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Francesca. Madonna GeoGebra Example

Francesca. Madonna GeoGebra Example
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2023-03-20 19:46
FunctionTrigonometryCoordinate GeometryIntegralGeometric Construction
In collections geometriadinamica.es
This example demonstrates the construction of complex geometric figures and function graphs using GeoGebra, focusing on operations like orthogonal lines, points, segments, rotations, and reflections. Key mathematical concepts include orthocenter, integration, function graphing, and plane figure construction. It utilizes commands and objects such as OrthogonalLine, Point, Segment, If, Dilate, Circle, Intersect, Polygon, Line, Midpoint, Rotate, Mirror. Suitable for high school and above learners to understand the interaction between geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. OrthogonalLine(B, xAxis) → a
  2. Point(a) → C
  3. Segment(B, C) → b
  4. Point(b) → L_2
  5. Point(b) → M_1
  6. If(pas > 1, 0, 100000) → t_2
  7. If(pas > 0, 0, 1000000000) → t_1
  8. OrthogonalLine(A, b) → e
  9. OrthogonalLine(A, e) → g
  10. OrthogonalLine(A, b) → d
  11. Point(d) → D
  12. OrthogonalLine(D, e) → i
  13. Dilate(D, 1.47, A) → E
  14. Circle(A, E) → f
  15. Intersect(f, g, 2) → F
  16. OrthogonalLine(F, g) → h
  17. Intersect(h, i) → G
  18. If(pas > 2, 0, 1000000) → t_3
  19. If(pas > 3, 0, 100000) → t_4
  20. If(pas > 4, 0, 100000) → t_5
  21. If(pas > 5, 0, 100000) → t_6
  22. Segment(P_1, P_7) → c
  23. Polygon(A, F, G, D) → P, a_1, f_1, g_1, d_1
  24. OrthogonalLine(B_1, d_1) → j
  25. Intersect(f_1, j) → I
  26. Segment(B_1, I) → k
  27. OrthogonalLine(B_2, k) → l
  28. Line(L_2, l) → r_2
  29. Midpoint(D, A) → L
  30. Intersect(d_1, k) → H
  31. Circle(H, A) → p
  32. Intersect(p, k) → J,
  33. Circle(J, H) → q
  34. Intersect(f_1, k) → K
  35. Intersect(f_1, k) → M
  36. Point(k) → N
  37. Point(q) → O
  38. Intersect(l, k) → Q
  39. Circle(Q, N) → r
  40. OrthogonalLine(B_3, k) → m
  41. Intersect(m, k) → R
  42. Rotate(O, 59.99999999999999°, R) → S
  43. Rotate(O, 29.999999999999996°, R) → T
  44. Rotate(O, 90°, R) → U
  45. Mirror(U, k) → V
  46. Mirror(A, a_1) → A'
  47. Mirror(F, a_1) → F'
  48. Segment(A', F') → n
  49. Mirror(S, k) → W
  50. Mirror(T, k) → Y
  51. Mirror(T, m) → Z
  52. Mirror(S, m) → C_1
  53. Mirror(O, m) → D_1
  54. Mirror(Z, k) → E_1
  55. Polygon(Y, T, U, Z, E_1, V) → Q_1, s, t, u, z, e_1, v
  56. Mirror(C_1, k) → F_1
  57. Polygon(O, S, C_1, D_1, F_1, W) → R_1, o, s_{1}, c_1, d_2, f_2, w
  58. Circle(Y, T) → h_1
  59. Circle(T, Y) → k_1
  60. Point(k_1) → G_1
  61. Polygon(T, G_1, Y) → S_1, y_1, t_7, g_2
  62. OrthogonalLine(B_4, k) → b_1
  63. Point(b_1) → H_1
  64. OrthogonalLine(B_5, k) → i_1
  65. Point(i_1) → I_1
  66. Point(b_1) → J_1
  67. OrthogonalLine(J_1, b_1) → j_1
  68. OrthogonalLine(H_1, b_1) → l_1
  69. Point(l_1) → K_1
  70. Point(j_1) → L_1
  71. Polygon(H_1, J_1, L_1, K_1) → T_1, h_2, j_2, l_2, k_2
  72. OrthogonalLine(B_5, b) → m_1
  73. OrthogonalLine(B_5, b) → n_1
  74. OrthogonalLine(B_5, b) → p_1
  75. OrthogonalLine(B_5, b) → q_1
  76. Line(B_5, d_1) → r_1
  77. Point(m_1) → N_1
  78. OrthogonalLine(I_1, m_1) → s_1
  79. OrthogonalLine(N_1, m_1) → a_2
  80. Point(s_1) → O_1
  81. Point(a_2) → U_1
  82. Polygon(C_1, O_1, U_1, N_1) → V_1, c_2, o_1, u_1, n_2
  83. Line(B_6, b) → b_2
  84. Point(b_2) → W_1
  85. Point(b_2) → Y_1
  86. Point(b_2) → Z_1
  87. OrthogonalLine(W_1, b) → e_2
  88. OrthogonalLine(Z_1, b) → i_2
  89. OrthogonalLine(Y_1, b) → m_2
  90. Point(m_2) → C_2
  91. Point(m_2) → D_2
  92. Point(i_2) → E_2
  93. Point(e_2) → F_2
  94. Point(e_2) → G_2
  95. Polygon(Y_1, G_2, D_2, Z_1, F_2, C_2, W_1, E_2) → Q_2, y_2, g_3, d_3, z_1, f_3, c_3, w_1, e_3
  96. OrthogonalLine(M_1, b) → p_2
  97. Intersect(p_2, c) → H_2
  98. Point(k) → J_2
  99. Circle(Q, J_2) → q_2
  100. Point(k_2) → K_2
  101. Point(r_2) → I_2
  102. Point(q_2) → M_2
  103. Point(q_2) → N_2
  104. Point(q_2) → O_2
  105. Point(q_2) → R_2
  106. Point(q_2) → S_2
  107. Point(q_2) → T_2
  108. Point(k_2) → U_2
  109. Point(q_2) → V_2
  110. Point(q_2) → W_2
  111. Point(q_2) → Y_2
  112. Point(q_2) → Z_2
  113. Segment(I_2, S_2) → s_2
  114. Segment(I_2, R_2) → a_3
  115. Segment(I_2, O_2) → b_3
  116. Segment(I_2, N_2) → h_3
  117. Segment(I_2, V_2) → i_3
  118. Segment(I_2, Y_2) → j_3
  119. Segment(I_2, W_2) → k_3
  120. Segment(I_2, M_2) → l_3
  121. Segment(I_2, Z_2) → m_3
  122. Segment(I_2, T_2) → n_3

AI Drawing Prompt Reference

Draw a complex geometric figure with orthogonal lines, points, segments, rotations, and reflections. Start by constructing an orthogonal line a through point B and the x-axis, then take point C on a and draw segment b between B and C. Next, take points L2 and M1 on b, construct orthogonal lines e and d through point A and b, and take point D on d. Continue by constructing a series of orthogonal lines and circles, forming a quadrilateral P, connecting the vertices of P to form a polygon, and using rotation and reflection operations to generate new points and segments, ultimately completing the figure.
The prompt above was compiled from the original drawing commands and is for reference only.