Max Bill Geometric Construction by Mihaela Git (2)

Max Bill Geometric Construction by Mihaela Git (2)
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2018-02-06 02:01
This example demonstrates the geometric construction of Max Bill's artistic figures, involving core concepts like regular polygons, orthogonal lines, circles, similarity transformations, and reflections. Key GeoGebra commands and objects used include Segment, OrthogonalLine, Point, Intersect, Polygon, Dilate, Midpoint, Line, Mirror. Suitable for high school and above mathematics enthusiasts learning geometric transformations and art geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → C
  5. OrthogonalLine(C, g) → i
  6. Intersect(h, i) → D
  7. Polygon(A, B, D, C) → q1, a, b, d, c
  8. Dilate(D, 1 / 8, B) → D'
  9. Dilate(D, 2 / 8, B) → D'_1
  10. Dilate(C, 1 / 8, A) → C'
  11. Dilate(C, 2 / 8, A) → C'_1
  12. Midpoint(C, A) → E
  13. Midpoint(D, B) → F
  14. Line(E, F) → j
  15. Polygon(C'_1, D'_1, D', C') → q2, c'_1, d'_1, d', c'
  16. Mirror(C'_1, j) → G
  17. Mirror(D'_1, j) → H
  18. Mirror(D', j) → D''
  19. Mirror(C', j) → C''
  20. Polygon(G, H, D'', C'') → q2', g_1, h_1, d'', c''
  21. Polygon(C, C'', D'', D) → q3, c_1, c''_1, d''_1, d_1
  22. Mirror(C, j) → C'_2
  23. Mirror(C'', j) → C'''
  24. Mirror(D'', j) → D'''
  25. Mirror(D, j) → D'_2
  26. Polygon(C'_2, C''', D''', D'_2) → q3', c'_2, c''', d''', d'_2
  27. Dilate(A, 1 / 8, B) → A'
  28. Midpoint(A', B) → I
  29. Mirror(B, A') → B'
  30. Midpoint(B', A') → J
  31. Mirror(B', d') → B''
  32. Mirror(A', d') → A''
  33. Mirror(J, d') → J'
  34. Polygon(J', J, A', A'') → q4, j', j_1, a', a''
  35. Polygon(B'', J', J, B') → q5, b'', j'_1, j_2, b'
  36. Mirror(A'', j) → A'''
  37. Midpoint(A''', H) → K
  38. Midpoint(A'', D'_1) → L
  39. Polygon(A''', A'', L, K) → q6, a''', a''_1, l, k
  40. Polygon(K, H, D'_1, L) → q7, k_1, h_2, d'_3, l_1
  41. Dilate(D, 1 / 8, C) → D'_3
  42. Dilate(D'_1, 1 / 8, C'_1) → M
  43. Midpoint(C'_1, M) → N
  44. Midpoint(C, D'_3) → O
  45. Polygon(C, C'_1, N, O) → q8, c_2, c'_3, n, o
  46. Polygon(O, D'_3, M, N) → q9, o_1, d'_4, m, n_1

AI Drawing Prompt Reference

Draw a complex geometric figure composed of regular polygons, orthogonal lines, circles, and similarity transformations. Start by drawing a segment, then create perpendicular lines from both endpoints, and connect the intersections to form a quadrilateral. Perform multiple levels of dilation and reflection on this quadrilateral, and finally combine the transformed shapes into a symmetrical, intricate pattern to showcase the beauty of geometric transformations in art.
The prompt above was compiled from the original drawing commands and is for reference only.