Reconstruction of the 2015 Ox Drove formation | ||

1. |
Draw a circle. Draw the horizontal and vertical centerlines. | |

2. |
Copy circle 1 two times, to its upper and righthand intersections with the horizontal and vertical centerlines. | |

3. |
Draw the connecting line between the mutual intersections of circles 2. | |

4. |
Construct the inscribed dodecagon (regular 12-sided polygon) of circle 1, with one angular point on line 3. Number the angular points clockwise 1 - 12, starting at the upper righthand one. | |

5. |
Draw a line between the upper intersection of circle 1 and the vertical centerline and angular point 4 nr. 6. | |

6. |
Draw a line between the righthand intersection of circle 1 and the horizontal centerline and angular point 4 nr. 10. | |

7. |
Construct a circle concentric to circle 1, passing through the intersection of lines 5 and 6. | |

8. |
Construct the inscribed dodecagon of circle 7, with one angular point on line 3. | |

9. |
Draw a line similar to line 5, with respect to circle 7 and dodecagon 8. | |

10. |
Draw a line similar to line 6, with respect to circle 7 and dodecagon 8. | |

11. |
Construct a circle concentric to circle 1, passing through the intersection of lines 9 and 10. | |

12. |
Draw a line between the upper intersection of circle 1 and the vertical centerline and angular point 4 nr. 2. | |

13. |
Construct a circle concentric to circle 1, tangent to line 12. | |

14. |
Copy circle 11 to the intersection of circle 13 and line 3, and move this circle (copy and delete original) to its own lower lefthand intersection with line 3. | |

15. |
Construct a circle concentric to circle 1, tangent to circle 14 at the lower lefthand side. | |

16. |
Construct a circle centered at intersection of circle 15 and line 3, tangent to circle 13 at the upper righthand side. | |

17. |
Construct a circle concentric to circle 1, tangent to circle 16 at the lower lefthand side. | |

18. |
Construct a circle centered at the intersection of circle 17 and line 3, tangent to circle 15 at the upper righthand side. | |

19. |
Construct a circle concentric to circle 1, tangent to circle 18 at the lower lefthand side. | |

20. |
Construct a circle centered at angular point 4 nr 3, passing through angular point 4 nr. 2. | |

21. |
Copy circle 20 to the center of circle 1. | |

22. |
Draw the twelve rays of dodecagon 4, from the center of circle 1 to the angular points, and number the rays according to the angular points. | |

23. |
Construct a circle centered at the righthand intersection of circle 19 and the horizontal centerline, passing through the intersection of circle 17 and ray 22 nr. 3. | |

24. |
Copy circle 23 to the intersection of circle 21 and ray 22 nr. 3. | |

25. |
Construct a circle concentric to circle 1, tangent to circle 24 at the lefthand side. | |

26. |
Copy circle 23 to the intersection of circle 20 and ray 22 nr. 3. | |

27. |
Construct a circle concentric to circle 1, tangent to circle 26 at the lefthand side. | |

28. |
Construct a line tangent to circles 20 and 21, both at the upper sides. | |

29. |
Copy circle 11 two times, to the intersections (tangent points) of line 28 and circles 20 and 21. | |

30. |
Construct two parallel lines, tangent to circles 29 at both sides, and extend the upper one to the left upto circle 19. | |

31. |
Construct two parallel lines, tangent to circle 11 and lefthand circle 29 at both sides, and extend the lefthand one upto the upper line 30. | |

32. |
Copy circle 23 to the center of lefthand circle 29. | |

33. |
Copy circle 11 two times, to the upper intersection of circle 15 and the vertical centerline, and to the intersection of circle 32 and line 28. | |

34. |
Construct two parallel lines, tangent to circles 33 at both sides, and extend the righthand one downto the lower line 30. | |

35. |
Remove all redundant parts from lines 30, 31 and 34, and create the pattern as shown. | |

36. |
Copy pattern 35 eleven times, by repeating all necessary steps with respect to the other angular points 4 (nrs. 1 - 11). | |

37. |
Construct a "two-points" circle (defined by the two end-points of a centerline) between the intersections of ray 22 nr. 2 and circles 17 and 19. | |

38. |
Construct a "two-points" circle between the center of circle 37 and the intersection of ray 22 nr. 2 and circle 13. | |

39. |
Repeat steps 37 and 38 with respect to rays 22 nrs. 5, 8, and 11. | |

40. |
Copy circle 11 four times, to the intersections of circle 1 and the horizontal and vertical centerlines. | |

41. |
Construct two pairs of parallel lines, parallel to the horizontal and vertical centerlines, pairwise tangent to circles 40 at both sides. | |

42. |
Circles 1, 7, 13, 15, 17, 19, 25, 27, 38, and 39, lines 22, and 41, and patterns 35 and 36, are used for the final reconstruction. | |

43. |
Remove all parts not visible within the formation itself. | |

44. |
Colour all areas corresponding to standing... | |

45. |
...or to flattened crop, and finish the reconstruction of the 2015 Ox Drove formation. | |

46. |
The final result, matched with the aerial image. |

Copyright © 2015, Zef Damen, The Netherlands |