Reconstruction of the
2022 Barbury Castle formation
Phase 1 and Phase 2 |
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| 1. |
| Draw a circle. Draw and extend the horizontal and vertical centerlines.
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| 2. |
| Construct the inscribed dodecagon (regular 12-sided polygon) of circle 1, pointing up.
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| 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.
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| 4. |
| Construct the inscribed hexagon (regular 6-sided polygon) of circle 1, pointing to the right.
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| 5. |
| Construct the circumscribed hexagon of circle 1, pointing up.
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| 6. |
| Draw the connecting line from the top of hexagon 5 to angular point 2 nr. 4.
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| 7. |
| Construct a circle concentric to circle 1, passing through the intersection of ray 3 nr. 2 and line 6.
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| 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.
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| 9. |
| Construct the inscribed hexagon of circle 7, pointing to the right.
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| 10. |
| Construct the inscribed hexagon of (the inscribed circle of) hexagon 9, pointing up.
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| 11. |
| Construct the inscribed hexagon of hexagon 10, pointing to the right.
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| 12. |
| Construct the inscribed hexagon of hexagon 11, pointing up.
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| 13. |
| Construct the inscribed hexagon of hexagon 12, pointing to the right.
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| 14. |
| Construct the inscribed hexagon of hexagon 13, pointing up.
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| 15. |
| Construct the inscribed hexagon of hexagon 14, pointing to the right.
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| 16. |
| Construct a circle centered at the upper intersection of hexagon 11 and the vertical centerline, tangent to hexagon 13 at the upper side.
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| 17. |
| Copy circle 16 to the righthand intersection of circle 1 and the horizontal centerline.
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| 18. |
| Construct a circle concentric to circle 1, tangent to circle 17 at the righthand side.
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| 19. |
| Lines 3, and 8, hexagons 4, 9, 10, 11, 12, 13, 14, and 15, and circle 16, are used for this reconstruction.
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| 20. |
| Remove all parts not visible within the formation itself.
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| 21. |
| The result, up to now, matched with the aerial image, shows a good fit.
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| 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.
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| 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"!
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| 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.
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| 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.
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| 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.
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| 27. |
| Construct the inscribed hexagon of circle 25, pointing to the right.
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| 28. |
| Construct the inscribed hexagon of (the inscribed circle of) hexagon 27, pointing up.
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| 29. |
| Construct the inscribed hexagon of hexagon 28, pointing to the right.
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| 30. |
| Construct the inscribed hexagon of hexagon 29, pointing up.
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| 31. |
| Construct the inscribed hexagon of hexagon 30, pointing to the right.
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| 32. |
| Construct the inscribed hexagon of hexagon 31, pointing up.
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| 33. |
| Construct the inscribed hexagon of hexagon 32, pointing to the right.
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| 34. |
| Construct the circumscribed square of circle 1, with sides horizontal and vertical.
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| 35. |
| Construct a circle concentric to circle 1, with an area equal to that of square 34.
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| 36. |
| Lines 3, and 26, hexagons 4, 27, 28, 29, 30, 31, 32, and 33, and circle 35, are used for the final reconstruction.
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| 37. |
| PHASE 1
Remove all parts not visible within the formation itself.
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| 38. |
| Colour all areas corresponding to standing...
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| 39. |
| ...or to flattened crop, and finish the reconstruction of the first phase of the 2022 Barbury Castle formation.
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| 40. |
| The result, matched with the aerial image of the first phase.
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| 41. |
| PHASE 2
Remove all parts not visible within the formation itself.
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| 42. |
| Colour all areas corresponding to standing...
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| 43. |
| ...or to flattened crop, and finish the reconstruction of the 2022 Barbury Castle formation.
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| 44. |
| The final result, matched with the aerial image.
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