Reconstruction of theThe Pilgrims Way 24-06-2006 formation | |||||

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

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

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

4. |
Construct a circle centered at the lower intersection of circle 3 and the vertical centerline, tangent to circle 1 at the lower side. See detail. | ||||

5. |
Copy circle 4 to the center of circle 1. | ||||

6. |
Construct the inscribed equilateral triangle of circle 1, pointing up. | ||||

7. |
Construct the inscribed hexagon (regular 6-sided polygon) of circle 1, pointing to the right. | ||||

8. |
Construct a circle centered at the intersection of the upper side of hexagon 7 and the vertical centerline, tangent to both upper sides of dodecagon 2. | ||||

9. |
Copy circle 8 to the top of triangle 6. | ||||

10. |
Copy circle 4 two times, to both intersections of circle 3 and the horizontal centerline. | ||||

11. |
Draw a line, tangent to both circles 10 at the lower sides. | ||||

12. |
Construct a triangle, by first drawing two lines, from the upper intersection of circle 9 and the vertical centerline to both intersections of line 11 and triangle 6, next extending these lines down to circle 1, and finally drawing the connecting line between the two intersections with circle 1 just created, as shown. | ||||

13. |
Construct a triangle, by first drawing two lines, from the lower intersection of circle 1 and the vertical centerline to both intersections of line 11 and triangle 6, next extending these lines up to circle 1, and finally drawing the connecting line between the two intersections with circle 1 just created, as shown. | ||||

14. |
Construct a triangle by connecting the upper and lower right and leftmost angular points of the 6-sided polygon enclosed by triangles 12 and 13. | ||||

15. |
Construct a triangle by connecting the other three angular points of the 6-sided polygon enclosed by triangles 12 and 13, as shown. | ||||

16. |
Construct a circle concentric to circle 8, tangent to circle 3 at the upper side. | ||||

17. |
Copy circle 16 six times, to the angular points of both triangles 14 and 15. | ||||

18. |
Construct a (enclosed) triangle inside triangle 15, by drawing three lines, tangent to the corresponding circles 17, at the inward sides, as shown. | ||||

19. |
Construct a triangle, similar to triangle 18, relative to triangle 14, as shown. | ||||

20. |
Draw three diagonals of the 6-sided polygon enclosed by triangles 12 and 13, by connecting opposite angular points. Extend these lines in both directions up to circle 3. | ||||

21. |
Construct a triangle, by connecting the upper left, lower left and rightmost intersections of lines 20 and circle 3. | ||||

22. |
Construct a triangle, by connecting the upper right, lower right and leftmost intersections of lines 20 and circle 3. | ||||

23. |
Construct a circle concentric to circle 1, tangent to circle 9 at the lower side. | ||||

24. |
Construct a triangle, by connecting the upper left, lower left and rightmost intersections of lines 20 and circle 23. | ||||

25. |
Construct a triangle, by connecting the upper right, lower right and leftmost intersections of lines 20 and circle 23. | ||||

26. |
Construct a circle, tangent to both upper sides of triangle 12, outside and tangent to circle 1 at the upper side. | ||||

27. |
Copy circle 26 three times, to the angular points of triangle 12. | ||||

28. |
Draw two lines outside triangle 12, tangent to upper circle 27 at both sides, and tangent to the lower left and lower right circles 27, at the lefthand and righthand sides, respectively. Extend these lines up to the vertical centerline, as shown. | ||||

29. |
Construct a circle concentric to circle 26, tangent to both lines 28. | ||||

30. |
Copy circle 29 to the intersection of both lines 28 (at the vertical centerline). | ||||

31. |
Copy circle 4 to the upper intersection of circle 30 and the vertical centerline. See detail. | ||||

32. |
Construct a "two-points" circle (defined by the end-points of a centerline), from the upper intersection of circle 23 to the lower intersection of circle 16, both with the vertical centerline. | ||||

33. |
Copy circle 16 to the center of circle 31. | ||||

34. |
Copy circle 32 to the upper intersection of circle 33 and the vertical centerline. | ||||

35. |
Construct a circle concentric to circle 34, tangent to circle 31 at the upper side. | ||||

36. |
Copy circle 16 to the upper intersection of circle 34 and the vertical centerline. | ||||

37. |
Copy circle 35 to the upper intersection of circle 36 and the vertical centerline. | ||||

38. |
Circles 1, 3, 5, 31, 34 and 37, triangles 12, 13, 14, 15, 21, 22, 24 and 25, and lines 18, 19 and 28 together make up all the necessary elements for the final reconstruction. | ||||

39. |
Remove all parts not visible in the formation itself. High resolution dwf-file | ||||

40. |
Colour all areas corresponding to standing... High resolution dwf-file | ||||

41. |
...or to flattened crop. This will finish the reconstruction of the The Pilgrims Way formation of 24-06-2006. High resolution dwf-file | ||||

42. |
courtesy the Crop Circle Connector photo by: Andrew King. | The final result, matched with the aerial image, shows a good fit, except for the two star-like points to the left and to the right. | |||

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Copyright © 2006, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||