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Max Bill Geometric Construction

Max Bill Geometric Construction
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2018-01-02 22:42
PolygonFunctionCoordinate GeometryGeometric ConstructionGraphing
In collections Paintings modeled in Geogebra
This example demonstrates the geometric construction of Max Bill's art using GeoGebra, highlighting polygon creation, midpoint calculation, and function visualization. Core concepts include polygons, function graphs, and coordinate geometry. Construction involves commands like Polygon and Midpoint, with objects such as f, g, h, i. Ideal for high school and above students exploring geometric constructions and function visualization.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(B, D) → E
  3. Midpoint(B, C) → F
  4. Midpoint(A, D) → G
  5. Midpoint(A, E) → H
  6. Midpoint(E, C) → I
  7. Polygon(B, A, E) → t1, e, b, a
  8. Polygon(A, H, G) → t2, g_1, a_1, h_1
  9. Polygon(H, E, G) → t3, g_2, h_2, e_1
  10. Polygon(G, E, D) → t4, d, g_3, e_2
  11. Polygon(B, F, E) → t5, e_3, b_1, f_1
  12. Polygon(F, E, I) → t6, i_1, f_2, e_4
  13. Polygon(F, C, I) → t7, i_2, f_3, c
  14. Polygon(E, C, D) → t8, d_1, e_5, c_1
  15. Polygon(E, F, I) → t9, i_3, e_6, f_4

AI Drawing Prompt Reference

Draw a geometric figure composed of multiple polygons. Start by creating a quadrilateral, then find the midpoints of its sides to construct new polygons. Specifically, first draw a quadrilateral, then use the midpoints of its sides and the original points to construct new polygons, repeating this process to form a complex geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.