长方锥体的表面展开图

长方锥体的表面展开图
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2019-01-13 00:53
本GeoGebra范例用于探索长方锥体的表面展开图及其表面积公式。它涉及立体几何中的核心概念,如锥体的表面积计算。通过使用GeoGebra命令,如Line(线)、Circle(圆)、Intersect(交点)、Vector(向量)等,可以动态展示锥体的构造过程。适合初中及以上学生学习锥体的相关知识。

GeoGebra 命令及参数

  1. Line(J, K) → h
  2. Circle(J, width) → g
  3. Intersect(g, h, 1) → M
  4. Vector(J, M) → w
  5. Translate(A, Vector[w / 2]) → C
  6. Dilate(I, length, H) → L
  7. Vector(H, L) → v
  8. Translate(C, v) → D
  9. Midpoint(C, D) → Q_1
  10. Translate(A, v) → B
  11. Midpoint(A, B) → Y
  12. Line(Y, Q_1) → g_1
  13. Midpoint(C, B) → N
  14. Circle(Q_1, N) → k_1
  15. Intersect(k_1, g_1, 2) → V_1
  16. Dilate(F, height, E) → G
  17. Vector(E, G) → u
  18. Translate(N, u) → O
  19. Polygon(A, B, D, C) → P, a, b, d, c
  20. Polygon(O, C, D) → Q, d_1, o, c_1
  21. Polygon(O, A, C) → R, c_2, o_1, a_1
  22. Polygon(O, D, B) → S, b_1, o_2, d_2
  23. Polygon(O, A, B) → T, b_2, o_3, a_2
  24. Midpoint(B, D) → U
  25. Segment(O, N) → e
  26. Segment(O, U) → f
  27. Midpoint(O, U) → W
  28. Midpoint(O, N) → V
  29. If(height ≤ 5, C) → Z
  30. Segment(Z, O) → i
  31. Segment(Z, A) → j
  32. Line(N, U) → k
  33. Intersect(k, c) → E_1
  34. OrthogonalLine(E_1, k) → l
  35. OrthogonalLine(U, k) → m
  36. Circle(E_1, width / 2) → p
  37. Intersect(p, l, 2) → F_1
  38. OrthogonalLine(F_1, l) → n
  39. Intersect(p, l, 1) → G_1
  40. OrthogonalLine(G_1, l) → q
  41. Intersect(m, n) → H_1
  42. Intersect(m, q) → I_1
  43. Midpoint(F_1, H_1) → J_1
  44. Midpoint(I_1, G_1) → K_1
  45. Line(J_1, K_1) → r
  46. Circle(E_1, A1) → s
  47. Midpoint(H_1, I_1) → L_1
  48. Circle(U, A1) → t
  49. Intersect(s, k, 1) → M_1
  50. Intersect(t, k, 2) → N_1
  51. Circle(J_1, A2) → e_1
  52. Circle(K_1, A2) → f_1
  53. Intersect(e_1, r, 1) → O_1
  54. Intersect(f_1, r, 2) → P_1
  55. Vector(O, M_1) → z_1
  56. Vector(O, N_1) → i_1
  57. Midpoint(Q_1, N) → R_1
  58. Midpoint(Y, N) → S_1
  59. Circle(S_1, O) → q_1
  60. Intersect(q_1, g_1, 1) → T_1
  61. Vector(T_1, P_1) → u_1
  62. Vector(O, T_1) → w_1
  63. Vector(A, G_1) → l_1
  64. Vector(B, I_1) → n_1
  65. Vector(D, H_1) → r_1
  66. Circle(V_1, O) → h_1
  67. Vector(C, F_1) → s_1
  68. Intersect(h_1, g_1, 2) → U_1
  69. Vector(O, U_1) → z
  70. Vector(U_1, O_1) → j_1
  71. CircleArc(S_1, O, T_1) → p_1
  72. CircleArc(V_1, U_1, O) → t_1
  73. CircumcircleArc(M_1, O, N_1) → e_2
  74. Center(e_2) → W_1
  75. Translate(O, Vector[w_1 * m_1]) → O'
  76. Translate(O, Vector[z_1 * (m_1 - 1)]) → O'_1
  77. Translate(O, Vector[z * (m_1 - 2)]) → O'_2
  78. Translate(O, Vector[i_1 * (m_1 - 3)]) → O'_3
  79. Translate(T_1, Vector[u_1 * (m_1 - 4)]) → Z_1
  80. Translate(U_1, Vector[j_1 * (m_1 - 4)]) → A_2
  81. Ray(S_1, O') → f_2
  82. Intersect(p_1, f_2, 1) → C_2
  83. If(m_1 ≤ 0, O, If[m_1 < 1, C_2, If[m_1 < 4, T_1, If[m_1 < 5, Z_1, P_1]]]) → B_2
  84. Ray(W_1, O'_1) → g_2
  85. Intersect(e_2, g_2, 1) → D_2
  86. If(m_1 ≤ 1, O, If[m_1 < 2, D_2, M_1]) → E_2
  87. Ray(W_1, O'_3) → h_2
  88. Intersect(e_2, h_2, 1) → F_2
  89. If(m_1 ≤ 3, O, If[m_1 < 4, F_2, N_1]) → G_2
  90. Ray(V_1, O'_2) → i_2
  91. Intersect(t_1, i_2, 1) → H_2
  92. If(m_1 ≤ 2, O, If[m_1 < 3, H_2, If[m_1 < 4, U_1, If[m_1 < 5, A_2, O_1]]]) → I_2
  93. Translate(A, Vector[l_1 * (m_1 - 4)]) → A'
  94. Translate(B, Vector[n_1 * (m_1 - 4)]) → B'
  95. Translate(D, Vector[r_1 * (m_1 - 4)]) → D'
  96. Translate(C, Vector[s_1 * (m_1 - 4)]) → C'
  97. If(m_1 ≤ 4, A, If[m_1 < 5, A', G_1]) → J_2
  98. If(m_1 ≤ 4, C, If[m_1 < 5, C', F_1]) → K_2
  99. If(m_1 ≤ 4, D, If[m_1 < 5, D', H_1]) → L_2
  100. If(m_1 ≤ 4, B, If[m_1 < 5, B', I_1]) → M_2
  101. Polygon(E_2, K_2, J_2) → poly1, j_2, e_3, k_2
  102. Polygon(J_2, M_2, B_2) → poly2, b_3, j_3, m_2
  103. Polygon(M_2, G_2, L_2) → poly3, l_2, m_3, g_3
  104. Polygon(L_2, I_2, K_2) → poly4, k_3, l_3, i_3
  105. Polygon(K_2, J_2, M_2, L_2) → poly5, k_4, j_4, m_4, l_4
  106. Segment(U, G_2) → n_2
  107. Midpoint(U, G_2) → N_2
  108. Midpoint(O, U) → O_2
  109. Vector(P_2, N_2) → u_2
  110. Vector(P_2, O_2) → v_2
  111. Segment(N, O) → p_2
  112. Midpoint(O, N) → Q_2
  113. Segment(A, O) → q_2
  114. Segment(B, O) → r_2
  115. Segment(D, O) → t_2
  116. Segment(C, O) → a_3
  117. Segment(U, O) → c_3
  118. Midpoint(K_2, L_2) → R_2
  119. Segment(R_2, A_2) → d_3
  120. Midpoint(Q_2, I_2) → S_2
  121. Vector(T_2, S_2) → w_2
  122. Segment(J_2, K_2) → f_3