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Fruit Boxes Geometric Model

Fruit Boxes Geometric Model
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2012-12-14 07:03
TrigonometryCoordinate GeometryOptimizationGeometric Construction
In collections Cuboids & their Nets
This example dynamically demonstrates the geometric construction of fruit boxes, showcasing polygonal rotations and intersection relationships. It involves core math concepts like geometric mean, percentages, rotation, standard deviation, and intersection calculations. Construction highlights include commands such as Point, Segment, Polygon, Circle, Intersect, OrthogonalLine, Tangent, Slope, Derivative, Rotate, Angle, Line, Ray, Locus. Suitable for high school mathematics teaching, integrating geometric transformations with data analysis.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 36]) → B
  2. Segment(A, B) → a
  3. Polygon(A, B, 4) → polígono1, a_1, b, c, d, C, D
  4. Circle(D, corte) → e
  5. Circle(C, corte) → g
  6. Intersect(e, c) → E,
  7. Intersect(e, d) → F,
  8. Intersect(g, c) → G,
  9. Intersect(g, b) → H,
  10. OrthogonalLine(E, c) → h
  11. OrthogonalLine(F, d) → i
  12. OrthogonalLine(G, c) → j
  13. Intersect(h, i) → I
  14. Intersect(i, j) → J
  15. Intersect(j, a_1) → K
  16. Intersect(h, a_1) → L
  17. Circle(I, 18 - corte) → k
  18. Intersect(k, h) → M, N
  19. OrthogonalLine(N, h) → l
  20. Intersect(j, l) → O
  21. Circle(N, corte) → p
  22. Intersect(p, h) → P, Q
  23. OrthogonalLine(Q, h) → m
  24. Intersect(j, m) → R
  25. Segment(E, L) → n
  26. Segment(Q, R) → q
  27. Segment(F, H) → r
  28. Segment(G, K) → s
  29. Intersect(d, l) → S
  30. Intersect(b, l) → T
  31. Segment(S, T) → t
  32. Polygon(F, I, N, S) → polígono2, f_1, i_1, n_1, s_1
  33. Polygon(J, H, T, O) → polígono3, j_1, h_1, t_1, o
  34. Polygon(E, I, J, G) → polígono4, e_1, i_2, j_2, g_1
  35. Polygon(N, Q, R, O) → polígono5, n_2, q_1, r_1, o_1
  36. Polygon(I, N, O, J) → polígono6, i_3, n_3, o_2, j_3
  37. Polygon(Q, L, K, R) → polígono7, q_2, l_1, k_1, r_2
  38. Intersect(f, xAxis, 1) → U
  39. Circle(U, corte) → c_1
  40. Intersect(c_1, xAxis, 2) → V
  41. OrthogonalLine(V, xAxis) → b_1
  42. OrthogonalLine(W, yAxis) → d_1
  43. Intersect(d_1, b_1) → Z
  44. Tangent(Z, f) → m_1
  45. Slope(m_1) → m_2
  46. Derivative(f) → f'
  47. Intersect(f', xAxis) → A_1, B_1
  48. OrthogonalLine(A_1, xAxis) → p_1
  49. Intersect(f', b_1, 1) → C_1
  50. OrthogonalLine(D_1, b) → a_2
  51. Point(a_2) → E_1
  52. Rotate(E_1, 18*°, D_1) → F_1
  53. Angle(E_1, D_1, F_1) → α
  54. Line(D_1, F_1) → b_2
  55. Point(a_2) → G_1
  56. Rotate(G_1, 348*°, D_1) → H_1
  57. Angle(H_1, D_1, G_1) → β
  58. Line(H_1, D_1) → c_2
  59. OrthogonalLine(D_1, a_2) → d_2
  60. Circle(D_1, corte) → e_2
  61. Intersect(e_2, d_2) → I_1, J_1
  62. Line(I_1, b_2) → f_2
  63. Line(I_1, c_2) → g_2
  64. Circle(I_1, 18 - corte) → h_2
  65. Intersect(h_2, f_2) → K_1, L_1
  66. OrthogonalLine(L_1, a_2) → k_2
  67. Intersect(b_2, k_2) → M_1
  68. Circle(I_1, 36 - 2 * corte) → p_2
  69. Intersect(p_2, g_2) → N_1, O_1
  70. OrthogonalLine(N_1, a_2) → l_2
  71. Line(N_1, f_2) → s_2
  72. Line(L_1, g_2) → t_2
  73. Intersect(s_2, t_2) → P_1
  74. Intersect(c_2, l_2) → Q_1
  75. Polygon(N_1, I_1, L_1, P_1) → polígono8, n_4, i_4, l_3, p_3
  76. Polygon(N_1, Q_1, D_1, I_1) → polígono9, n_5, q_3, d_3, i_5
  77. Polygon(I_1, D_1, M_1, L_1) → polígono10, i_6, d_4, m_3, l_4
  78. OrthogonalLine(R_1, b) → a_3
  79. OrthogonalLine(R_1, a_3) → b_3
  80. Point(a_3) → S_1
  81. Ray(R_1, S_1) → c_3
  82. Point(b_3) → T_1
  83. Ray(R_1, T_1) → e_3
  84. Point(Circle[R_1, corte * 3]) → U_1
  85. Segment(R_1, U_1) → f_3
  86. OrthogonalLine(U_1, c_3) → g_3
  87. Circle(U_1, volumen / 50) → h_3
  88. Intersect(h_3, g_3) → V_1, W_1
  89. Locus(W_1, corte) → lugar1

AI Drawing Prompt Reference

Draw a geometric model consisting of multiple polygons, including a circle and four polygons generated by the intersection of circles and lines. Start by drawing a circle, then use the intersection points of circles and lines to form multiple polygons, with each polygon made up of intersection points and points on the circle. Finally, draw a line tangent to a given curve and calculate its slope.
The prompt above was compiled from the original drawing commands and is for reference only.