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Max Bill Geometric Construction by Mihaela Git (3)

Max Bill Geometric Construction by Mihaela Git (3)
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2017-12-29 21:45
PolygonTrigonometryCoordinate GeometryOptimizationGeometric Construction
In collections Paintings modeled in Geogebra
This example demonstrates the construction of Max Bill's geometric shapes using GeoGebra, showcasing the combination of polygons, trapezoids, and triangles. It involves core mathematical concepts such as polygon construction, similarity transformations, intersection calculations, trigonometric functions, and arithmetic mean analysis. Key construction steps utilize GeoGebra commands like Polygon, Dilate, and Intersect, along with points, lines, and polygons. Suitable for high school and above students for understanding geometric transformations and comprehensive applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poligon1, f, g, h, i, C, D
  2. Dilate(D, 1 / 4, C) → D'
  3. Dilate(D, 2 / 4, C) → D'_1
  4. Dilate(D, 3 / 4, C) → D'_2
  5. Dilate(A, 1 / 4, B) → A'
  6. Dilate(A, 2 / 4, B) → A'_1
  7. Dilate(A, 3 / 4, B) → A'_2
  8. Dilate(D, 1 / 4, A) → D'_3
  9. Dilate(D, 2 / 4, A) → D'_4
  10. Dilate(D, 3 / 4, A) → D'_5
  11. Dilate(C, 1 / 4, B) → C'
  12. Dilate(B, 1 / 4, C) → B'
  13. Dilate(C, 2 / 4, B) → C'_1
  14. Polygon(D, D'_2, B, A') → q1, d, d'_2, b, a'
  15. Polygon(D', A, A'_2, C) → q2, d', a, a'_2, c
  16. Intersect(a', d') → E
  17. Polygon(D, E, A) → t1, a_1, d_1, e
  18. Intersect(d'_2, d') → F
  19. Polygon(D'_2, F, D') → t2, d'_1, d'_3, f_1
  20. Intersect(d'_2, a'_2) → G
  21. Polygon(C, G, B) → t3, b_1, c_1, g_1
  22. Intersect(a', a'_2) → H
  23. Polygon(A'_2, H, A') → t4, a'_1, a'_3, h_1
  24. Polygon(H, A'_2, A') → t5, a'_4, h_2, a'_5
  25. Polygon(A', H, G, B) → q3, a'_6, h_3, g_2, b_2
  26. Polygon(A, E, H, A'_2) → q4, a_2, e_1, h_4, a'_7
  27. Polygon(A, E, D) → t6, d_2, a_3, e_2
  28. Polygon(E, F, D'_2, D) → q5, e_3, f_2, d'_4, d_3
  29. Polygon(F, D'_2, D') → t7, d'_5, f_3, d'_6
  30. Polygon(G, F, D', C) → q6, g_3, f_4, d'_7, c_2
  31. Polygon(E, F, G, H) → q7, e_4, f_5, g_4, h_5

AI Drawing Prompt Reference

Create a complex geometric shape composed of multiple polygons, trapezoids, and triangles, demonstrating the use of similarity transformations, intersection calculations, and trigonometric functions. Start by constructing a quadrilateral, then scale one of its vertices by 1/4, 2/4, and 3/4 to generate multiple scaled points. Use these points to form several trapezoids and triangles, refining the shape through intersections to create a nested and overlapping arrangement of polygons.
The prompt above was compiled from the original drawing commands and is for reference only.