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Squared Square

Squared Square
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2019-03-21 00:38
Coordinate GeometryOptimizationGeometric Construction
In collections Cutting up squares
This example demonstrates the construction and transformation of a geometric figure. Core math concepts include coordinate geometry, geometric construction, and optimization. It utilizes GeoGebra commands such as Intersect, Segment, Circle, OrthogonalLine, and Line. Suitable for high school and university-level mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → D
  2. Segment(D, C) → a
  3. Segment(C, E) → b
  4. Segment(G, D) → c
  5. Segment(G, E) → d
  6. Circle(D, A) → e
  7. Intersect(e, c, 1) → F
  8. OrthogonalLine(A, a) → f
  9. OrthogonalLine(F, c) → g
  10. Intersect(f, g) → H
  11. Segment(F, H) → h
  12. Segment(H, A) → i
  13. Circle(C, B) → k
  14. Intersect(k, b, 1) → I
  15. OrthogonalLine(I, b) → j
  16. OrthogonalLine(B, a) → l
  17. Intersect(j, l) → J
  18. Segment(J, I) → m
  19. Segment(J, B) → n
  20. Circle(F, 29) → p
  21. Intersect(p, c, 1) → K
  22. OrthogonalLine(K, c) → q
  23. Circle(K, 29) → r
  24. Intersect(r, q, 2) → L
  25. Circle(G, 50) → s
  26. Intersect(s, d, 1) → M
  27. OrthogonalLine(M, d) → t
  28. Intersect(q, t) → N
  29. Segment(M, N) → a_1
  30. OrthogonalLine(L, q) → b_1
  31. Intersect(b_1, h) → O
  32. Segment(L, O) → c_1
  33. Segment(K, N) → d_1
  34. Circle(O, 4) → e_1
  35. Intersect(e_1, c_1, 1) → P
  36. OrthogonalLine(P, c_1) → f_1
  37. Intersect(f_1, n) → Q
  38. Segment(P, Q) → g_1
  39. OrthogonalLine(H, h) → h_1
  40. Intersect(h_1, g_1) → R
  41. Segment(R, H) → i_1
  42. Circle(E, 27) → k_1
  43. Intersect(k_1, d, 1) → S
  44. Intersect(k_1, b, 1) → T
  45. OrthogonalLine(S, d) → j_1
  46. OrthogonalLine(T, b) → l_1
  47. Intersect(j_1, l_1) → U
  48. Segment(S, U) → m_1
  49. Segment(U, T) → n_1
  50. Circle(T, 19) → p_1
  51. Intersect(p_1, n_1, 1) → V
  52. Intersect(p_1, b, 1) → W
  53. OrthogonalLine(V, n_1) → q_1
  54. OrthogonalLine(W, b) → r_1
  55. Intersect(q_1, r_1) → Z
  56. Segment(V, Z) → s_1
  57. Segment(Z, W) → t_1
  58. Circle(I, 24) → c_2
  59. Intersect(c_2, m, 1) → A_1
  60. OrthogonalLine(A_1, m) → a_2
  61. OrthogonalLine(Z, b) → b_2
  62. Intersect(a_2, b_2) → B_1
  63. Segment(B_1, W) → d_2
  64. Segment(B_1, A_1) → e_2
  65. Circle(M, 35) → f_2
  66. Intersect(f_2, a_1, 1) → C_1
  67. OrthogonalLine(C_1, a_1) → g_2
  68. Intersect(g_2, s_1) → D_1
  69. Segment(C_1, D_1) → h_2
  70. OrthogonalLine(U, h_2) → i_2
  71. Intersect(i_2, h_2) → E_1
  72. Segment(U, E_1) → j_2
  73. Circle(D_1, 11) → k_2
  74. Intersect(k_2, h_2, 1) → F_1
  75. Circle(A_1, 18) → p_2
  76. Intersect(p_2, e_2, 1) → G_1
  77. OrthogonalLine(G_1, e_2) → l_2
  78. OrthogonalLine(J, m) → m_2
  79. Intersect(l_2, m_2) → H_1
  80. Segment(H_1, G_1) → n_2
  81. Segment(H_1, J) → q_2
  82. Circle(G_1, 6) → r_2
  83. OrthogonalLine(B_1, e_2) → t_2
  84. Circle(P, 25) → s_2
  85. Intersect(s_2, g_1, 1) → J_1
  86. OrthogonalLine(J_1, g_1) → a_3
  87. Line(K, L) → b_3
  88. Intersect(a_3, b_3) → K_1
  89. Circle(K_1, 9) → c_3
  90. Intersect(c_3, b_3, 2) → L_1
  91. Circle(L_1, 2) → d_3
  92. Intersect(d_3, b_3) → M_1, N_1
  93. Segment(K_1, N_1) → e_3
  94. Segment(L, K_1) → f_3
  95. Segment(K_1, J_1) → g_3
  96. Circle(J_1, 16) → h_3
  97. Intersect(h_3, g_3) → O_1,
  98. OrthogonalLine(O_1, g_3) → i_3
  99. Intersect(i_3, q_2) → P_1
  100. Segment(O_1, P_1) → j_3
  101. OrthogonalLine(L_1, j_3) → k_3
  102. Intersect(k_3, j_3) → Q_1
  103. Segment(L_1, Q_1) → l_3
  104. OrthogonalLine(H_1, q_2) → m_3
  105. Intersect(m_3, l_3) → R_1
  106. OrthogonalLine(N_1, e_3) → n_3
  107. Intersect(h_2, n_3) → S_1
  108. Segment(R_1, H_1) → p_3
  109. Intersect(n_3, p_3) → T_1
  110. Segment(S_1, T_1) → q_3
  111. Circle(T_1, 17) → r_3
  112. Intersect(r_3, n_2, 1) → U_1
  113. Segment(F_1, U_1) → s_3
  114. OrthogonalLine(B_1, e_2) → t_3
  115. Intersect(t_3, s_3) → V_1
  116. Segment(V_1, B_1) → a_4

AI Drawing Prompt Reference

Draw a geometric figure starting from the intersection of coordinate axes. Connect the intersection with two other points to form line segments. Draw a circle with one point as the center, intersecting the line segments at new points. Create perpendicular lines from these points, connecting them to form new shapes. Repeat the process with other points as centers, intersecting line segments and drawing perpendiculars to build a complex pattern of connected circles and lines, showcasing geometric construction and optimization.
The prompt above was compiled from the original drawing commands and is for reference only.