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Max Bill's Geometric Construction by Mihaela Git

Max Bill's Geometric Construction by Mihaela Git
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2017-12-29 21:42
TriangleCirclePolygonTransformationGeometric Construction
In collections Paintings modeled in Geogebra
This example demonstrates Max Bill's work through geometric construction, showcasing transformations and constructions of triangles, circles, and polygons. Key mathematical concepts include triangles, circles, polygons, and their transformations. It uses commands like Point, Polygon, Dilate, Segment, etc., for construction. Suitable for high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 3) → poly1, f, g, h, C
  4. Dilate(C, 1 / 3, A) → C'
  5. Dilate(C, 1 / 2, C') → C'_1
  6. Dilate(C, 1 / 3, B) → C'_2
  7. Dilate(C, 1 / 2, C'_2) → C'_3
  8. Dilate(A, 1 / 3, B) → A'
  9. Dilate(A, 1 / 2, A') → A'_1
  10. Segment(C', A'_1) → i
  11. Segment(A', C'_2) → j
  12. Segment(C'_1, C'_3) → k
  13. Polygon(C', A'_1, 3) → poly2, l, m, n, D
  14. Polygon(A', C'_2, 3) → poly3, p, q, r, E
  15. Polygon(C'_1, C'_3, 3) → poly4, s, t, a, F
  16. Polygon(C'_3, D, 3) → poly5, b, c, d, G
  17. Polygon(C'_1, D, 3) → poly6, e, f_1, g_1, H
  18. Polygon(C'_1, C', 3) → poly7, h_1, i_1, j_1, I
  19. Polygon(A'_1, A', 3) → poly8, k_1, l_1, m_1, J
  20. Polygon(C', A, 3) → poly9, n_1, p_1, q_1, K
  21. Polygon(C'_2, B, 2) → poly10, r_1, s_1
  22. Polygon(A', B, 3) → poly11, t_1, a_1, b_1, L

AI Drawing Prompt Reference

Draw a geometric pattern consisting of triangles, circles, and polygons, showcasing their transformation relationships. Start by drawing two line segments to form a triangle, then scale the vertices of the triangle by different ratios to create new points. Connect these points to form new triangles and polygons, resulting in a complex geometric design that illustrates the process of transformation and construction.
The prompt above was compiled from the original drawing commands and is for reference only.