Reconstruction of the 2016 Ox Drove formation | ||

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

2. |
Construct the circumscribed octagon (regular 8-sided polygon) of circle 1, with the mid-point of a side on the horizontal centerline. | |

3. |
Draw eight rays of circle 1, from the center to the intersections (tangent points) with octagon 2. Number the rays 1 - 8 clockwise, starting at the top. | |

4. |
Draw the diagonal of octagon 2 between the lefthand and righthand angular points just above the horizontal centerline. | |

5. |
Construct a circle concentric to circle 1, passing through the intersection of ray 3 nr. 2 and diagonal 4. | |

6. |
Copy circle 5 to the upper end-point of ray 3 nr. 1. | |

7. |
Construct a circle centered at the righthand intersection of circle 5 and diagonal 4, tangent to circle 6 at the near side. | |

8. |
Copy circle 7 to the center of circle 1. | |

9. |
Construct the circumscribed octagon of circle 5, with the sides parallel to those of octagon 2. | |

10. |
Construct a circle centered at the mid-point of the upper side of octagon 9, passing through the upper lefthand intersection of circle 7 and the upper righthand side of octagon 9. | |

11. |
Draw the eight rays of octagon 2, from the center to the angular points. Number these rays as well as the angular points 1 - 8 clockwise, starting next to the top to the right. | |

12. |
Copy circle 10 to the upper lefthand angular point of octagon 9. | |

13. |
Copy circle 10 to the upper intersection of circle 12 and ray 11 nr. 8. | |

14. |
Copy circle 10 two times, to the intersections of circles 12 and 13. | |

15. |
Create the shown pattern, by removing all parts from circles 12, 13, and 14, not visible within the formation. | |

16. |
Copy pattern 15 three times, by repeating all necessary steps with respect to rays 11 nrs. 2, 4 and 6, in stead of 8. | |

17. |
Construct a circle concentric to circle 1, passing through the intersection (tangent point) of circles 6 and 7. See detail. | |

18. |
Construct a circle centered at the intersection of circle 17 and ray 11 nr. 1, tangent to circle 5 at the near side. | |

19. |
Copy circle 18 three times, to its upper intersection with ray 11 nr. 1, and consecutively to the corresponding intersections, as shown. | |

20. |
Copy circle 18 to the intersection of circle 1 and ray 11 nr. 1. | |

21. |
Copy circle 18 four times, to the lower intersection of circle 20 and ray 11 nr. 1, and consecutively to the corresponding intersections, as shown. | |

22. |
Construct nine circles concentric to circle 1, passing through the upper intersections of circles 18 and 19, and the lower intersections of circles 20 and 21, all with ray 11 nr. 1. See detail. | |

23. |
Copy circle 18 to the center of circle 1. | |

24. |
Copy circle 18 two times, to the righthand intersection of circle 23 and the horizontal centerline, and consecutively to the corresponding intersection. | |

25. |
Construct two circles concentric to circle 1, tangent to circles 24 at the righthand sides. | |

26. |
Construct a circle centered at the upper intersection, and passing through the lower intersection of circle 8 and the vertical centerline. | |

27. |
Copy circle 26 to angular point 11 nr. 1. | |

28. |
Draw a line tangent to circle 23 at the righthand side, and tangent to circle 27 at the lefthand side. | |

29. |
Draw a line from the center of circle 1, tangent to circle 27 at the righthand side. | |

30. |
Copy circles 23 and 25 to the intersection (tangent point) of circle 27 and line 28. | |

31. |
Copy circles 23 and 25 to the intersection (tangent point) of circle 27 and line 29. | |

32. |
Copy circle 18 to the righthand intersection of the outer circle 25 and the horizontal centerline. | |

33. |
Construct a circle concentric to circle 1, tangent to circle 32 at the righthand side. | |

34. |
Draw three lines parallel to line 28, tangent to circles 25 and 33, and tangent to circles 30, all at the righthand sides. | |

35. |
Draw three lines parallel to line 29, tangent to circles 23 and 25, and tangent to circles 31, all at the upper lefthand sides. | |

36. |
Draw two parallel lines, tangent to circles 18 and 20 at both sides. | |

37. |
Copy lines 28, 29, 34, 35, and 36, three times, by repeating all necessary steps with respect to rays 11 nrs. 3, 5, and 7, in stead of 1. | |

38. |
Circles 1, 5, 8, 17, and 22, patterns 15 and 16, and lines 28, 29, 34, 35, 36, and 37, are used for the final reconstruction. | |

39. |
Remove all parts not visible within the formation itself. | |

40. |
Colour all areas corresponding to standing... | |

41. |
...or to flattened crop, and finish the reconstruction of the 2016 Ox Drove formation. | |

42. |
The final result, matched with the aerial image. |

Copyright © 2016, Zef Damen, The Netherlands |