Reconstruction of theWayland's Smithy 9-08-2005 formation | |||||

1. |
Many of the constructs in this reconstruction can not be done by ruler and compass alone. Nevertheless, the combination of "drawing instructions" and diagrams should result in unambiguous descriptions.Draw a circle. Draw and extend the horizontal and vertical centerlines. | ||||

2. |
Construct two circles, one centered at the upper, one at the lower intersection of circle 1 and the vertical centerline, each passing through the center of the other ("Vesica Pisces"-pattern). | ||||

3. |
Construct a circle concentric to circle 1, passing through the mutual intersections of circles 2. | ||||

4. |
Construct the inscribed equilateral triangle of circle 3, pointing up. | ||||

5. |
Construct the inscribed circle of triangle 4. | ||||

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

7. |
Construct the inscribed circle of triangle 6. | ||||

8. |
Construct a circle centered on the horizontal centerline, tangent to circle 5 at the lefthand side, and tangent to circle 7 at the righthand side. | ||||

9. |
Construct a circle centered on the horizontal centerline, tangent both to circle 5 and circle 7 at the lefthand sides. | ||||

10. |
Copy circle 9 to the lower intersection of circle 1 and the vertical centerline. | ||||

11. |
Construct a circle concentric to upper circle 2, tangent to circle 10 at the lower side. | ||||

12. |
Construct a circle concentric to circle 1, passing through both intersections of circle 11 and the horizontal centerline. | ||||

13. |
Construct a circle centered at the lower intersection of circle 1 and the vertical centerline, tangent to circle 5 at the lower side, and move this circle to the corresponding intersection of circle 11. | ||||

14. |
Construct a circle concentric to upper circle 2, tangent to circle 13 at the lower side. | ||||

15. |
Construct a circle centered at the righthand intersection of circle 12 and the horizontal centerline, passing through the corresponding intersection of circle 14. | ||||

16. |
Copy circle 15 three times, the first to its righthand intersection with the horizontal centerline, the second to the corresponding intersection of the first, and so on (making up a series of Vesica Pisces patterns). | ||||

17. |
Construct three circles concentric to circle 1, passing through the centers of consecutive circles 16. | ||||

18. |
Construct a circle concentric to circle 1, tangent to the rightmost circle 16 at the righthand side. | ||||

19. |
Copy circle 15 five times, the first to the righthand intersection of the rightmost circle 16 and the horizontal centerline, the second to the corresponding intersection of the first, and so on. | ||||

20. |
Construct five circles concentric to circle 1, tangent to consecutive circles 19 at the righthand sides. | ||||

21. |
Construct a circle concentric to upper circle 2, tangent to circle 18 at the lower side. | ||||

22. |
Construct a circle concentric to circle 1, passing through both intersections of circle 21 and the horizontal centerline. | ||||

23. |
Construct a circle centered at the righthand intersection of circle 22 and the horizontal centerline, tangent to the outer circle 20 at the righthand side. | ||||

24. |
Copy circle 23 three times, the first to its righthand intersection with the horizontal centerline, the second to the corresponding intersection of the first, and so on. | ||||

25. |
Construct four circles concentric to circle 1, tangent to circle 23 and consecutive circles 24 at the righthand sides. | ||||

26. |
Copy circle 23 two times, the first to the righthand intersection of the rightmost circle 24 and the horizontal centerline, the second to the corresponding intersection of the first. | ||||

27. |
Copy circle 23 to the righthand intersection of the rightmost circle 26 and the horizontal centerline. | ||||

28. |
Copy circle 23 to the righthand intersection of circle 27 and the horizontal centerline. | ||||

29. |
Construct a circle centered on the horizontal centerline, tangent to circle 27 at the righthand side, and tangent to circle 28 at the lefthand side. | ||||

30. |
Construct a circle concentric to circle 1, passing through the center of circle 29. | ||||

31. |
Copy circle 23 four times, the first to the righthand intersection of circle 28 and the horizontal centerline, the second to the corresponding intersection of the first, and so on. | ||||

32. |
Construct four circles concentric to circle 1, tangent to consecutive circles 31 at the righthand sides. | ||||

33. |
Copy circle 23 to the righthand intersection of the rightmost circle 31 and the horizontal centerline. | ||||

34. |
Construct a circle concentric to circle 1, tangent to circle 33 at the righthand side. | ||||

35. |
Copy circle 23 five times, the first to the righthand intersection of circle 33 and the horizontal centerline, the second to the corresponding intersection of the first, and so on. | ||||

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

37. |
Construct the circumscribed 242-sided regular polygon of circle 34, such that the middle of one side coincides with the lefthand intersection of circle 34 and the horizontal centerline. Number the angular points, starting with number 8 for the lefthand angular point just below the horizontal centerline, counting counterclockwise downto 1, and continue with number 9 for the lefthand angular point just above the horizontal centerline, counting clockwise upto and including 242. See detail. | ||||

38. |
Draw twenty rays of polygon 37 from the center to the angular points, starting at angular point nr. 1, and consecutively to each twelfth angular point, that means to nrs. 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 145, 157, 169, 181, 193, 205, 217, and 229. See detail. These rays divide all circles concentric to circle 1 (except circle 36) into nineteen equal sections, each enclosing twelve sides of polygon 37, and one section enclosing fourteen sides (from 229 to 1). | ||||

39. |
Divide the section of circle 22 in between rays 38 nrs. 1 and 13 into ten equal parts (arcs). Number the dividing nodes 1 through 10, starting at ray 38 nr. 1. | ||||

40. |
Draw nine connecting lines, from angular points of polygon 37 nrs. 2, 3, 4, 5, 8, 9, 10, 11 and 12 towards nodes of divisions 39 nrs. 2, 3, 4, 5, 6, 7, 8, 9 and 10, respectively. | ||||

41. |
Create the pattern within this section according to the pattern in the formation, by removing all superfluous parts of ray 38 nr. 1, lines 40, and circles 22, 25, 32 and 34. | ||||

42. |
Construct two circles, the end-points of the centerline of one of which coincide with angular points of polygon 37 nrs. 6 and 7, and of the other with dividing nodes 39 nrs. 5 and 6. | ||||

43. |
Draw the connecting line between the centers of both circles 42. | ||||

44. |
Construct a circle, the end-points of the centerline of which coincide with the intersections of circles 5 and 8 with ray 38 nr. 229. | ||||

45. |
Copy circle 44 to the intersection of line 43 and circle 30. | ||||

46. |
Copy pattern 41 together with circle 45 eighteen times (nineteen in total), and distribute them evenly to the other (equal) sections. That means, repeat construction steps 39 through 45 (except 44) eighteen times for all sections in between successive rays 38 from nr. 13 up to nr. 229. | ||||

47. |
Divide the section of circle 22 in between rays 38 nrs. 229 and 1 into eleven equal parts (arcs). Number the dividing nodes 1 through 11, starting at ray 38 nr. 229. | ||||

48. |
Firstly, draw seven connecting lines, from angular points of polygon 37 nrs. 230, 231, 232, 233, 234, 235 and 236 towards dividing nodes 47 nrs. 2, 3, 4, 5, 6, 7 and 8, respectively. Additionally, draw another six connecting lines, from angular points of polygon 37 nrs. 237, 238, 239, 240, 241 and 242 towards dividing nodes 47 nrs. 6, 7, 8, 9, 10 and 11, respectively. | ||||

49. |
Create the pattern within this section according to the pattern in the formation, by removing all superfluous parts of ray 38 nr. 229, lines 48, and circles 22, 25, 32 and 34. | ||||

50. |
Draw the connecting line between the intersection of lines 48, starting at angular points 236 and 237, and dividing node 47 nr. 7. | ||||

51. |
Copy circle 44 to the intersection of line 50 and circle 30. | ||||

52. |
Extend upto circle 1 the lines of patterns 46 and 49, that correspond to angular points of polygon 37 nrs. 24, 36, 48, 60, 84, 96, 108, 120, 144, 156, 168, 180, 204, 216, 228 and 241(!) (each 1 less than the corresponding ray 38, except the last one), see detail. | ||||

53. |
Create the patterns between circles 3 and 22, according to the patterns in the formation, by removing all superfluous parts of rays 38, lines 52, and circles 12, 17, 18 and 20. | ||||

54. |
Divide the sections of circles 1 and 3 in between ray 38 nr. 73 and line 52 nr. 120, and between ray 38 nr. 133 and line 52 nr. 180, each into eight equal parts (arcs), four times eight parts in total. | ||||

55. |
Construct a circle, the end-points of the centerline of which coincide with the intersections of circles 5 and 8 with ray 38 nr. 25. | ||||

56. |
Copy circle 55 to all dividing nodes 54, 28 times in total. | ||||

57. |
Draw fourteen pairs of parallel lines, tangent at both sides of circles 56, from circles 56 with centers on circle 3 to corresponding circles 56 with centers on circle 1, see detail. | ||||

58. |
Construct four circles, all tangent to circle 3 at the inner side, one tangent to ray 38 nr. 73, one tangent to line 52 nr. 120, one tangent to ray 38 nr. 133, and one tangent to line 52 nr. 180, all tangent to the nearest line 57. | ||||

59. |
Construct two sets of six circles, similar to circles 58, all tangent to circle 3 at the inner side, and each tangent to a pair of successive, remaining lines 57, as shown. | ||||

60. |
Circles 1, 2, 3, 5, 8, 36, 45, 51, 58 and 59, lines 38, 52 and 57, and patterns 41, 46, 49 and 53, together, make up all necessary constituents for the final reconstruction. | ||||

61. |
Remove all superfluous parts not visible within the formation itself. High resolution dwf-file | ||||

62. |
Colour all areas coresponding to standing... High resolution dwf-file | ||||

63. |
...or to flattened crop, to finish the reconstruction of the Wayland's Smithy formation of 9-08-2005. High resolution dwf-file | ||||

64. |
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. | |||||