金字塔的展开图

金字塔的展开图
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2019-02-13 16:54
①本范例演示金字塔的展开图,即其表面展开后的平面图形;②涉及核心数学概念包括多边形、立体几何、几何作图、旋转与平移;③作图要点提炼自GeoGebra命令:Point, Segment, Line, Circle, Intersect, Rotate, Polygon, OrthogonalLine, Midpoint, Vector, Translate, LineBisector, CircleArc, Ray, If等,用于构建金字塔的各个面和边;④适合高中立体几何教学,帮助学生理解三维图形与二维展开图的关系,培养空间想象能力。

GeoGebra 命令及参数

  1. Point(Circle[A, l]) → B
  2. Segment(A, B) → a
  3. Line(A, B) → b_2
  4. Circle(B, (3 * l / 4.5)) → c
  5. Intersect(c, b_2, 2) → C
  6. Rotate(C, 30°, B) → C'
  7. Line(C', b_2) → d
  8. Segment(B, C') → e
  9. Line(A, e) → f
  10. Intersect(d, f) → D
  11. Polygon(A, B, C', D) → poly1, a_1, b_1, c', d_1
  12. Segment(A, C') → g
  13. Segment(D, B) → h_1
  14. Intersect(g, h_1) → E
  15. OrthogonalLine(E, a_1) → i
  16. Circle(E, h) → k
  17. Intersect(k, i, 2) → F
  18. Segment(B, F) → j
  19. Segment(C', F) → l_5
  20. Segment(F, D) → m
  21. Segment(F, A) → n
  22. Segment(A, D) → q
  23. Midpoint(b_1) → G
  24. Segment(G, F) → r
  25. Line(E, G) → c_1
  26. Circle(G, F) → f_1
  27. Intersect(f_1, c_1, 2) → H
  28. Intersect(c_1, d_1) → I
  29. Circle(I, F) → g_1
  30. Intersect(g_1, c_1, 1) → J
  31. Vector(F, J) → u
  32. Point(c') → L
  33. Circle(L, F) → q_1
  34. Vector(F, H) → w
  35. Midpoint(A, B) → K
  36. Line(K, E) → e_1
  37. Circle(K, h) → p_1
  38. Intersect(e_1, c') → M
  39. Circle(M, h) → r_1
  40. Intersect(r_1, e_1, 2) → N
  41. Intersect(p_1, e_1, 1) → O
  42. Vector(F, N) → v
  43. Vector(F, O) → z
  44. Translate(F, Vector[(z * o)]) → F'_1
  45. Translate(F, Vector[(u * (o - 1))]) → F'_2
  46. Translate(F, Vector[(v * (o - 2))]) → F'_3
  47. Translate(F, Vector[(w * (o - 3))]) → F'
  48. Segment(F, N) → s
  49. LineBisector(s) → a_2
  50. Intersect(a_2, c') → P
  51. CircleArc(P, N, F) → c_2
  52. Ray(P, F'_3) → d_2
  53. Intersect(c_2, d_2, 1) → Q
  54. Segment(F, O) → e_2
  55. LineBisector(e_2) → f_2
  56. Intersect(f_2, a_1) → R
  57. CircleArc(R, F, O) → g_2
  58. Ray(R, F'_1) → h_2
  59. Intersect(g_2, h_2, 1) → S
  60. CircleArc(I, F, J) → k_2
  61. CircleArc(G, H, F) → p_2
  62. Ray(I, F'_2) → i_2
  63. Intersect(k_2, i_2, 1) → T
  64. Ray(G, F') → j_2
  65. Intersect(p_2, j_2, 1) → U
  66. Circle(I, E) → s_1
  67. OrthogonalLine(I, a_1) → i_1
  68. Intersect(s_1, i_1, 2) → V
  69. Intersect(s_1, i_1, 1) → W
  70. OrthogonalLine(V, i_1) → j_1
  71. OrthogonalLine(W, i_1) → k_1
  72. OrthogonalLine(G, k_1) → l_1
  73. Intersect(j_1, l_1) → Z
  74. Intersect(k_1, l_1) → A_1
  75. Midpoint(V, Z) → B_1
  76. Midpoint(A_1, W) → C_1
  77. Circle(B_1, r) → t_1
  78. Circle(C_1, r) → q_2
  79. OrthogonalLine(B_1, k_1) → m_1
  80. Intersect(t_1, m_1, 1) → D_1
  81. Intersect(q_2, m_1, 2) → E_1
  82. Vector(C', Z) → u_1
  83. Vector(B, A_1) → v_1
  84. Vector(N, D_1) → w_1
  85. Vector(O, E_1) → z_1
  86. Translate(N, Vector[(w_1 * (o - 4))]) → N'
  87. Translate(O, Vector[(z_1 * (o - 4))]) → O'
  88. Translate(B, Vector[(v_1 * (o - 4))]) → B'
  89. Translate(A, Vector[(v_1 * (o - 4))]) → A'
  90. Translate(C', Vector[(u_1 * (o - 4))]) → C''
  91. Translate(D, Vector[(u_1 * (o - 4))]) → D'
  92. If(o < 1, S, If[o < 4, O, If[o < 5, O', E_1]]) → F_1
  93. If(o < 1, F, If[o < 2, T, J]) → G_1
  94. If(o < 3, F, If[o < 4, U, H]) → H_1
  95. If(o < 2, F, If[o < 3, Q, If[o < 4, N, If[o < 5, N', D_1]]]) → I_1
  96. If(o < 4, A, If[o < 5, A', W]) → J_1
  97. If(o < 4, B, If[o < 5, B', A_1]) → K_1
  98. If(o < 4, C', If[o < 5, C'', Z]) → L_1
  99. If(o < 4, D, If[o < 5, D', V]) → M_1
  100. Polygon(F_1, J_1, K_1) → poly2, k_3, f_3, j_3
  101. Polygon(L_1, H_1, K_1) → poly3, k_4, l_2, h_3
  102. Polygon(L_1, I_1, M_1) → poly4, m_2, l_3, i_3
  103. Polygon(M_1, G_1, J_1) → poly5, j_4, m_3, g_3
  104. Intersect(m, j_3) → N_1
  105. Segment(I_1, N_1) → n_1
  106. Intersect(j_3, i_3) → O_1
  107. Intersect(c', i_3) → Q_1
  108. Intersect(c', i_3) → R_1
  109. Intersect(c', i_3) → S_1
  110. Intersect(c', i_3) → U_1
  111. Intersect(c', i_3) → A_2
  112. Intersect(l_2, i_3) → B_2
  113. Segment(B_2, O_1) → n_2
  114. Segment(B_2, M_1) → r_2
  115. Midpoint(M_1, L_1) → C_2
  116. Midpoint(L_1, K_1) → D_2
  117. Midpoint(K_1, J_1) → E_2
  118. Midpoint(J_1, M_1) → F_2
  119. Polygon(J_1, M_1, L_1, K_1) → poly6, j_5, m_4, l_4, k_5
  120. Intersect(j_3, d_1) → P_1
  121. Segment(P_1, M_1) → c_3
  122. Midpoint(r) → T_1
  123. Point(a_2) → G_2

AI 绘图提示语参考

绘制一个四棱锥的展开图。首先,创建一个圆心为A的圆,从中选取一点B。接着,连接A和B,再创建一条平行于AB的线b2。以B为圆心,创建一个圆c,与b2相交于C点。将C绕B旋转30度得到C',连接B和C',再创建一条平行于BC'的线d。d与AB的交点为D。使用A、B、C'、D作为顶点,绘制一个多边形。继续构造其他边和辅助线,最终形成四棱锥的展开图。
以上提示语为根据原始绘图命令整理而来,仅供参考。