangle 20. | |||||

22. |
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Construct a "two-points" circle between the intersections of circles 2 and 3. | |||||

23. |
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Construct a circle concentric to circle 12, tangent to circle 22 at the lefthand side. | |||||

24. |
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Copy circle 23 to the center of circle 1. | |||||

25. |
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Copy circle 2 to its lefthand intersection with the horizontal centerline. | |||||

26. |
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Copy circle 3 to its righthand intersection with the horizontal centerline. | |||||

27. |
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Copy circle 11 to the upper intersection of circles 2 and 25. | |||||

28. |
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Draw a (horizontal) line, tangent to circles 23 and 24 at the lower sides. | |||||

29. |
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Construct a circle centered at the righthand intersection of circle 13 and line 28, tangent to circle 27 at the lower side. | |||||

30. |
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Copy circle 23 to the lower intersection of circles 2 and 3. | |||||

31. |
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Draw a (vertical) line, tangent to circles 24 and 30 at the righthand sides. | |||||

32. |
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Construct a circle, passing through the intersection of circle 29 and line 31, passing through the lefthand intersection of circles 2 and 29, and tangent to circle 27 at the upper side. | |||||

33. |
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Construct a circle, tangent to circle 27 at the lower lefthand side, and tangent to circles 29 and 32 at the upper lefthand sides, as shown. | |||||

34. |
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Construct a circle, tangent to circle 33 at the lower lefthand side, and tangent to circles 29 and 32 at the upper lefthand sides, as shown. | |||||

35. |
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Construct a circle, tangent to circle 34 at the lower lefthand side, and tangent to circles 29 and 32 at the lefthand sides, as shown. | |||||

36. |
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Construct a circle, tangent to circle 35 at the lower side, and tangent to circles 29 and 32 at the lefthand sides, as shown. | |||||

37. |
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Construct a circle, tangent to circle 36 at the lower side, and tangent to circles 29 and 32 at the lefthand sides, as shown. | |||||

38. |
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Copy circles 27, 33, 34, 35, 36 and 37 as a whole, from the center of circle 27 to the lower intersection of circles 3 and 26, while at the same time rotating over 180°. | |||||

39.
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Construct a "two-points" circle between the righthand intersections of circles 17 and 23 with the horizontal centerline. | |||||

40. |
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Copy circle 39 to the lefthand intersection of circle 2 and the horizontal centerline. | |||||

41. |
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Construct a circle concentric to circle 2, tangent to circle 40 at the righthand side. | |||||

42. |
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Copy circle 41 to the center of circle 3. | |||||

43. |
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For clarity reasons, the results of a number of previous steps are left out temporarily.Construct a "two-points" circle between the lefthand intersections of circles 3 and 42 with the horizontal centerline. See detail. | |||||

44. |
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Construct a "two-points" circle between the righthand intersections of circles 2 and 41 with the horizontal centerline. | |||||

45. |
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Construct a circle concentric to circle 1, passing through the centers of circles 43 and 44. | |||||

46. |
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Construct the inscribed equilateral triangle of circle 45, pointing to the left. | |||||

47. |
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Construct a circle, passing through the center of circle 44, and tangent to the upper and lower (lefthand) sides of triangle 46. | |||||

48. |
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Construct a "two-points" circle between the lefthand intersections of circles 45 and 47 with the horizontal centerline. | |||||

49. |
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Copy circle 48 three times, to its own righthand intersection, and to the corresponding intersections of the copied circles themselves, all with the horizontal centerline, as shown. | |||||

50. |
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Copy circle 43 five times, to all intersections of circles 49 with the horizontal centerline. | |||||

51. |
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Copy circles 43 and 50 as a whole, from the center of circle 43 to the lefthand intersection of circle 41 and the horizontal centerline. | |||||

52. |
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Copy circles 44 and 50 as a whole, from the center of circle 44 to the righthand intersection of circle 42 and the horizontal centerline. | |||||

53. |
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Copy circles 2 and 41 as a whole six times, to the centers of circles 51. | |||||

54. |
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Copy circles 3 and 42 as a whole six times, to the centers of circles 52. | |||||

55. |
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Circles 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 18, 19, 21, 24, 27, 33, 34, 35, 36, 37, 38, 41, 42, 53 and 54 are used for the final steps. | |||||

56. |
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Remove all redundant parts not visible within the formation itself. High resolution dwf-file | |||||

57. |
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Colour all areas corresponding to standing... High resolution dwf-file | |||||

58. |
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...or to flattened crop, and finish the reconstruction of the Windmill Hill formation of 25-05-2009. High resolution dwf-file | |||||

59. |
courtesy the Crop Circle Connector photo by: Lucy Pringle | ||||

The final result, matched with the aerial image. | |||||

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Copyright © 2009, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||