水果箱几何模型

水果箱几何模型
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2012-12-14 07:03
①本范例通过动态演示水果箱的几何构造,展示多边形的旋转与交点关系;②涉及核心数学概念包括几何平均数、百分比、旋转、标准差和交点计算;③构造要点提炼自命令:点、线段、多边形、圆、交点、垂线、切线、斜率、导数、旋转、角度、直线、射线、轨迹;④适合高中数学教学,用于理解几何变换与数据分析的结合应用。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个由多个多边形组成的几何模型,包括一个圆和四个由圆与直线相交生成的多边形。首先绘制一个圆,然后通过圆与直线的交点生成多个多边形,每个多边形由圆与直线的交点和圆上的点构成。最后,绘制一个与给定曲线相切的直线,并计算其斜率。
以上提示语为根据原始绘图命令整理而来,仅供参考。