Reconstruction of the 2016 Figsbury Ring 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 up. | |

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

4. |
Draw the diagonal of heptagon 2 from the upper lefthand to the upper righthand angular points. | |

5. |
Construct a circle centered at the mid-point of diagonal 4, passing through the center of circle 1. | |

6. |
Copy circle 1 to the upper intersection of circle 5 and the vertical centerline. | |

7. |
Construct a circle centered at the upper intersection of circle 3 and the vertical centerline, tangent to circle 1 at the lower side. | |

8. |
Construct a circle concentric to circle 7, tangent to circle 3 at the lower side. | |

9. |
Copy circle 3 to its lower intersection with the vertical centerline. | |

10. |
Construct the inscribed heptagon of circle 9, pointing up. | |

11. |
Draw the diagonal of heptagon 10 from the upper lefthand to the upper righthand angular points. | |

12. |
Construct a circle centered at the mid-point, and passing through the end-points of diagonal 11. | |

13. |
Construct a circle centered at the lower intersection of circle 12 and the vertical centerline, tangent to diagonal 11. | |

14. |
Construct a circle centered at the lower intersection of circle 9 and the vertical centerline, passing through the lower angular points of heptagon 10. | |

15. |
Construct the inscribed heptagon of circle 7, pointing up. | |

16. |
Construct a circle passing through the lower intersection of circle 14 and the vertical centerline, and passing through the lefthand intersection of the upper lefthand side, and through the righthand intersection of the upper righthand side of heptagon 15 with circle 8. | |

17. |
Construct a circle centered at the lower intersection of circle 1 and the vertical centerline, tangent to circle 12 at the lower side. | |

18. |
Copy circle 17 to the upper intersection of circle 7 and the vertical centerline. | |

19. |
Construct a circle concentric to circle 16, tangent to circle 18 at the upper side. | |

20. |
Construct a circle concentric to circle 18, tangent to circle 8 at the upper side. | |

21. |
Copy circle 20 to the upper intersection of circle 18 and the vertical centerline. | |

22. |
Construct a circle concentric to circle 16, tangent to circle 21 at the upper side. | |

23. |
Draw two lines, from the center of circle 1 to the intersections of circles 7 and 16. Extend these lines upto circle 19. | |

24. |
Draw the lefthand arc of circle 19 between the intersection with the lefthand line 23 and the lower intersection with the vertical centerline, as shown. | |

25. |
Divide arc 24 into sixteen equal parts. | |

26. |
Draw the righthand arc of circle 19 between the intersection with the righthand line 23 and the lower intersection with the vertical centerline, as shown. | |

27. |
Divide arc 26 into fifteen equal parts. | |

28. |
Construct a circle centered at the intersection of circle 19 and the righthand line 23, passing through the upper division node 27. | |

29. |
Draw thirty-one rays, from the center of circle 1 to the division nodes 25 and 27, to the lower intersection of circle 19 and the vertical centerline, and to the upper lefthand intersection of circles 19 and 28. Number these rays, and lines 23, consecutively 1 - 33 counterclockwise, starting at the lefthand line 23. | |

30. |
Draw sixteen lines, from the intersections of rays 29 nrs. 1 - 16 with circle 16, to the intersections of rays 29 nrs. 2 - 17 with circle 19, respectively, as shown. | |

31. |
Draw sixteen lines, from the intersections of rays 29 nrs. 17 - 32 with circle 19, to the intersections of rays 29 nrs. 18 - 33 with circle 16, respectively, as shown. | |

32. |
Remove all redundant parts from circles 7, 9, and 19, and lines 23, 29, 30, and 31,... | |

33. |
...to create the shown pattern. | |

34. |
Draw two lines, from the lower intersection of circle 1 and the vertical centerline to the upper end-points of lines 23. | |

35. |
Draw the upper arc of circle 19 between the intersections with lines 34. | |

36. |
Divide arc 35 into six equal parts. | |

37. |
Draw four lines, from the intersection of lines 34, to the division nodes 36, except the middle one. | |

38. |
Construct the inscribed circle of heptagon 10. | |

39. |
Remove all redundant parts from lines 37, and circle 38,... | |

40. |
...to create the shown pattern. | |

41. |
Construct the inscribed heptagon of circle 38, pointing up. | |

42. |
Construct a circle centered at the mid-point of the lower side of heptagon 41, passing through its lower angular points. | |

43. |
Construct a circle centered at the lower intersection of circle 9 and the vertical centerline, tangent to circle 38 at the lower side. | |

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

45. |
Construct a circle concentric to circle 42, tangent to circle 44 at the lower side. | |

46. |
Construct a circle concentric to circle 42, tangent to circle 44 at the upper side. | |

47. |
Construct a "two-points" circle (defined by the two end-points of a centerline) between the mid-point of the lower side of heptagon 2 and the upper intersection of circle 46 and the vertical centerline. | |

48. |
Construct the inscribed equilateral triangle of circle 47, pointing up. | |

49. |
Draw a line parallel to the vertical centerline, from the lower righthand angular point of heptagon 41 upto the intersection of circle 38 and the upper righthand side of heptagon 10. | |

50. |
Extend the lower side of heptagon 2 to the right, upto circle 38. | |

51. |
Construct a circle centered at the intersection of the lower side of heptagon 2 and line 49, passing through the intersection of circle 7 and line 50. | |

52. |
Construct the inscribed equilateral triangle of circle 51, pointing to the right. | |

53. |
Construct a circle concentric to circle 51, passing through the intersections of line 49 and triangle 52. | |

54. |
Construct a circle centered at the lower, and passing through the upper intersections of circle 53 and line 49. | |

55. |
Construct a circle centered at the upper, and passing through the lower intersections of circle 53 and line 49. | |

56. |
Construct a circle centered at the intersection of line 50 and circle 53, passing through the intersections of line 49 and circle 53. | |

57. |
Construct a circle centered at the intersection of the lower side of heptagon 2 and circle 53, passing through the intersections of line 49 and circle 53. | |

58. |
Remove all redundant parts from circles 53, 54, 55, 56, and 57,... | |

59. |
...to create the shown pattern. | |

60. |
Draw a line parallel to the vertical centerline, from the lower lefthand angular point of heptagon 41 upto the intersection of circle 38 and the upper lefthand side of heptagon 10. | |

61. |
Copy pattern 59 from the intersection of the lower side of heptagon 2 and line 49, to its intersection with line 60. | |

62. |
Construct a circle centered at the upper intersection of circle 3 and righthand line 34, tangent to circle 1 at the near side. | |

63. |
Copy circle 62 to the intersection of lines 34. | |

64. |
Construct a line parallel to the righthand line 34, tangent to circles 62 and 63 at the lower righthand sides. | |

65. |
Copy circle 62 to the upper intersection of circle 3 and lefthand line 34. | |

66. |
Construct a line parallel to the lefthand line 34, tangent to circles 63 and 65 at the lower lefthand sides. | |

67. |
Construct a circle centered at the upper righthand, and passing through the upper lefthand angular points of heptagon 10. | |

68. |
Construct a circle centered at the upper lefthand, and passing through the upper righthand angular points of heptagon 10. | |

69. |
Construct a "two-points" circle between the center of circle 17 and its upper intersection with the vertical centerline. | |

70. |
Copy circle 69 two times, to the top of heptagon 2, and to the center of circle 42. | |

71. |
Construct two parallel lines, tangent to circles 70 at both sides. | |

72. |
Remove all redundant parts from pattern 33 and circle 45... | |

73. |
...to create the shown pattern. | |

74. |
Remove all redundant parts from circles 1, 3, 6, 9, 13, 42, 46, 67, and 68, lines 34, 64, 66, and 71, pattern 40, and triangle 48... | |

75. |
...to create the shown pattern. | |

76. |
Circles 8 and 22, and patterns 59, 61, 73, and 75, are used for the final reconstruction. | |

77. |
Remove all parts not visible within the formation itself. | |

78. |
Colour all areas corresponding to standing... | |

79. |
...or to flattened crop, and finish the reconstruction of the 2016 Figsbury Ring formation. | |

80. |
The final result, matched with the aerial image. |

Copyright © 2016, Zef Damen, The Netherlands |