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Mondrian Style Geometric Construction

Mondrian Style Geometric Construction
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2017-12-21 02:49
PolygonFunctionTransformation
In collections Paintings modeled in Geogebra
This example demonstrates a Mondrian-style artwork through geometric construction. It involves core concepts of geometric construction such as points, line segments, polygons, and transformations. Using GeoGebra commands like Segment, OrthogonalLine, Polygon, and Dilate, users can create geometric figures in the Mondrian style. Suitable for high school mathematics education and the intersection of art and mathematics.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. Point(g) → C
  4. OrthogonalLine(C, g) → h
  5. OrthogonalLine(B, f) → i
  6. Intersect(h, i) → D
  7. Polygon(A, C, D, B) → q1, a, c, d, b
  8. Midpoint(A, C) → E
  9. Polygon(E, A, 4) → poly1, j, k, l, m, F, G
  10. Midpoint(B, D) → H
  11. Polygon(H, G, F, B) → q2, h_1, g_1, f_1, b_1
  12. Dilate(D, 1 / 3, H) → D'
  13. Dilate(E, 2 / 3, C) → E'
  14. Segment(E', D') → n
  15. Dilate(E', 1 / 3, D') → E''
  16. Polygon(G, E'', D', H) → q3, g_2, e'', d', h_2
  17. Dilate(E, 2 / 3, G) → E'_1
  18. Polygon(E, E'_1, 4) → poly2, p, q, r, s, I, J
  19. Polygon(D', D, 4) → poly3, t, e, i_1, j_1, K, L
  20. Dilate(E', 1 / 3, C) → E''_1
  21. Dilate(L, 1 / 3, K) → L'
  22. Polygon(E''_1, C, K, L') → q4, e''_1, c_1, k_1, l'
  23. Polygon(C, E''_1, 4) → poly4, l_1, m_1, n_1, p_1, M, N
  24. Dilate(L', 5 / 9, M) → L''
  25. OrthogonalLine(L'', l') → q_1
  26. Intersect(q_1, n) → O
  27. Polygon(L, O, L'', L') → q5, l_2, o, l'', l'_1
  28. Polygon(I, E'', G, E'_1) → q6, i_2, e''_2, g_3, e'_1
  29. Polygon(E', E''_1, L'', O) → q7, e', e''_3, l''_1, o_1
  30. Polygon(O, L'', L', L) → q8, o_2, l''_2, l'_2, l_3
  31. Polygon(A, E, G, F) → q9, a_1, e_1, g_4, f_2
  32. Polygon(F, G, H, B) → q10, f_3, g_5, h_3, b_2
  33. Polygon(E, E', I, E'_1) → q11, e_2, e'_2, i_3, e'_3
  34. Polygon(E'_1, I, E'', G) → q12, e'_4, i_4, e''_4, g_6
  35. Polygon(G, E'', D', H) → q13, g_7, e''_5, d'_1, h_4
  36. Intersect(n, o) → P
  37. Polygon(E', E''_1, L'', P) → q14, e'_5, e''_6, l''_3, p_2
  38. Polygon(P, L'', L', L) → q15, p_3, l''_4, l'_3, l_4
  39. Polygon(L, K, D, D') → q16, l_5, k_2, d_1, d'_2
  40. Polygon(E''_1, C, N, M) → q17, e''_7, c_2, n_2, m_2
  41. Polygon(M, N, K, L') → q18, m_3, n_3, k_3, l'_4

AI Drawing Prompt Reference

Create a Mondrian-style geometric design with multiple squares and rectangles, constructed using points, line segments, and polygons, with symmetry and scaling transformations. Start by drawing line segment AB, then construct a line g perpendicular to AB, and take point C on g. Next, draw lines h and i perpendicular to f and g, respectively, and find intersection point D. Use this as one vertex of the polygon ABCD. Continue with multiple symmetry and scaling transformations to build the complex geometric design.
The prompt above was compiled from the original drawing commands and is for reference only.