2021 Herepath formation
In the following steps, this is repeated sixteen times, relative to the most recently added hexagon and each consecutive ray 4.
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Reconstruction of the 2021 Herepath 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. |
| Construct the inscribed regular 29-sided polygon of circle 1, pointing up. |
| 4. |
| Draw the twenty-nine rays of polygon 3, from the center to the angular points. Number the rays 1 - 29, clockwise, starting at the top. |
| 5. |
| Construct the inscribed hexagon of hexagon 2, with one angular point on the intersection of hexagon 2 and ray 4 nr. 2. In the following steps, this is repeated sixteen times, relative to the most recently added hexagon and each consecutive ray 4. |
| 6. |
| Construct the inscribed hexagon of hexagon 5, with one angular point on the intersection of hexagon 5 and ray 4 nr. 3. |
| 7. |
| Construct the inscribed hexagon of hexagon 6, with one angular point on the intersection of hexagon 6 and ray 4 nr. 4. |
| 8. |
| Construct the inscribed hexagon of hexagon 7, with one angular point on the intersection of hexagon 7 and ray 4 nr. 5. |
| 9. |
| Construct the inscribed hexagon of hexagon 8, with one angular point on the intersection of hexagon 8 and ray 4 nr. 6. |
| 10. |
| Construct the inscribed hexagon of hexagon 9, with one angular point on the intersection of hexagon 9 and ray 4 nr. 7. |
| 11. |
| Construct the inscribed hexagon of hexagon 10, with one angular point on the intersection of hexagon 10 and ray 4 nr. 8. |
| 12. |
| Construct the inscribed hexagon of hexagon 11, with one angular point on the intersection of hexagon 11 and ray 4 nr. 9. |
| 13. |
| Construct the inscribed hexagon of hexagon 12, with one angular point on the intersection of hexagon 12 and ray 4 nr. 10. |
| 14. |
| Construct the inscribed hexagon of hexagon 13, with one angular point on the intersection of hexagon 13 and ray 4 nr. 11. |
| 15. |
| Construct the inscribed hexagon of hexagon 14, with one angular point on the intersection of hexagon 14 and ray 4 nr. 12. |
| 16. |
| Construct the inscribed hexagon of hexagon 15, with one angular point on the intersection of hexagon 15 and ray 4 nr. 13. |
| 17. |
| Construct the inscribed hexagon of hexagon 16, with one angular point on the intersection of hexagon 16 and ray 4 nr. 14. |
| 18. |
| Construct the inscribed hexagon of hexagon 17, with one angular point on the intersection of hexagon 17 and ray 4 nr. 15. |
| 19. |
| Construct the inscribed hexagon of hexagon 18, with one angular point on the intersection of hexagon 18 and ray 4 nr. 16. |
| 20. |
| Construct the inscribed hexagon of hexagon 19, with one angular point on the intersection of hexagon 19 and ray 4 nr. 17. |
| 21. |
| Construct the inscribed hexagon of hexagon 20, with one angular point on the intersection of hexagon 20 and ray 4 nr. 18. |
| 22. |
| Construct a circle centered at the intersection of circle 1 and ray 4 nr. 2, tangent to the upper righthand side of hexagon 2. |
| 23. |
| Construct a circle concentric to circle 1, tangent to circle 22 at the upper righthand side. |
| 24. |
| Extend ray 4 nr. 2 upto circle 22. |
| 25. |
| Construct the inscribed equilateral triangle of circle 22, with one angular point on its intersection with line 24. |
| 26. |
| Construct a circle tangent to circle 22 at the inner side, and tangent to the upper lefthand and righthand sides of triangle 25. |
| 27. |
| Construct a circle centered at the intersection of circle 26 and line 24, tangent to circle 1 at the upper side. |
| 28. |
| Construct two circles concentric to circle 1, tangent to circles 26 and 27 at the upper sides. See detail. |
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| 29. |
| Copy circle 27 eighteen times, to the intersection of hexagon 2 and ray 4 nr. 1, and to the intersections of the following pairs of hexagons and rays 4: 5-2, 6-3, 7-4, 8-5, 9-6, 10-7, 11-8, 12-9, 13-10, 14-11, 15-12, 16-13, 17-14, 18-15, 19-16, 20-17, and 21-18, as shown. |
| 30. |
| Draw seventeen connecting lines, the first between the intersections of the first and second circles 29 with the upper lefthand sides of hexagons 2 and 5, and further between all consecutive pairs of corresponding intersections of circles 29 and the respective hexagons, as shown. See detail. |
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| 31. |
| Remove all redundend parts from hexagon 2, hexagons 5 through 21, and lines 30, such that the shown pattern remains. |
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| 32. |
| Repeat all necessary steps, to copy and rotate pattern 31 five times, with respect to the other angular points of hexagon 2, as shown. |
| 33. |
| Construct the inscribed regular 288-sided polygon of circle 23, pointing up. |
| 34. |
| Draw all the rays of polygon 33, from the center to the angular points. See detail. |
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| 35. |
| Remove from circles 28 and rays 34 all redundend parts, such that... |
| 36. |
| ...this pattern remains. |
| 37. |
| Circle 23, and patterns 31, 32, and 36, together, make up the final reconstruction. |
| 38. |
| Colour all areas corresponding to standing... |
| 39. |
| ...or to flattened crop, and finish the reconstruction of the 2021 Herepath formation. |
| 40. |
| The final result, matched with the aerial image. |
| Copyright © 2021, Zef Damen, The Netherlands |
