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金字塔构造与几何演示 by rowanw

金字塔构造与几何演示 by rowanw
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2015-10-08 01:49
立体几何最值优化几何作图
①本范例通过 GeoGebra 动态演示金字塔的几何构造与相关属性；②涉及核心数学概念包括面积计算、指数函数、分布特征、统计特性及线性规划；③作图要点提炼自构造摘要，运用了 Circle（圆）、Intersect（交点）、Point（点）、Segment（线段）、Midpoint（中点）等命令与对象；④适合高中及以上数学学习者，用于理解立体几何构造与优化问题。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Circle(B, C) → d
  3. Circle(C, A) → e
  4. Circle(C, B) → f
  5. Circle(C, D) → g
  6. Intersect(c, e, 1) → E
  7. Circle(C, E) → h
  8. Circle(C, F) → k
  9. Point(c) → G
  10. Circle(C, G) → p
  11. Point(d) → H
  12. Circle(C, H) → q
  13. Point(q) → I
  14. Circle(C, I) → r
  15. Circle(C, G) → s
  16. Circle(C, I) → t
  17. Circle(C, J) → c_1
  18. Point(c_1) → K
  19. Circle(C, K) → d_1
  20. Circle(C, L) → e_1
  21. Segment(M, N) → a
  22. Segment(O, N) → b
  23. Segment(M, O) → i
  24. Midpoint(i) → P
  25. Midpoint(b) → Q
  26. Midpoint(a) → R
  27. Segment(P, Q) → j
  28. Segment(R, Q) → l
  29. Segment(R, P) → m
  30. Midpoint(j) → S
  31. Midpoint(P, O) → T
  32. Midpoint(Q, O) → U
  33. Midpoint(Q, N) → V
  34. Midpoint(R, N) → W
  35. Midpoint(R, Q) → Z
  36. Midpoint(R, P) → A_1
  37. Midpoint(P, M) → B_1
  38. Midpoint(R, M) → C_1
  39. Segment(B_1, A_1) → n
  40. Segment(C_1, A_1) → a_1
  41. Segment(B_1, C_1) → b_1
  42. Segment(A_1, S) → f_1
  43. Segment(Z, A_1) → g_1
  44. Segment(S, Z) → h_1
  45. Segment(Z, V) → i_1
  46. Segment(Z, W) → j_1
  47. Segment(W, V) → k_1
  48. Segment(S, U) → l_1
  49. Segment(S, T) → m_1
  50. Segment(U, T) → n_1
  51. Midpoint(C_1, B_1) → D_1
  52. Midpoint(M, B_1) → E_1
  53. Midpoint(M, C_1) → F_1
  54. Midpoint(C_1, A_1) → G_1
  55. Midpoint(C_1, R) → H_1
  56. Midpoint(A_1, R) → I_1
  57. Midpoint(A_1, P) → J_1
  58. Midpoint(P, B_1) → K_1
  59. Midpoint(A_1, B_1) → L_1
  60. Midpoint(T, P) → M_1
  61. Midpoint(S, P) → N_1
  62. Midpoint(T, S) → O_1
  63. Midpoint(S, A_1) → P_1
  64. Midpoint(S, Z) → Q_1
  65. Midpoint(A_1, Z) → R_1
  66. Midpoint(Z, R) → S_1
  67. Midpoint(Z, W) → T_1
  68. Midpoint(W, R) → U_1
  69. Midpoint(T, U) → V_1
  70. Midpoint(O, U) → W_1
  71. Midpoint(O, T) → Z_1
  72. Midpoint(U, S) → A_2
  73. Midpoint(U, Q) → B_2
  74. Midpoint(S, Q) → C_2
  75. Midpoint(Q, Z) → D_2
  76. Midpoint(Q, V) → E_2
  77. Midpoint(Z, V) → F_2
  78. Midpoint(V, W) → G_2
  79. Midpoint(V, N) → H_2
  80. Midpoint(W, N) → I_2
  81. Segment(E_1, F_1) → p_1
  82. Segment(D_1, F_1) → q_1
  83. Segment(E_1, D_1) → r_1
  84. Segment(L_1, D_1) → s_1
  85. Segment(G_1, D_1) → t_1
  86. Segment(L_1, G_1) → a_2
  87. Segment(A_1, G_1) → b_2
  88. Segment(I_1, G_1) → c_2
  89. Segment(G_1, H_1) → d_2
  90. Segment(I_1, H_1) → e_2
  91. Segment(J_1, L_1) → f_2
  92. Segment(K_1, L_1) → g_2
  93. Segment(J_1, K_1) → h_2
  94. Segment(N_1, J_1) → i_2
  95. Segment(P_1, J_1) → j_2
  96. Segment(R_1, I_1) → k_2
  97. Segment(S_1, I_1) → l_2
  98. Segment(R_1, S_1) → m_2
  99. Segment(S_1, U_1) → n_2
  100. Segment(U_1, E_2) → p_2
  101. Segment(W, V) → q_2
  102. Segment(H_2, I_2) → r_2
  103. Segment(G_2, S_1) → s_2
  104. Segment(H_2, G_2) → t_2
  105. Segment(W, G_2) → a_3
  106. Segment(G_2, I_2) → b_3
  107. Segment(Z_1, G_2) → c_3
  108. Segment(M_1, B_2) → d_3
  109. Segment(R_1, B_2) → e_3
  110. Segment(N_1, W_1) → f_3
  111. Segment(M_1, R_1) → g_3
  112. Segment(P_1, E_2) → h_3
  113. Segment(Z_1, W_1) → i_3
  114. Midpoint(M, F_1) → J_2
  115. Midpoint(F_1, C_1) → K_2
  116. Midpoint(C_1, H_1) → L_2
  117. Midpoint(H_1, R) → M_2
  118. Midpoint(R, U_1) → N_2
  119. Midpoint(U_1, W) → O_2
  120. Midpoint(W, I_2) → P_2
  121. Midpoint(I_2, N) → Q_2
  122. Midpoint(M, E_1) → R_2
  123. Midpoint(E_1, B_1) → S_2
  124. Midpoint(B_1, K_1) → T_2
  125. Midpoint(K_1, P) → U_2
  126. Midpoint(P, M_1) → V_2
  127. Midpoint(M_1, T) → W_2
  128. Midpoint(T, Z_1) → Z_2
  129. Midpoint(Z_1, O) → A_3
  130. Midpoint(O, W_1) → B_3
  131. Midpoint(W_1, U) → C_3
  132. Midpoint(U, B_2) → D_3
  133. Midpoint(B_2, Q) → E_3
  134. Midpoint(Q, E_2) → F_3
  135. Midpoint(E_2, V) → G_3
  136. Midpoint(V, H_2) → H_3
  137. Midpoint(H_2, N) → I_3
  138. Segment(R_2, I_3) → j_3
  139. Segment(J_2, B_3) → k_3
  140. Segment(K_2, C_3) → l_3
  141. Segment(L_2, D_3) → m_3
  142. Segment(M_2, E_3) → n_3
  143. Segment(N_2, F_3) → p_3
  144. Segment(O_2, G_3) → q_3
  145. Segment(P_2, H_3) → r_3
  146. Segment(Q_2, I_3) → s_3
  147. Segment(S_2, H_3) → t_3
  148. Segment(T_2, G_3) → a_4
  149. Segment(U_2, F_3) → b_4
  150. Segment(V_2, E_3) → c_4
  151. Segment(W_2, D_3) → d_4
  152. Segment(Z_2, C_3) → e_4
  153. Segment(A_3, B_3) → f_4
  154. Segment(S_2, K_2) → g_4
  155. Segment(T_2, L_2) → h_4
  156. Segment(U_2, M_2) → i_4
  157. Segment(V_2, N_2) → j_4
  158. Segment(W_2, O_2) → k_4
  159. Segment(Z_2, P_2) → l_4
  160. Segment(A_3, Q_2) → m_4
  161. Segment(R_2, J_2) → n_4