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四维超立方体透视演示

四维超立方体透视演示
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2019-09-26 07:33
立体几何矩阵参数方程几何作图
①本范例通过交互式演示展示了四维超立方体（Tesseract）在三维空间中的投影形态；②涉及的核心数学概念包括立体几何、矩阵变换、参数方程以及积分计算；③作图要点提炼自构造摘要，使用了射线(Ray)、点(Point)、线段(Segment)、交点(Intersect)等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解高维几何与空间变换的直观表示。

GeoGebra 命令及参数

  1. Ray(F_3, H_3) → r_7
  2. Point(r_7) → J_3
  3. Segment(E, G) → l
  4. Segment(G, F) → m
  5. Segment(F, E) → n
  6. Ray(E, H) → p
  7. Point(p) → I
  8. Segment(I, H) → q
  9. Ray(F, H) → r
  10. Point(r) → J
  11. Segment(H, J) → s
  12. Ray(G, H) → t
  13. Point(t) → K
  14. Segment(H, K) → a
  15. Ray(G, J) → b
  16. Ray(G, I) → c
  17. Ray(E, K) → d
  18. Ray(F, K) → e
  19. Intersect(b, e) → L
  20. Segment(L, K) → f_1
  21. Intersect(c, d) → M
  22. Segment(M, K) → g_1
  23. Segment(J, L) → h_1
  24. Segment(I, M) → i_1
  25. Ray(E, J) → j_1
  26. Ray(F, I) → k_1
  27. Intersect(j_1, k_1) → N
  28. Ray(G, N) → l_1
  29. Segment(N, J) → m_1
  30. Segment(N, I) → n_1
  31. Ray(E, L) → p_1
  32. Ray(F, M) → q_1
  33. Intersect(l_1, p_1) → O
  34. Segment(O, M) → r_1
  35. Segment(O, L) → s_1
  36. Segment(N, O) → t_1
  37. Ray(E_1, H_1) → p_2
  38. Point(p_2) → I_1
  39. Segment(I_1, H_1) → q_2
  40. Ray(F_1, H_1) → r_3
  41. Point(r_3) → J_1
  42. Segment(H_1, J_1) → s_2
  43. Ray(G_1, H_1) → t_3
  44. Point(t_3) → K_1
  45. Segment(H_1, K_1) → a_1
  46. Ray(G_1, J_1) → b_1
  47. Ray(G_1, I_1) → c_1
  48. Ray(E_1, K_1) → d_1
  49. Ray(F_1, K_1) → e_1
  50. Intersect(b_1, e_1) → L_1
  51. Segment(L_1, K_1) → f_2
  52. Intersect(c_1, d_1) → M_1
  53. Segment(M_1, K_1) → g_2
  54. Segment(J_1, L_1) → h_2
  55. Segment(I_1, M_1) → i_2
  56. Ray(E_1, J_1) → j_2
  57. Ray(F_1, I_1) → k_2
  58. Intersect(j_2, k_2) → N_1
  59. Ray(G_1, N_1) → l_3
  60. Segment(N_1, J_1) → m_3
  61. Segment(N_1, I_1) → n_3
  62. Ray(E_1, L_1) → p_3
  63. Ray(F_1, M_1) → q_3
  64. Intersect(l_3, p_3) → O_1
  65. Segment(O_1, M_1) → r_2
  66. Segment(O_1, L_1) → s_3
  67. Segment(N_1, O_1) → t_2
  68. Segment(F_2, E_2) → n_4
  69. Ray(E_2, H_2) → p_4
  70. Segment(I_2, H_2) → q_4
  71. Ray(F_2, H_2) → r_5
  72. Segment(H_2, J_2) → s_4
  73. Ray(G_2, H_2) → t_5
  74. Segment(H_2, K_2) → a_2
  75. Ray(G_2, J_2) → b_2
  76. Ray(G_2, I_2) → c_2
  77. Ray(E_2, K_2) → d_2
  78. Ray(F_2, K_2) → e_2
  79. Intersect(b_2, e_2) → L_2
  80. Segment(L_2, K_2) → f_3
  81. Intersect(c_2, d_2) → M_2
  82. Segment(M_2, K_2) → g_3
  83. Segment(J_2, L_2) → h_3
  84. Segment(I_2, M_2) → i_3
  85. Ray(E_2, J_2) → j_3
  86. Ray(F_2, I_2) → k_3
  87. Intersect(j_3, k_3) → N_2
  88. Ray(G_2, N_2) → l_5
  89. Segment(N_2, J_2) → m_5
  90. Segment(N_2, I_2) → n_5
  91. Ray(E_2, L_2) → p_5
  92. Ray(F_2, M_2) → q_5
  93. Intersect(l_5, p_5) → O_2
  94. Segment(O_2, M_2) → r_4
  95. Segment(O_2, L_2) → s_5
  96. Segment(N_2, O_2) → t_4
  97. Segment(E_3, G_3) → l_6
  98. Segment(G_3, F_3) → m_6
  99. Ray(E_3, H_3) → p_6
  100. Segment(I_3, H_3) → q_6
  101. Segment(H_3, J_3) → s_6
  102. Ray(G_3, H_3) → t_7
  103. Segment(H_3, K_3) → a_3
  104. Ray(G_3, J_3) → b_3
  105. Ray(G_3, I_3) → c_3
  106. Ray(E_3, K_3) → d_3
  107. Ray(F_3, K_3) → e_3
  108. Intersect(b_3, e_3) → L_3
  109. Segment(L_3, K_3) → f_4
  110. Intersect(c_3, d_3) → M_3
  111. Segment(M_3, K_3) → g_4
  112. Segment(J_3, L_3) → h_4
  113. Segment(I_3, M_3) → i_4
  114. Ray(E_3, J_3) → j_4
  115. Ray(F_3, I_3) → k_4
  116. Intersect(j_4, k_4) → N_3
  117. Ray(G_3, N_3) → l_7
  118. Segment(N_3, J_3) → m_7
  119. Segment(N_3, I_3) → n_7
  120. Ray(E_3, L_3) → p_7
  121. Ray(F_3, M_3) → q_7
  122. Intersect(l_7, p_7) → O_3
  123. Segment(O_3, M_3) → r_6
  124. Segment(O_3, L_3) → s_7
  125. Segment(N_3, O_3) → t_6
  126. Segment(E_4, G_4) → l_8
  127. Segment(G_4, F_4) → m_8
  128. Segment(F_4, E_4) → n_8
  129. Ray(E_4, H_4) → p_8
  130. Segment(I_4, H_4) → q_8
  131. Ray(F_4, H_4) → r_9
  132. Segment(H_4, J_4) → s_8
  133. Ray(G_4, H_4) → t_9
  134. Segment(H_4, K_4) → a_4
  135. Ray(G_4, J_4) → b_4
  136. Ray(G_4, I_4) → c_4
  137. Ray(E_4, K_4) → d_4
  138. Ray(F_4, K_4) → e_4
  139. Intersect(b_4, e_4) → L_4
  140. Segment(L_4, K_4) → f_5
  141. Intersect(c_4, d_4) → M_4
  142. Segment(M_4, K_4) → g_5
  143. Segment(J_4, L_4) → h_5
  144. Segment(I_4, M_4) → i_5
  145. Ray(E_4, J_4) → j_5
  146. Ray(F_4, I_4) → k_5
  147. Intersect(j_5, k_5) → N_4
  148. Ray(G_4, N_4) → l_9
  149. Segment(N_4, J_4) → m_9
  150. Segment(N_4, I_4) → n_9
  151. Ray(E_4, L_4) → p_9
  152. Ray(F_4, M_4) → q_9
  153. Intersect(l_9, p_9) → O_4
  154. Segment(O_4, M_4) → r_8
  155. Segment(O_4, L_4) → s_9
  156. Segment(N_4, O_4) → t_8
  157. Ray(E_1, O_2) → a_5
  158. Ray(F_1, O_3) → b_5
  159. Ray(D, O_1) → c_5
  160. Intersect(a_5, b_5) → P
  161. Segment(P, O_3) → d_5
  162. Segment(O_2, P) → e_5
  163. Segment(O_1, P) → f_6
  164. Ray(G_1, P) → g_6
  165. Segment(O_4, P) → h_6