Reconstruction of the2001 Beckhampton (2) formation |
|||||

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

2. |
Construct the inscribed pentagon (regular 5-sided polygon) of circle 1, pointing to the right. Repeat this iteratively; this means: construct a second pentagon, inscribed in (the inscribed circle of) the first pentagon. | ||||

3. |
Construct the inscribed circle of the smaller pentagon 2. | ||||

4. |
Draw the diagonal on the right of the larger pentagon 2. | ||||

5. |
Construct a circle concentric to circle 1, tangent to diagonal 4. Construct the circumscribed pentagon of this circle, pointing to the left. | ||||

6. |
Draw the diagonal on the left of pentagon 5. | ||||

7. |
Construct a circle concentric to circle 1, tangent to diagonal 6. | ||||

8. |
Construct the circumscribed pentagon of circle 7, pointing to the right. Repeat this one more time, iteratively. | ||||

9. |
Construct the circumscribed circle of the larger pentagon 8. | ||||

10. |
Construct the circumscribed pentagon of circle 9, pointing to the left. Extend the upper and lower right sides of this pentagon, until they meet at the horizontal centerline. | ||||

11. |
Construct a circle concentric to circle 1, passing through the intersection of both extended sides of pentagon 10 (and the horizontal centerline). | ||||

12. |
Construct the inscribed pentagon of circle 3, pointing to the right. Repeat this two more times (three in total), iteratively. | ||||

13. |
Draw the rays to all corner-points of pentagons 2 (except for the rays coincident with the horizontal centerline), and extend these up to circle 1. | ||||

14. |
Extend the side on the left of the smallest pentagon 12 in both directions, until it meets the extensions of both indicated rays (the two rays next to the vertical centerline on the left). | ||||

15. |
Construct a circle concentric to circle 1, passing through the intersections of the extended side of pentagon 12 and both extended rays. | ||||

16. |
Extend both horizontal and vertical centerlines up to circle 15. | ||||

17. |
Construct the inscribed pentagon of circle 15, pointing to the left. Repeat this another five times (six in total), iteratively. | ||||

18. |
Construct the inscribed circle of the smallest pentagon 17. | ||||

19. |
Draw the connecting line between the intersections of the two indicated rays with circle 1. | ||||

20. |
Copy circle 18 to the intersection of line 19 and the vertical centerline. | ||||

21. |
Extend the vertical centerline to the upper side of circle 20. | ||||

22. |
Construct a circle concentric to circle 1, passing through the intersection of the (extended) vertical centerline and circle 20. | ||||

23. |
Construct a circle concentric to circle 1, passing through the intersections of the extended sides of pentagon 10 and line 4. | ||||

24. |
Copy circle 23 to the upper intersection of the vertical centerline and circle 1, and another time to the lower intersection of it with this copy itself. | ||||

25. |
Construct the inscribed pentagon of the lower circle 24, pointing down. Construct the inscribed circle of this pentagon. Construct a circle concentric to circle 1, tangent to the last circle at the upper side. Repeat these three steps another two times (three in total), iteratively. | ||||

26. |
Construct the inscribed pentagon of the smallest pentagon 17, pointing to the left. Construct the inscribed circle of this pentagon. | ||||

27. |
Construct the inscribed pentagon of circle 7, pointing to the right. Repeat this one more time, iteratively. Draw the diagonal on the left of the smaller pentagon. | ||||

28. |
Construct a circle concentric to circle 1, tangent to diagonal 27. Copy this circle to the intersection on the left of circle 26 and the horizontal centerline. | ||||

29. |
Construct two lines, parallel to each other, tangent to both circles 28 on both sides. Extend both lines to the right up to circle 22. | ||||

30. |
Construct a circle, with its center on the vertical centerline, tangent to both circles 22 and 1, both at the upper side. Copy this circle two times, to the intersections of upper line 29 with the outer one of the large circles 25 and with circle 26 on the left. | ||||

31. |
Construct a line tangent to both copied circles 30 at the upper sides. | ||||

32. |
Copy circle 30 another time, to the intersection of circle 11 and line 31. | ||||

33. |
Copy circle 30 a last time, to the upper intersection of the middle one of the large circles 25 and the righthand one of copied circles 30. | ||||

34. |
Construct a circle, with its center at the intersection of the upper line 29 and the inner one of the large circles 25, tangent to the middle one of these, at the near side. Copy this circle to the upper intersection of itself with the same inner one of the large circles 25. | ||||

35. |
Copy circles 32, 33 and the copied one of 34, at the same time mirroring relative to the indicated ray. | ||||

36. |
Construct a circle, with its center at the intersection of the (same) indicated ray and circle 3, tangent to circle 32 (and its mirrored copy). | ||||

37. |
Copy circles 32, 33, the copied one of 34, 35, 36, the copied one of 28, and the lines 29 four times (five in total), rotating and distributing the sets evenly around the main center (of circle 1), each centered along the indicated rays. | ||||

38. |
The original and copied sets 37, together with circles 1, 7, 9, 22, and the three larger circles 25, form all necessary parts for the reconstruction. | ||||

39. |
Removing all parts not used eventually, and making black areas corresponding to standing crop, finish the reconstruction of the 2001 Beckhampton (2) formation. | ||||

40. |
courtesy The Crop Circle Connector photo by: Steve Alexander | The final result, matched with the aerial image. | |||

| |||||

Copyright © 2001, Zef Damen, The Netherlands Personal use only, commercial use prohibited. | |||||

Since 1-February-2005 |