Reconstruction of theMonument Hill 6-08-2013 formation | |||||

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

2. |
Construct the inscribed dodecagon (regular 12-sided polygon) of circle 1, pointing up. | ||||

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

4. |
Construct a circle centered at the top of dodecagon 2, tangent to circle 3 at the upper side. | ||||

5. |
Copy circle 4 to its righthand intersection with dodecagon 2. | ||||

6. |
Construct a circle centered at the righthand angular point of dodecagon 2 next to the top, tangent to circle 5 at the righthand side. | ||||

7. |
Draw a line from the center of circle 1 to the lefthand intersection of circles 1 and 6. Call this intersection point A. | ||||

8. |
Copy line 7 while mirroring with respect to the vertical centerline. Call the mirror of point A point B. | ||||

9. |
Call the lower intersection of circle 1 and the vertical centerline point C. Divide the part of circle 1 defined by arc ACB into twelve equal parts (arcs). | ||||

10. |
Construct a circle centered at the first division node 9 clockwise from the top, passing through point A. | ||||

11. |
Copy circle 10 ten times, to the other division nodes 9. | ||||

12. |
Copy circle 4 to point A. | ||||

13. |
Construct a circle concentric to circle 10, tangent to circle 12 at the far end. | ||||

14. |
Copy circle 13 ten times, to the centers of circles 11. | ||||

15. |
Construct a circle concentric to circle 4, passing through point A. | ||||

16. |
Construct a circle concentric to circle 1, tangent to circle 15 at the upper side. | ||||

17. |
Construct a circle concentric to circle 10, passing through the righthand intersection of uppermost circle 14 and circle 16. | ||||

18. |
Construct a circle concentric to circle 1, tangent to circle 17 at the upper righthand side. | ||||

19. |
Construct the circumscribed dodecagon of circle 18, with the mid-point of the upper side on the vertical centerline. | ||||

20. |
Construct the circumscribed circle of dodecagon 19. | ||||

21. |
Construct a circle centered at the upper righthand intersection of circle 10 and upper righthand circle 11, tangent to circle 18 at the near side. | ||||

22. |
Copy circle 4 to the tangent point of circles 18 and 21. | ||||

23. |
Construct a circle concentric to circle 21, tangent to circle 22 at the near side. | ||||

24. |
Copy circles 21 and 23 nine times, to the corresponding mutual intersections of circles 11. | ||||

25. |
Construct a circle concentric to circle 1, passing through the upper righthand intersection of circle 13 and upper righthand circle 14. | ||||

26. |
Construct a circle centered at the upper intersection of circle 18 and the vertical centerline, tangent to circle 20 at the upper side. | ||||

27. |
Construct a circle centered at the upper intersection of circle 25 and the vertical centerline, tangent to circle 26 at the lower side. | ||||

28. |
Draw two lines, from the center of circle 27 to the lefthand intersection of circle 13, and to the righthand intersection of uppermost circle 14, both with circle 16. | ||||

29. |
Draw a line from the center of circle 1 to the lower righthand intersection of circles 1 and 10. | ||||

30. |
Construct a circle centered at the upper intersection of circle 3 and the vertical centerline, passing through the intersection of line 29 and circle 3.(For clarity reasons, the results of some previous steps are temporarily removed).
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31. |
Copy circle 30 five times, to its clockwise next intersection with circle 3, and consecutively to the corresponding intersections, as shown. | ||||

32. |
Construct a (non-regular) 6-sided polygon, by connecting the centers of adjacent circles 30 and 31, as shown. | ||||

33. |
Copy circle 4 six times, to the angular points of polygon 32. | ||||

34. |
Construct six lines, parallel to the sides of polygon 32 and inside the polygon, pairwise tangent to circles 33, as shown. | ||||

35. |
Construct a "two-points" circle (defined by the two end-points of a centerline) between the center of circle 4 and its lower intersection with the vertical centerline. | ||||

36. |
Copy circle 35 four times, to the center of circle 1, and to the upper, the lower lefthand and lower righthand mutual intersections of lines 34, as shown. | ||||

37. |
Construct three pairs of parallel lines, all tangent to central circle 36 at both sides, and pairwise tangent to the other circles 36 at both sides, as shown. | ||||

38. |
Copy circle 4 six times, to the mutual intersections of lines 34. | ||||

39. |
Construct six lines, parallel to lines 34 at the inward sides, pairwise tangent to circles 38, as shown. | ||||

40. |
Copy circle 4 nine times, to the mutual intersections of lines 37, and to the intersections of lines 37 and 39. | ||||

41. |
Construct three pairs of lines, parallel to lines 37 at the outward sides, pairwise tangent to circles 40, as shown. | ||||

42. |
Circles 1, 3, 10, 11, 13, 14, 16, 18, 20, 21, 23, 24, and 27, lines 28, 34, 37, 39, and 41, and polygon 32, are used for the final reconstruction. | ||||

43. |
Remove all parts not visible within the formation itself. High resolution dwf-file | ||||

44. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

45. |
...or to flattened crop, and finish the reconstruction of the Monument Hill formation of 6-08-2013. High resolution dwf-file | ||||

46. |
Courtesy the Crop Circle Connector | The final result, matched with the aerial image. | |||

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Copyright © 2013, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||