Max Bill's Geometric Construction

Max Bill's Geometric Construction
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2017-12-29 21:40
This example demonstrates Max Bill's work through geometric construction using GeoGebra commands such as Point, Polygon, Midpoint, and Segment. It involves core mathematical concepts such as coordinate geometry and geometric construction. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Midpoint(f) → E
  5. Midpoint(i) → F
  6. Midpoint(g) → G
  7. Midpoint(h) → H
  8. Polygon(G, H, 4) → poly2, j, k, l, m, I, J
  9. Midpoint(B, E) → K
  10. Midpoint(B, G) → L
  11. Midpoint(A, E) → M
  12. Midpoint(A, F) → N
  13. Midpoint(F, D) → O
  14. Midpoint(D, H) → P
  15. Midpoint(H, C) → Q
  16. Midpoint(C, G) → R
  17. Segment(K, L) → n
  18. Segment(M, N) → p
  19. Segment(O, P) → q
  20. Segment(Q, R) → r
  21. Polygon(B, L, K) → t1, k_1, b, l_1
  22. Polygon(A, M, N) → t2, n_1, a, m_1
  23. Polygon(O, P, D) → t3, d, o, p_1
  24. Polygon(R, Q, C) → t4, c, r_1, q_1
  25. Polygon(K, L, G, E) → q1, k_2, l_2, g_1, e
  26. Polygon(M, E, F, N) → q2, m_2, e_1, f_1, n_2
  27. Polygon(G, H, Q, R) → q3, g_2, h_1, q_2, r_2
  28. Polygon(F, O, P, H) → q4, f_2, o_1, p_2, h_2
  29. Polygon(E, F, H, G) → q5, e_2, f_3, h_3, g_3
  30. Polygon(E, F, H, G) → q6, e_3, f_4, h_4, g_4

AI Drawing Prompt Reference

Draw a complex geometric pattern composed of multiple quadrilaterals. Start by taking points A and B on the x-axis and y-axis respectively, then construct a quadrilateral with A and B as opposite vertices. Next, take the midpoints E, F, G, and H of the diagonals of the quadrilateral, and construct another quadrilateral. Using these midpoints and the vertices of the original quadrilateral, further construct multiple quadrilaterals to form the final pattern.
The prompt above was compiled from the original drawing commands and is for reference only.