2018 Winterbourne Stoke Down formation
Construct a circle concentric to circle 1, passing through the lower intersection of circle 5 and ray 3 nr. 2.
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Reconstruction of the 2018 Winterbourne Stoke Down formation | ||
| 1. |
| Draw a circle. Draw and extend the horizontal and vertical centerlines. |
| 2. |
| Construct the inscribed decagon (regular 10-sided polygon) of circle 1, pointing up. Number the angular points clockwise 1 - 10, starting at the top. |
| 3. |
| Draw the ten rays of circle 1, to the angular points of decagon 2. Number the rays according to the angular points. |
| 4. |
| Draw the diagonal of decagon 2 between angular points nrs. 3 and 9. |
| 5. |
| Construct a circle passing through angular point nr. 1, and passing through the intersections of rays 3 nrs. 2 and 10 and diagonal 4. |
| 6. |
| Draw the diagonal of decagon 2 between angular points nrs. 2 and 8. |
| 7. |
| Construct a circle passing through angular point nr. 10, and passing through the intersections of rays 3 nrs. 1 and 9 and diagonal 6. |
| 8. |
| Construct a circle concentric to circle 1, passing through the lower intersection of circles 5 and 7. |
| 9. |
| Construct a circle concentric to circle 1, passing through the upper intersection of circles 5 and 7. |
| 10. |
| Construct the inscribed decagon of circle 9, pointing to the right. |
| 11. |
| Construct a circle centered at the intersection of the upper side of decagon 10 and the vertical centerline, passing through the lower intersection of circle 5 and ray 3 nr. 2. |
| 12. |
| Construct a circle concentric to circle 1, tangent to circle 11 at the upper side. |
| 13. |
| Construct a line tangent to circle 7 at the righthand side, and parallel to rays 3 nrs. 1 and 6, and extend this line in both directions upto circle 1. |
| 14. |
| Repeat step 13 nine times, with respect to the other corresponding rays 3. |
| 15. |
| Remove from circles 5, 7, and 8, and lines 14, all parts.... |
| 16. |
| ...such that the shown pattern remains. |
| 17. |
| Copy pattern 16 four times, relative to rays 3 nrs. 2 and 3, 4 and 5, 6 and 7, and 8 and 9, as shown. |
| 18. |
| (For reasons of clarity, the results of some previous steps are temporarily removed). Construct a circle concentric to circle 1, passing through the lower intersection of circle 5 and ray 3 nr. 2. |
| 19. |
| Construct the inscribed decagon of circle 18, pointing to the right. |
| 20. |
| Construct the inscribed circle of decagon 19. |
| 21. |
| Construct a circle concentric to circle 1, passing through the upper intersection of circle 5 and ray 3 nr. 2. |
| 22. |
| Draw the connecting line between the intersections of circles 5 and 21. |
| 23. |
| Construct a circle concentric to circle 1, tangent to line 22. |
| 24. |
| Construct the circumscribed decagon of circle 21, pointing to the right. |
| 25. |
| Construct the circumscribed circle of decagon 24. |
| 26. |
| Construct the inscribed circle of decagon 10. |
| 27. |
| Construct a circle centered at the righthand intersection of circle 23 and the horizontal centerline, tangent to the nearest sides of decagon 24, as shown. |
| 28. |
| Construct the inscribed pentagon (regular 5-sided polygon) of circle 12, pointing up. |
| 29. |
| Copy circle 27 five times, to the angular points of pentagon 28. |
| 30. |
| Extend line 13 upto circle 12. |
| 31. |
| Copy line 30, while mirroring with respect to the vertical centerline. |
| 32. |
| Repeat steps 30 and 31 four times, relative to the other angular points of pentagon 28. |
| 33. |
| Construct a circle concentric to circle 1, passing through the outer mutual intersections of lines 14. |
| 34. |
| Construct a line tangent to circle 33 at the righthand side, and parallel to rays 3 nrs. 1 and 6, and extending upto circle 1 in both directions. |
| 35. |
| Repeat step 34 four times, with respect to rays 3 nrs. 3 and 8, 5 and 10, 7 and 2, and 9 and 4. |
| 36. |
| Find the two angular points of decagon 19 in between rays 3 nrs. 1 and 2, and 5 and 6. Draw the connecting line between these two points, and extend this line upto circle 1 in both directions. |
| 37. |
| Repeat step 36 four times, in a similar way as step 35. |
| 38. |
| Construct a circle centered at the intersection of line 36 and the horizontal centerline, tangent to circle 33 at the righthand side. |
| 39. |
| Construct a line tangent to circle 38 at the righthand side, and parallel to line 36, and extend this line upto circle 1 in both directions. |
| 40. |
| Repeat step 39 four times, in a similar way as step 35. |
| 41. |
| Copy circle 38 to the intersection of circle 26 and ray 3 nr. 1. |
| 42. |
| Construct a circle concentric to circle 1, tangent to circle 41 at the lower side. |
| 43. |
| Copy circle 38 to the intersection of circle 25 and ray 3 nr. 1. |
| 44. |
| Construct a circle concentric to circle 1, tangent to circle 43 at the upper side. |
| 45. |
| Copy circle 38 to the intersection of circle 20 and ray 3 nr. 1. |
| 46. |
| Construct a circle concentric to circle 1, tangent to circle 45 at the upper side. |
| 47. |
| Remove from circles 20, 23, 25, 26, 42, 44, and 46, and from lines 34, 35, 36, 37, 39, and 40, all parts.... |
| 48. |
| ...such that these patterns remain. |
| 49. |
| Circles 1, and 29, lines 30, 31, and 32, and patterns 16, 17, and 48, are used for the final reconstruction. |
| 50. |
| Remove all parts not visible within the formation itself. |
| 51. |
| Colour all areas corresponding to standing... |
| 52. |
| ...or to flattened crop, and finish the reconstruction of the 2018 Winterbourne Stoke Down formation. |
| 53. |
| The final result, matched with the aerial image. |
| Copyright © 2018, Zef Damen, The Netherlands |
