Reconstruction of theOliver's Castle 16-08-2008 formation | |||||

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

2. |
Construct the inscribed equilateral triangle of circle 1, pointing up. | ||||

3. |
Construct the inscribed equilateral triangle of circle 1, pointing down. | ||||

4. |
Construct the inscribed circle of triangles 2 and 3. | ||||

5. |
Construct the inscribed hexagon (regular 6-sided polygon) of circle 4, pointing up. | ||||

6. |
Construct the inscribed hexagon (of the inscribed circle) of hexagon 5, pointing to the right. | ||||

7. |
Construct a circle centered at the rightmost angular point of hexagon 6, tangent to circle 4 at the righthand side. | ||||

8. |
Draw six rays, from the center of circle 1 to the angular points of triangles 2 and 3. | ||||

9. |
Copy circle 7 six times, to the intersections of hexagon 6 and rays 8. | ||||

10. |
Copy circle 7 to the righthand intersection of circle 1 and the horizontal centerline. | ||||

11. |
Construct a circle concentric to circle 1, tangent to circle 10 at the righthand side. | ||||

12. |
Construct the inscribed equilateral triangle of circle 11, pointing down. | ||||

13. |
Construct the inscribed equilateral triangle of circle 11, pointing up. | ||||

14. |
Construct a "two-points" circle, defined by the end-points of a centerline (diameter), between the intersections of the upper sides of triangles 3 and 12 with the vertical centerline. | ||||

15. |
Copy circle 14 to the center of circle 1. | ||||

16. |
Copy circle 14 to the rightmost angular point of hexagon 6. | ||||

17. |
Draw two lines, parallel to the horizontal centerline, tangent to circles 15 and 16 at both sides. | ||||

18. |
Copy circle 14 two times, to the upper and lower lefthand angular points of hexagon 6. | ||||

19. |
Repeat step 17 two times, for circles 18 in stead of 16, as shown. | ||||

20. |
Copy circle 14 three more times, to the other three angular points of hexagon 6. | ||||

21. |
Repeat step 17 three more times, for circles 20 in stead of 16, as shown. | ||||

22. |
Draw the connecting line between the intersections of hexagon 6 and lines 17. | ||||

23. |
Construct a circle concentric to circle 1, tangent to line 22. | ||||

24. |
Construct the circumscribed hexagon of circle 23, pointing up. | ||||

25. |
Draw two connecting lines, from both intersections of hexagon 24 and lines 17 to its both intersections with the upper pair of lines 19, as shown. | ||||

26. |
Repeat step 25 two times, for the lower pair of lines 19, and between the intersections of both pairs of lines 19, as shown. | ||||

27. |
Repeat steps 25 and 26 for the intersections of hexagon 24 and lines 21, as shown. | ||||

28. |
Copy circle 14 three times, to the centers of upper lefthand, upper righthand and lower circles 9. | ||||

29. |
Draw a line tangent to both upper circles 28 at the lower ("inner") side. Repeat this two times, for the other two pairs of circles 28, as shown. | ||||

30. |
Copy circle 14 three times, to the centers of the other three circles 9. | ||||

31. |
Construct a circle centered at the lower intersection of circle 14, passing through the upper intersection, both with the vertical centerline. | ||||

32. |
Copy circle 31 three times, to the angular points of triangle 3. | ||||

33. |
Copy circle 31 three more times, to the angular points of triangle 2. | ||||

34. |
Draw three lines tangent to all three pairs of circles 32 at the "inner" sides, similar to step 29, as shown. | ||||

35. |
Repeat step 34 for circles 33. | ||||

36. |
Draw a line tangent to both upper circles 28 at the upper ("outer") sides. Extend this line in both directions up to lines 34. | ||||

37. |
Repeat step 36 five times, for the other pairs of circles 28, and for all three pairs of circles 30. Extend the lines up to lines 34 and 35 respectively, as shown. | ||||

38. |
Construct a circle concentric to circle 1, passing through the uppermost mutual intersection of lines 37. | ||||

39. |
Construct the circumscribed equilateral triangle of circle 38, pointing down. | ||||

40. |
Construct the circumscribed circle of triangle 39. | ||||

41. |
Construct the inscribed hexagon of circle 40, pointing up. | ||||

42. |
Draw the connecting line between the upper righthand angular points of triangles 3 and 12. | ||||

43. |
Copy circle 14 to the intersection of upper righthand circle 32 and line 42. | ||||

44. |
Copy circle 14 two more times, to the upper righthand pair of intersections of circle 1 and triangle 12. | ||||

45. |
Repeat steps 43 and 44 five times, to corresponding points relative to the other five angular points of triangles 12 and 13, as shown. | ||||

46. |
Triangles 2, 3, 12 and 13, hexagons 6, 24 and 41, circles 9, 43, 44 and 45, and lines 17, 19, 21, 25, 26, 27, 29, 34, 35, 36 and 37, are all used for the final reconstruction. | ||||

47. |
Remove all redundant parts not visible in the formation itself. High resolution dwf-file | ||||

48. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

49. |
...or to flattened plants, and complete the reconstruction of the Oliver's Castle formation of 16-08-2008. High resolution dwf-file | ||||

50. |
courtesy the Crop Circle Connector photo by: Janet Ossebaard | The final result, matched with the aerial image. | |||

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