Reconstruction of theSilbury Hill 5-07-2009 formation | |||||

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

2. |
Construct two inscribed decagons (regular 10-sided polygons) of circle 1, one pointing up, on pointing to the right. | ||||

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

4. |
Draw the twenty rays of decagons 2, from the center of circle 1 to the angular points, and number them from 1 for the rightmost one to 20, counterclockwise. | ||||

5. |
Construct the inscribed square of circle 1, pointing to the right. | ||||

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

7. |
Find the circle passing through the mutual intersections of decagons 2. Construct the inscribed square of this circle, sides horizontal and vertical. | ||||

8. |
Construct the inscribed circle of square 7. | ||||

9. |
Construct a circle centered at the upper intersection of circle 6 and the vertical centerline, tangent to circle 8 at the upper side. | ||||

10. |
Copy circle 9 to the upper intersection of circle 3 and the vertical centerline, and move it (copy and delete original) to its own lower intersection with the vertical centerline. | ||||

11. |
Construct two circles concentric to circle 1, one passing through the center, one tangent to the lower side of circle 10. | ||||

12. |
Construct the inscribed pentagon (regular 5-sided polygon) of circle 1, pointing up. | ||||

13. |
Construct the inscribed circle of pentagon 12. | ||||

14. |
Copy circle 13 to the center of circle 9, and move it to its own lower intersection with the vertical centerline. | ||||

15. |
Construct a circle concentric to circle 14, tangent to circle 8 at the upper side. | ||||

16. |
Copy circle 9 to the center of circle 1. | ||||

17. |
Draw a line, tangent to circle 16 at the lower side, parallel to the horizontal centerline, and extending up to circle 1 in both directions. | ||||

18. |
Construct a circle, above line 17 and tangent to it, and tangent to circles 6 and 15 at the lefthand sides. | ||||

19. |
Construct a circle concentric to circle 18, tangent to circle 8 at the lefthand side. | ||||

20. |
Draw a line through the center of circle 18, parallel to the horizontal centerline, and extending to the right. | ||||

21. |
Construct a circle centered at the intersection of circle 19 and line 20, tangent to circle 18 at the rigthand side. Copy this circle to its own corresponding (righthand) intersection. | ||||

22. |
Construct two circles concentric to circle 18, tangent to circles 21 at the righthand sides. | ||||

23. |
Construct a circle tangent to inner circle 11 and circle 14 at the lefthand sides, and tangent to outer circle 22 at the near side. | ||||

24. |
Copy circles 18, 19, 22 and 23 as a whole, while mirroring with respect to the vertical centerline. | ||||

25. |
From inner circle 11, circles 14, 23 and 24, remove all parts not visible within the formation itself. | ||||

26. |
From circles 6, 15, 18 and 24, remove all parts not visible within the formation itself. | ||||

27. |
Draw the connecting line between the lower intersections of circles 6 and 15 with the vertical centerline, and divide this line into ten equal parts. | ||||

28. |
Construct five circles concentric to circle 15, passing through the lower five divisions of line 27. | ||||

29. |
Construct five circles concentric to circle 6, passing through the upper five divisions of line 27. | ||||

30. |
Construct a "two-points" circle (defined by the end-points of a centerline) between the lower intersections of circle 6 and innermost circle 29 with the vertical centerline. | ||||

31. |
Copy circle 30 to the center of circle 1. | ||||

32. |
Copy circle 30 to the righthand intersection of circle 31 and the horizontal centerline, and move it to its own corresponding intersection. Repeat this four more times with respect to each newly copied-and-moved circle, as shown. | ||||

33. |
Construct five circles concentric to circle 31, tangent to circles 32 at the righthand sides. | ||||

34. |
Copy circles 31 and 33 as a whole to the lower intersection of circle 1 and the vertical centerline. | ||||

35. |
Draw ten parallel lines, tangent to circles 31, 33 and 34 at both sides, as shown. See detail. | ||||

36. |
Repeat step 34 eight times, with respect to the intersections of rays 4 nrs. 12, 13, 14, 15, 17, 18, 19 and 20, with circle 1. | ||||

37. |
Repeat step 35 eight times, for circles 31, 33 and the eight sets of circles 36, as shown. | ||||

38. |
From circles 6, 15, 19, 22, 24, 28 and 29, and lines 35 and 37, remove all parts not visible within the formation itself. | ||||

39. |
Draw the connecting line between the intersections of circle 6 with rays 4 nrs. 13 and 19. | ||||

40. |
Copy circle 9 to the intersection of line 39, and move it to its own upper intersection, both with the vertical centerline. | ||||

41. |
Construct a circle concentric to circle 40, tangent to circle 8 at the lower side. | ||||

42. |
Construct a circle concentric to circle 40, tangent to circle 6 at the lower side. | ||||

43. |
Draw thirteen pairs of lines from the intersections of circle 6 with rays 4 nrs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 20, tangent to circle 40 at both sides, and two single lines from the intersections of circle 6 with rays 4 nrs. 13 and 19, tangent to circle 40 at the upper side, as shown. | ||||

44. |
From circle 42, and lines 43, remove all parts not visible within the formation itself. Notice that lines 43 are cut off at circle 8. | ||||

45. |
Construct the inscribed square of circle 42, pointing to the right. | ||||

46. |
Construct the inscribed circle of square 45. | ||||

47. |
Copy circle 9 to the lower intersection of circle 46 and the vertical centerline. | ||||

48. |
Construct a circle concentric to circle 46, tangent to circle 47 at the lower side. | ||||

49. |
Copy circle 9 to the intersection of line 39 and the vertical centerline. | ||||

50. |
Copy circles 46 and 48 to the lower intersection of circle 49 and the vertical centerline. | ||||

51. |
Draw a line passing through the center of circle 40, parallel to line 39 (horizontal), extending up to outer circle 50 in both directions. | ||||

52. |
Construct the inscribed square of circle 40, pointing to the right. | ||||

53. |
Construct the inscribed circle of square 52. | ||||

54. |
Construct a circle passing through the center of circle 40, tangent to both righthand sides of square 52. | ||||

55. |
Copy circle 54 to the center of circle 40. | ||||

56. |
Draw three lines, parallel to line 51, tangent to circle 40 at the upper side, and tangent to circle 55 at both sides. Number the lines a, b and c from top to bottom. | ||||

57. |
Draw the connecting line between the upper intersections of circle 40 and inner circle 50 with the vertical centerline, and divide this line into nine equal parts. | ||||

58. |
Construct eight circles concentric to circle 40, passing through the divisions of line 57. Number these circles 1 to 8 from inside outwards. | ||||

59. |
Construct two circles concentric to circles 50, tangent to circles 58 nrs. 7 and 8 at the upper sides. | ||||

60. |
Construct seven circles centered at the lefthand intersection of line 56c and the outer circle 50, passing through the righthand intersections of circles 58 nrs. 2, 3, 4, 5, 6, 7 and 8, with the same line c. Repeat this for the mirrored case with respect to the vertical centerline, as shown. | ||||

61. |
Draw ten lines parallel to line 51, six tangent to circles 58 nrs. 1, 2 and 3, at both sides, and four tangent to circles 58 nrs. 4, 5, 6 and 7 at the lower sides, all extending up to outer circle 50 in both directions. Number these lines d, e, f, g, h, i, j, k, l and m from top to bottom. | ||||

62. |
Draw ten lines parallel to the vertical centerline, passing through the intersections of circles 55, 40, and 58 nrs. 1, 2 and 3, with line 51, extending up to outer circle 50. Number these lines 1 through 10 from left to right. | ||||

63. |
Construct two circles centered at the intersection of line 61f and line 62 nr. 3, passing through the lefthand intersections of circles 58 nrs. 6 and 7 with line 61f. Repeat this for the mirrored case with respect to the vertical centerline, as shown. | ||||

64. |
Draw two lines from the center of circle 40 to the intersections of line 61d with lines 62 nrs 1 and 10, and extend these lines up to outer circles 63. | ||||

65. |
Construct two "two-points" circles, between the intersections of lines 64 with inner circles 63 and circle 58 nr. 3, as shown. | ||||

66. |
Copy circle 40 two times, to the centers of circles 65. | ||||

67. |
Construct two circles centered at the intersections of circle 55 and line 51, tangent to circle 40 at the nearest sides. | ||||

68. |
Construct a "two-points" circle between the intersections of circles 67 and line 51 closest to the center of circle 40. Copy this circle five times, to the intersections of circle 40 and line 51, and to the intersections of lines 61h, 61j and 61l with the vertical centerline. | ||||

69. |
Construct two "two-points" circles between the intersections of circle 40 and line 51 and the lefthand respectively righthand intersection of the righthand respectively lefthand upper copied circles 68, as shown. Copy one of these to the center of circle 40. | ||||

70. |
Draw six lines parallel to the vertical centerline, tangent to circles 69 at both sides, extending downto inner circle 59. See detail. | ||||

71. |
Draw three lines parallel to line 51, tangent to the lower three circles 68 at the lower sides, extending to circle 58 nr. 8 in both directions. | ||||

72. |
From circles 40, 50, 58, 59, 60, 63 and 66, and lines 39, 56, 61, 62, 70 and 71, remove all parts not visible within the formation itself. | ||||

73. |
Draw two lines, from the center of circle 40, to the intersections of inner circle 50 with rays 4 nrs. 15 and 17, and extend these lines downto circle 8. | ||||

74. |
Find the two arcs of circle 8, in between line 39 and lines 73. Divide the lefthand arc into seven, and the righthand arc into eight equal parts. | ||||

75. |
Draw thirteen lines, from the center of circle 40 to the divisions of arcs 74. | ||||

76. |
Construct fifteen circles, tangent to circle 8 at the inner side, and tangent to adjacent lines 39, 75 and 73. See detail. | ||||

77. |
From circles 8, 42 and 76, and lines 39, 73 and 75, remove all parts not visible within the formation itself. | ||||

78. |
From circles 41 and 50, remove all parts not visible within the formation itself. | ||||

79. |
Construct a circle concentric to circle 1, tangent to circle 9 at the upper side. | ||||

80. |
Copy circle 79 to the center of circle 40. | ||||

81. |
Draw the connecting line between the upper intersections of circles 42 and 80 with the vertical centerline. Divide this line into seventeen equal parts. Construct sixteen circles concentric to circle 40, passing through the divisions of this line. Number (the spaces between) these circles 1 through 16 from inside outwards. See detail. | ||||

82. |
Construct a circle concentric to circle 1, tangent to circle 80 at the upper side. | ||||

83. |
Copy outer circle 50 to the center of circle 1. | ||||

84. |
Construct a circle passing through the upper intersection of circle 80 and the vertical centerline, and passing through the intersections of circle 83 and the horizontal centerline. | ||||

85. |
Step 85 consists of four parts. Find the intersection of the righthand side of the top pointed feature of pattern 44 with circle 8. See detail. Construct a circle centered at the intersection of ray 4 nr. 8 and circle 81 nr. 16, passing through the found intersection. | ||||

85a. |
Construct a circle centered at the intersection of ray 4 nr. 6 and circle 84, passing through the corresponding intersection of the next righthand pointed feature of pattern 44. | ||||

85b. |
Construct five more circles centered at intersections of rays 4 nrs. 5, 4, 3, 2 and 1 with circle 84, passing through the corresponding intersections of the successive pointed features of pattern 44. | ||||

85c. |
Repeat steps 85 and 85b for the mirrored case with respect to the vertical centerline, as shown. | ||||

86. |
From pattern 44 and all circles 85, remove all parts not visible within the formation itself. | ||||

87. |
Draw twenty rays, from the center of circle 1 to the mutual intersections of decagons 2. | ||||

88. |
Draw fourteen rays, from the center of circle 40 to the intersections of rays 87 with circle 6, except for the lower six rays, as shown. Number these rays 1 through 14, from the lower right, counterclockwise. | ||||

89. |
Construct nineteen "two-points" circles, the first between the intersections of circles 81 nrs. 3 and 4 (space 3) and ray 88 nr. 1. See detail. Repeat this for the combinations of ray 88 nr. 2 and space nr. 5, 3-7, 4-9, 5-11, 6-14, 7-8, 7-14, 7-16, 8-8, 8-14, 8-16, 9-14, 10-7, 10-11, 11-9, 12-5, 13-5 and 14-3. | ||||

90. |
Find outer circle 28 and inner circle 29. Construct a circle concentric to circle 18, tangent to both found circles at the near sides. See detail. | ||||

91. |
Construct a (temporary) "two-points" circle between the center of circle 90 and its righthand intersection with line 20. Repeat this for this circle itself, and move this last circle to the center of circle 90. | ||||

92. |
Construct a circle outside circle 90 and tangent to it at the upper side, and tangent to the outer and inner circles 28 and 29 (step 90) at the near sides. | ||||

93. |
Copy circle 91 to the center of circle 92. | ||||

94. |
Construct a circle concentric to circle 92, tangent to circle 90 at the upper side. | ||||

95. |
Repeat step 92 for circle 94 in stead of 90, as shown. | ||||

96. |
Copy circles 90, 91, 92, 93 and 95 as a whole, while mirroring with respect to the vertical centerline. | ||||

97. |
Copy circles 90 and 91 nineteen times, to the centers of circles 89. | ||||

98. |
From circles 81 and pattern 86, remove all parts not visible within the formation itself. | ||||

99. |
Circles 1, 3, outer 11, 90, 91, 92, 93, 95, 96 and 97, and patterns 25, 26, 38, 72, 77, 78 and 98, together make up the final reconstruction. High resolution dwf-file | ||||

100. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

101. |
...or to flattened crop, and finish the reconstruction of the Silbury Hill formation of 5-07-2009. High resolution dwf-file | ||||

102. |
Photo by: Jack Turner Photo by: John Montgomery Photo by: Lucy Pringle Courtesy the Crop Circle Connector | The final result, matched with three different aerial images. | |||

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