Max Bill's Geometric Construction by Mihaela Git (2)

Max Bill's Geometric Construction by Mihaela Git (2)
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2017-12-29 21:44
This example demonstrates Max Bill's work through geometric transformations and polygon construction. Key mathematical concepts include geometric transformations, polygons, and triangles. It uses commands like Polygon and Dilate in GeoGebra. Suitable for high school geometry education and teaching.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(C, B) → E
  3. Midpoint(E, B) → F
  4. Midpoint(C, E) → G
  5. Midpoint(D, A) → H
  6. Midpoint(H, A) → I
  7. Midpoint(D, H) → J
  8. Polygon(D, G, C) → t1, c, d, g_1
  9. Dilate(I, 2 / 3, F) → I'
  10. Dilate(A, 2 / 3, B) → A'
  11. Dilate(H, 2 / 3, E) → H'
  12. Dilate(J, 2 / 3, G) → J'
  13. Polygon(D, J', G) → t2, g_2, d_1, j'
  14. Polygon(J, J', D) → t3, d_2, j, j'_1
  15. Polygon(E, J, G) → t4, g_3, e, j_1
  16. Polygon(E, H', J) → t5, j_2, e_1, h'
  17. Polygon(H', H, J) → t6, j_3, h'_1, h_1
  18. Polygon(F, H, E) → t7, e_2, f_1, h_2
  19. Polygon(F, I', H) → t8, h_3, f_2, i'
  20. Polygon(I', I, H) → t9, h_4, i'_1, i_1
  21. Polygon(B, I, F) → t10, f_3, b, i_2
  22. Polygon(A', I, B) → t11, b_1, a', i_3
  23. Polygon(A', A, I) → t12, i_4, a'_1, a
  24. Polygon(G, E, J) → t13, j_4, g_4, e_3
  25. Polygon(B, I, F) → t14, f_4, b_2, i_5

AI Drawing Prompt Reference

Create a complex geometric figure composed of multiple triangles and quadrilaterals. Start by drawing a quadrilateral, then construct a series of new points using midpoints. Use these points and the original points to draw multiple triangles and quadrilaterals. The final figure includes several triangles and quadrilaterals connected through geometric transformations and midpoint constructions.
The prompt above was compiled from the original drawing commands and is for reference only.