Reconstruction of theWaden Hill 16-07-2005 formation | |||||

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

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

3. |
Construct three inscribed octagons (regular 8-sided polygons) of circle 1, each with one angular point coincident with successive angular points of triangle 2. | ||||

4. |
Draw the 24 rays from the center of circle 1 to all angular points of octagons 3. | ||||

5. |
Construct the inscribed square of circle 1, sides horizontal and vertical. | ||||

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

7. |
Construct the circumscribed dodecagon (reguler 12-sided polygon) of circle 6, with the mid-point of one side on the horizontal centerline. | ||||

8. |
Construct the circumscribed circle of dodecagon 7. | ||||

9. |
Construct the inscribed equilateral triangle of circle 8, pointing down. | ||||

10. |
Construct a circle concentric to circle 1, passing through all innermost mutual intersections of octagons 3. | ||||

11. |
Construct the inscribed equilateral triangle of circle 10, pointing up. | ||||

12. |
Construct the inscribed circle of triangle 11. | ||||

13. |
Construct the inscribed equilateral triangle of circle 12, pointing down. | ||||

14. |
Draw the connecting line between the intersections of circle 8 and the two (lefthand and righthand) rays 4, just below the horizontal centerline, as shown. | ||||

15. |
Construct a circle concentric to circle 1, tangent to line 14. | ||||

16. |
Construct the inscribed equilateral triangle of circle 15, pointing down. | ||||

17. |
Construct the inscribed dodecagon of circle 1, pointing to the right. | ||||

18. |
Construct the inscribed circle of dodecagon 17. | ||||

19. |
Construct a circle centered at the righthand intersection of circle 18 and the horizontal centerline, tangent to the nearest sides of dodecagon 17, as shown. | ||||

20. |
Copy circle 19 to the intersection of the upper side of triangle 13 and the vertical centerline. | ||||

21. |
Construct a circle concentric to circle 1, tangent to circle 20 at the lower side. | ||||

22. |
Construct the circumscribed equilateral triangle of circle 21, pointing down. | ||||

23. |
Copy circle 19 to the intersection of the upper side of triangle 16 and the vertical centerline. | ||||

24. |
Repeat steps 21 and 22 for triangle 16 and circle 23. (Construct an equilateral triangle centered at the center of circle 1, pointing down, and the upper side of which is tangent to circle 23 at the lower side). | ||||

25. |
Construct a circle, centered at the righthand intersection of circle 21 and the horizontal centerline, tangent to the righthand side of triangle 22. | ||||

26. |
Copy circle 25 to the righthand intersection of circle 8 and the horizontal centerline. | ||||

27. |
Extend the sides of triangle 13 upto the sides of triangle 9. | ||||

28. |
Draw three connecting lines between the pairs of intersections of lines 27 and the sides of triangle 9, closest to its angular points, as shown. | ||||

29. |
Extend the sides of triangle 22 in a clockwise direction upto the sides of triangle 9, as shown. | ||||

30. |
Extend the sides of triangle 16 in a clockwise direction upto the sides of triangle 13, as shown. | ||||

31. |
Extend the sides of triangle 24 in a clockwise direction upto the sides of triangle 22, as shown. | ||||

32. |
Create the central pattern of the formation, by removing all irrelevant parts from triangles 9, 13, 16, 22 and 24, and from lines 27, 29, 30 and 31. | ||||

33. |
Copy circle 26 to its righthand intersection with the horizontal centerline. | ||||

34. |
Construct three circles concentric to circle 1, tangent to circle 26 at both sides, and tangent to circle 33 at the righthand side. | ||||

35. |
Copy circle 26 to the center of circle 19. | ||||

36. |
Construct a circle concentric to circle 1, tangent to circle 35 at the lefthand side. | ||||

37. |
Copy circle 26 three times, the first to the lefthand intersection of circle 35 and the horizontal centerline, the second to the corresponding intersection of the first, and so on. | ||||

38. |
Construct three circles concentric to circle 1, tangent to successive circles 37 at the lefthand sides. | ||||

39. |
Copy circle 19 two times, the first to the lefthand intersection of circle 26 and the horizontal centerline, the second to the corresponding intersection of the first. | ||||

40. |
Construct two circles concentric to circle 1, tangent to successive circles 39 at the lefthand sides. | ||||

41. |
Construct two circles centered at the intersections of circle 1 with the rightmost ray 4 and the one just above it, each passing through the center of the other. | ||||

42. |
Draw the connecting line between the center of circle 1 and the righthand intersection of circles 41. | ||||

43. |
Construct two circles centered at the intersections of circle 1 with the righthand ray 4 just above the horizontal centerline and with line 42, each passing through the center of the other. | ||||

44. |
Draw the connecting line between the center of circle 1 and the righthand intersection of circles 43. | ||||

45. |
Construct two circles centered at the intersections of circle 1 with the righthand ray 4 just above the horizontal centerline and with line 44, each passing through the center of the other. | ||||

46. |
Draw the connecting line between the center of circle 1 and the righthand intersection of circles 45. (Lines 42, 44 and 46 are the bisectors of their respective angles. The angle between the last two lines, therefore, is one 192nd part of the circle; that is, one eighth of the section between two successive rays 4, which is one 24th part of the circle). | ||||

47. |
Construct two circles centered at the intersections of circle 1 with the righthand ray 4 just above the horizontal centerline and with line 46, each passing through the center of the other. | ||||

48. |
Draw the connecting line between the mutual intersections of circles 47. | ||||

49. |
Copy upper circle 47 to the intersection of circle 1 and line 48. | ||||

50. |
Copy circle 49 six times, the first to its lower intersection with circle 1, the second to the corresponding intersection of the first, and so on. | ||||

51. |
Draw eight rays, from the center to the circumference of circle 1, tangent to circles 50 at the upper and lower sides, see detail. | ||||

52. |
Create one of the 24 peripheral patterns of the formation, by removing all irrelevant parts from circles 8, 34, 36 and 38, and from lines 51. | ||||

53. |
Copy pattern 52 23 times, to the corresponding positions within the other sections. That means, repeat steps 41 through 52 for all other 23 sections, defined by rays 4. | ||||

54. |
Circles 1, 18, 36 and 40, and patterns 32, 52 and 53, together, make up all that is necessary for the final reconstruction. | ||||

55. |
Remove parts from circle 36 not visible within the formation. High resolution dwf-file | ||||

56. |
Colouring all areas corresponding to standing... High resolution dwf-file | ||||

57. |
...or to flattened crop, will finish the reconstruction of the Waden Hill formation of 16-07-2005. High resolution dwf-file | ||||

58. |
courtesy the Crop Circle Connector photo by: Steve Alexander | The final result, matched with the aerial image. | |||

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Copyright © 2005, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||