Reconstruction of theEast Field (4) 25-08-2008 formation | |||||

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

2. |
Construct the inscribed heptagon (regular 7-sided polygon) of circle 1, pointing down. | ||||

3. |
Construct the inscribed, sharp-pointing heptagram (regular 7-pointed star) of circle 1, by drawing the diagonals of heptagon 2 between all angular points three apart. | ||||

4. |
Construct the inscribed circle of heptagram 3. | ||||

5. |
Construct the inscribed heptagon of circle 4, pointing up. | ||||

6. |
Construct the inscribed circle of heptagon 5. | ||||

7. |
Construct a circle centered at the lower righthand angular point of heptagon 2, passing through both adjacent angular points. | ||||

8. |
Copy circle 7 to the lowermost angular point of heptagon 2. | ||||

9. |
Copy circle 7 to the lower lefthand angular point of heptagon 2. | ||||

10. |
Copy circle 6 two times, to the lower intersections of circle 8 with circles 7 and 9. | ||||

11. |
Construct a circle, passing through the set of outer mutual intersections of the sides of heptagram 3 (not the angular points), as shown. | ||||

12. |
Copy circle 11 to the lowermost angular point of heptagon 2. | ||||

13. |
Construct a "two-points" circle, defined by the end-points of a centerline (diameter), between the (upper) intersections of the lefthand side of the lower star-point of heptagram 3 with circles 7 and 12, as shown. | ||||

14. |
Copy circle 13 to the upper intersection of righthand circle 10 and circle 8. Move this circle (copy and delete original) to its own corresponding intersection with circle 8. See detail. | ||||

15. |
Construct the circumscribed circle of the heptagon enclosed by heptagram 3. | ||||

16. |
Copy circle 15 to the upper intersection of circle 14 and circle 8. Move this circle to its own corresponding intersection with circle 8. | ||||

17. |
Construct a circle concentric to circle 16, passing through the lower intersection of circle 14 and circle 8. | ||||

18. |
Construct a circle concentric to righthand circle 10, passing through the upper intersection of circle 14 and circle 8. | ||||

19. |
Copy righthand circle 10 to its lower intersection with circle 8 and move this circle to its own corresponding intersection. | ||||

20. |
Construct a circle concentric to circle 19, passing through the lower intersection of circles 8 and 18. | ||||

21. |
Copy circle 20 to its lower lefthand intersection with circle 8 and move this circle to its own corresponding intersection. | ||||

22. |
Construct a circle concentric to circle 21, passing through the lefthand intersection of circles 8 and 19. | ||||

23. |
Copy circle 22 to its lefthand intersection with circle 8 and move this circle to its own corresponding intersection. | ||||

24. |
Construct a circle concentric to circle 23, passing through the lefthand intersection of circles 8 and 21. | ||||

25. |
Copy circle 24 to the lefthand intersection of circles 8 and 22 and move this circle to its own corresponding intersection. | ||||

26. |
Construct a circle concentric to circle 25, passing through the lefthand intersection of circles 8 and 21. | ||||

27. |
Copy circle 26 to the lefthand intersection of circles 8 and 24 and move this circle to its own corresponding intersection. | ||||

28. |
Construct a circle concentric to circle 27, passing through the lefthand intersection of circles 8 and 23. | ||||

29. |
Copy circle 28 to its lefthand intersection with circle 8 and move this circle to its own corresponding intersection. | ||||

30. |
Construct a "two-points" circle between the lefthand intersections of circle 8 with circles 27 and 29. | ||||

31. |
Construct a "two-points" circle between the upper lefthand intersection of circle 30 and the lower righthand intersection of lefthand circle 10, both with circle 8. | ||||

32. |
Construct a circle concentric to circle 30, passing through the lefthand intersection of circles 8 and 28. | ||||

33. |
Construct a circle concentric to circle 31, passing through the upper lefthand intersection of circles 8 and 32. | ||||

34. |
Copy circle 7 four times, to the upper four angular points of heptagon 2. | ||||

35. |
Copy circles 10 (righthand), 16, 17, 20, 22, 24, 28, 30 and 33 all six times, to their corresponding positions with respect to circles 7, 9 and 34 (except for lefthand circle 10), as shown. | ||||

36. |
Copy circle 13 two times, to its both intersections with the lefthand side of the lower star-point of heptagram 3, as shown. See detail. | ||||

37. |
Construct three circles concentric to circle 12, passing through the intersections of circles 36 and the lefthand side of the lower star-point of heptagram 3. | ||||

38. |
Copy circles 37 six times, to the other angular points of heptagon 2. | ||||

39. |
Draw the connecting line between the leftmost and rightmost outer mutual intersections of the sides of heptagram 3 (not the angular points), as shown. | ||||

40. |
Copy circle 15 to the intersection of line 39 and the vertical centerline. | ||||

41. |
Copy circle 15 to the top of heptagon 5. | ||||

42. |
Draw the connecting line between the intersections of circles 40 and 41. | ||||

43. |
Construct a circle centered at the intersection of the lower side of heptagon 5 and the vertical centerline, tangent to the lower sides of the heptagon enclosed by heptagram 3, as shown. | ||||

44. |
Copy circle 43 to the intersection of line 42 and the vertical centerline. | ||||

45. |
Construct a circle centered at the upper intersection of circle 8 and the vertical centerline, passing through the upper intersection of circles 7 and 8. | ||||

46. |
Copy circle 45 to the center of circle 44. | ||||

47. |
Construct a circle concentric to circle 43, passing through the upper intersection of circles 7 and 8. | ||||

48. |
Copy circle 47 to the center of circle 44. | ||||

49. |
Construct a circle centered at the righthand intersection of circle 48 and line 42, tangent to circle 40 at the upper side. | ||||

50. |
Repeat step 49 for the lefthand intersection of circle 48. | ||||

51. |
Draw the connecting line between the lower lefthand and righthand angular points of the heptagon enclosed by heptagram 3, as shown. | ||||

52. |
Draw two lines, both from the lower intersection of circle 8 and the vertical centerline, to the lower angular points of heptagon 5, and extend these lines up to line 51. See detail. | ||||

53. |
Draw a line, perpendicular to the vertical centerline, passing through the lower angular point of the heptagon enclosed by heptagram 3, extending to both lines 52. | ||||

54. |
Draw the connecting line between the intersections of the lower sides of the lower lefthand and righthand star-points of heptagram 3 and the outer circles of both lower sets of circles 38, as shown. | ||||

55. |
Construct two circles, centered at both lower angular points of heptagon 5, both tangent to line 51. | ||||

56. |
Draw two lines, both from the intersection of lines 52, to the intersections of circles 55 and the lower side of heptagon 5. See detail. | ||||

57. |
Copy circle 13 to the lower intersection of circle 1 and the vertical centerline. | ||||

58. |
Copy circle 13 two times, to both intersections of circle 57 and the vertical centerline. | ||||

59. |
Copy circle 13 one more time, to the upper intersection of upper circle 58 and the vertical centerline, and move this circle to its own corresponding intersection. | ||||

60. |
Construct three circles, all concentric to circle 1, passing through the upper and lower intersections of circles 58 and the upper intersection of circle 59 with the vertical centerline. See detail. | ||||

61. |
Draw the connecting line between the two lower intersections of the inner circle 60 and the inner circles of the two lower sets of circles 38. | ||||

62. |
Construct a circle centered at the intersection of line 61 and the righthand line 56, tangent to the righthand side of the lower star-point of heptagram 3, as shown. | ||||

63. |
Copy circle 62 to the lower angular point of heptagram 3. | ||||

64. |
Draw two lines, from the intersections of line 61 with lines 56, parallel to the sides of the lower star-point of heptagram 3, tangent to circle 63 at opposite sides, as shown. | ||||

65. |
Copy circle 13 two times, to the intersections of lines 54 and 61 with the vertical centerline. | ||||

66. |
Draw two lines, parallel to the vertical centerline, tangent to circles 65 at both sides. | ||||

67. |
Copy circle 62 two times, to the intersections of circle 12 and lines 66. | ||||

68. |
Construct two circles, both centered at the intersection of outer circle 37 and righthand line 66, tangent to righthand circle 67 at both sides. | ||||

69. |
Copy inner circle 68 to the lower intersection of lefthand circle 67 and lefthand line 66, and move it to its own corresponding intersection. | ||||

70. |
Copy outer circle 68 to the center of circle 69. | ||||

71. |
Draw two lines, perpendicular and in between lines 66, tangent to the inner circle 68 at the upper side and tangent to circle 69 at the lower side, respectively. | ||||

72. |
Draw two parallel lines, tangent to circles 67 at both sides. | ||||

73. |
Copy circle 13 to the top of heptagon 5, and move it to its upper intersection with the vertical centerline. See detail. | ||||

74. |
Copy circle 13 another two times, the first to the upper intersection of circle 73 and the vertical centerline; move this circle to its own corresponding intersection. Repeat this for the second circle with respect to the first, as shown. See detail. | ||||

75. |
Draw three lines, parallel to the horizontal side of heptagram 3, passing through the intersections of circles 74 with the vertical centerline, and extending to circle 1 in both directions. See detail. | ||||

76. |
Copy lines 75 six times, as a whole, to the corresponding positions with respect to the other sides of heptagram 3, as shown. | ||||

77. |
Circles 1, 10, 16, 17, 20, 22, 24, 28, 30, 33, 35, 37, 38, 40, 41, 44, 46, 48, 49, 50, 60, 68, 69 and 70, lines 3, 39, 51, 52, 53, 54, 56, 61, 64, 66, 71, 72, 75 and 76, and heptagon 5, are all used for the final reconstruction. | ||||

78. |
Remove all redundant parts with no role in the formation. High resolution dwf-file | ||||

79. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

80. |
...or to flattened crop. This completes the reconstruction of the East Field (4) formation of 25-08-2008. High resolution dwf-file | ||||

81. |
courtesy the Crop Circle Connector photo's by: Russell Stannard | The final result, matched with two aerial images. | |||

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Copyright © 2008, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||