2012 Hackpen Hill (3) formation
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Reconstruction of the 2012 Hackpen Hill (3) formation | ||
| 1. |
| Draw a circle. Draw and extend the horizontal and vertical centerlines. |
| 2. |
| Construct the inscribed hexagon (regular six-sided polygon) of circle 1, pointing up. |
| 3. |
| Draw three rays of circle 1, from its center to the upper lefthand, upper righthand and lower angular points of hexagon 2. |
| 4. |
| Divide upper lefthand ray 3 into six equal parts. Number the nodes from the center outwards 1 - 5. |
| 5. |
| Divide upper righthand ray 3 into six equal parts. Number the nodes from the center outwards 1 - 5. |
| 6. |
| Divide lower ray 3 into six equal parts. Number the nodes from the center downwards 1 - 5. |
| 7. |
| Copy upper lefthand ray 3 ten times, from the center of circle 1 to division nodes 5 and 6. |
| 8. |
| Copy upper righthand ray 3 ten times, from the center of circle 1 to division nodes 4 and 6. |
| 9. |
| Copy lower ray 3 ten times, from the center of circle 1 to division nodes 4 and 5. |
| 10. |
| Draw three line-segments, from the center of circle 1 to nodes 4, 5 and 6 nrs. 1. |
| 11. |
| Divide the upper line-segments 10 both into six equal parts. |
| 12. |
| Copy upper lefthand line-segment 10 five times, from the center of circle 1 to the righthand division nodes 11. |
| 13. |
| Copy upper righthand line-segment 10 five times, from the center of circle 1 to the lefthand division nodes 11. |
| 14. |
| Copy lower line-segment 10 ten times, from the center of circle 1 to all division nodes 11. Extend these lines upwards to the nearest lines 7 and 8. |
| 15. |
| Extend the lower line-segment 10 upwards to the intersection of the nearest lines 7 and 8. |
| 16. |
| Remove all redundant parts from lines 7, 8, 10, 12, 13, 14 and 15, such that the shown pattern remains. |
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| 17. |
| Copy pattern 16, while rotating it 120° counterclockwise about the center of circle 1. |
| 18. |
| Copy pattern 16, while rotating it 120° clockwise about the center of circle 1. |
| 19. |
| Copy pattern 16 eight times, from the center of circle 1 to the nodes 4 and 5 nrs. 1-4. |
| 20. |
| Copy pattern 17 eight times, from the center of circle 1 to the nodes 4 and 6 nrs. 1-4. |
| 21. |
| Copy pattern 18 eight times, from the center of circle 1 to the nodes 5 and 6 nrs. 1-4. |
| 22. |
| Copy pattern 16, from the center of circle 1 to the upper angular point of hexagon 2, while rotating it 180°. |
| 23. |
| Copy pattern 17, from the center of circle 1 to the lower lefthand angular point of hexagon 2, while rotating it 180°. |
| 24. |
| Copy pattern 18, from the center of circle 1 to the lower righthand angular point of hexagon 2, while rotating it 180°. |
| 25. |
| Copy pattern 22 ten times, from the upper angular point of hexagon 2 to the intersections of the upper five lines 7 and 8 with the upper sides of hexagon 2. |
| 26. |
| Copy pattern 23 ten times, from the lower lefthand angular point of hexagon 2 to the intersections of the lower five lines 7 and the lefthand side of hexagon 2 and to the intersections of the lefthand five lines 9 and the lower lefthand side of hexagon 2. |
| 27. |
| Copy pattern 24 ten times, from the lower righthand angular point of hexagon 2 to the intersections of the lower five lines 8 and the righthand side of hexagon 2 and to the intersections of the righthand five lines 9 and the lower righthand side of hexagon 2. |
| 28. |
| Construct the circumscribed hexagon of circle 1, pointing to the right. |
| 29. |
| Construct the circumscribed circle of hexagon 28. |
| 30. |
| Construct the circumscribed dodecagon (regular 12-sided polygon) of circle 29, with the mid-point of a side on the vertical centerline. |
| 31. |
| Construct the circumscribed circle of dodecagon 30. |
| 32. |
| Construct a "two-points" circle (defined by the two end-points of a centerline) between the upper intersection of circle 1 and the lower intersection of circle 29, both with the vertical centerline. |
| 33. |
| Circles 1, 29, 31 and 32, and patterns 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 and 27, together make up the final reconstruction. |
| 34. |
| Colour all areas corresponding to standing... |
| 35. |
| ...or to flattened crop, and finish the reconstruction of the 2012 Hackpen Hill (3) formation. |
| 36. |
| The final result, matched with the aerial image. |
| Copyright © 2012, Zef Damen, The Netherlands |
