Reconstruction of the 2022 Barbury Castle formation Phase 1 and Phase 2 | ||
1. | Draw a circle. Draw and extend the horizontal and vertical centerlines. | |
2. | Construct the inscribed dodecagon (regular 12-sided polygon) of circle 1, pointing up. | |
3. | Draw the twelve rays of dodecagon 2, from the center to the angular points. Number these rays (and angular points), clockwise, 1 - 12, starting at the top. | |
4. | Construct the inscribed hexagon (regular 6-sided polygon) of circle 1, pointing to the right. | |
5. | Construct the circumscribed hexagon of circle 1, pointing up. | |
6. | Draw the connecting line from the top of hexagon 5 to angular point 2 nr. 4. | |
7. | Construct a circle concentric to circle 1, passing through the intersection of ray 3 nr. 2 and line 6. | |
8. | Draw two connecting lines, from the intersection of ray 3 nr. 1 and hexagon 4 to the intersection of ray 3 nr. 2 and circle 7, and from this last point to the intersection of ray 3 nr. 3 and hexagon 4. Repeat this five times, for all other corresponding sets of intersections, as shown. | |
9. | Construct the inscribed hexagon of circle 7, pointing to the right. | |
10. | Construct the inscribed hexagon of (the inscribed circle of) hexagon 9, pointing up. | |
11. | Construct the inscribed hexagon of hexagon 10, pointing to the right. | |
12. | Construct the inscribed hexagon of hexagon 11, pointing up. | |
13. | Construct the inscribed hexagon of hexagon 12, pointing to the right. | |
14. | Construct the inscribed hexagon of hexagon 13, pointing up. | |
15. | Construct the inscribed hexagon of hexagon 14, pointing to the right. | |
16. | Construct a circle centered at the upper intersection of hexagon 11 and the vertical centerline, tangent to hexagon 13 at the upper side. | |
17. | Copy circle 16 to the righthand intersection of circle 1 and the horizontal centerline. | |
18. | Construct a circle concentric to circle 1, tangent to circle 17 at the righthand side. | |
19. | Lines 3, and 8, hexagons 4, 9, 10, 11, 12, 13, 14, and 15, and circle 16, are used for this reconstruction. | |
20. | Remove all parts not visible within the formation itself. | |
21. | The result, up to now, matched with the aerial image, shows a good fit. | |
22. | However, the area of circle 7 is almost exactly equal to the area of the inscribed square of circle 1. The circle is only 0.53% larger. | |
23. | And also, the area of circle 18 is only 0.27% larger than the area of the circumscribed square of circle 1. Both cases are equivalent to "squaring the circle"! | |
24. | Therefore, the reconstruction can be based on "squaring the circle". As follows. The first four steps are the same as steps 1 to 4 above. Construct the inscribed square of circle 1, pointing up. | |
25. | Construct a circle concentric to circle 1, with an area equal to that of square 24. Hint: the diameter of the circle is approximately equal to 112.84% of (1.12837926 times) one side of the square. | |
26. | Draw two connecting lines, from the intersection of ray 3 nr. 1 and hexagon 4 to the intersection of ray 3 nr. 2 and circle 25, and from this last point to the intersection of ray 3 nr. 3 and hexagon 4. Repeat this five times, for all other corresponding sets of intersections, as shown. | |
27. | Construct the inscribed hexagon of circle 25, pointing to the right. | |
28. | Construct the inscribed hexagon of (the inscribed circle of) hexagon 27, pointing up. | |
29. | Construct the inscribed hexagon of hexagon 28, pointing to the right. | |
30. | Construct the inscribed hexagon of hexagon 29, pointing up. | |
31. | Construct the inscribed hexagon of hexagon 30, pointing to the right. | |
32. | Construct the inscribed hexagon of hexagon 31, pointing up. | |
33. | Construct the inscribed hexagon of hexagon 32, pointing to the right. | |
34. | Construct the circumscribed square of circle 1, with sides horizontal and vertical. | |
35. | Construct a circle concentric to circle 1, with an area equal to that of square 34. | |
36. | Lines 3, and 26, hexagons 4, 27, 28, 29, 30, 31, 32, and 33, and circle 35, are used for the final reconstruction. | |
37. | PHASE 1 Remove all parts not visible within the formation itself. | |
38. | Colour all areas corresponding to standing... | |
39. | ...or to flattened crop, and finish the reconstruction of the first phase of the 2022 Barbury Castle formation. | |
40. | The result, matched with the aerial image of the first phase. | |
41. | PHASE 2 Remove all parts not visible within the formation itself. | |
42. | Colour all areas corresponding to standing... | |
43. | ...or to flattened crop, and finish the reconstruction of the 2022 Barbury Castle formation. | |
44. | The final result, matched with the aerial image. |
Copyright © 2022, Zef Damen, The Netherlands |
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