四维空间的复数线

四维空间的复数线
几何画板及绘图内容加载中,请稍等……
2015-06-12 17:12
所属专题 Complex Math
这个范例展示了复数线的几何表示。它涉及复数的基本概念,如实部和虚部。通过使用GeoGebra命令如OrthogonalLine、Intersect、Polygon等,可以动态地探索复数线的性质。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. OrthogonalLine(A, yAxis) → a
  2. OrthogonalLine(B, yAxis) → b
  3. OrthogonalLine(C, xAxis) → c
  4. OrthogonalLine(D, xAxis) → d
  5. Intersect(b, c) → E
  6. Intersect(b, d) → F
  7. Intersect(a, d) → G
  8. Intersect(a, c) → H
  9. Polygon(E, F, G, H) → poly1, e, f, g, h
  10. Vector(I, J) → u
  11. Translate(E, u) → E'
  12. Translate(F, u) → F'
  13. Translate(G, u) → G'
  14. Translate(H, u) → H'
  15. Polygon(E', F', G', H') → poly1', e', f', g', h'
  16. Intersect(e', f') → K
  17. Intersect(e, f) → L
  18. Intersect(e, h) → M
  19. Intersect(e', h') → N
  20. Polygon(K, L, M, N) → poly2, k, l, m, n
  21. Intersect(f', g') → O
  22. Intersect(f, g) → P
  23. Intersect(g, h) → Q
  24. Intersect(g', h') → R
  25. Polygon(O, P, Q, R) → poly3, o, p, q, r
  26. Intersect(e, h) → S
  27. Intersect(e', h') → T
  28. Intersect(g', h') → U
  29. Intersect(g, h) → V
  30. Polygon(S, T, U, V) → poly4, s, t, u_1, v
  31. Intersect(e, f) → W
  32. Intersect(e', f') → Z
  33. Intersect(f', g') → A_1
  34. Intersect(f, g) → B_1
  35. Polygon(W, Z, A_1, B_1) → poly5, w, z_1, a_1, b_1
  36. Intersect(e, h) → C_1
  37. Intersect(f', g') → D_1
  38. Vector(C_1, D_1) → i
  39. Point(h) → K_1
  40. Point(f) → L_1
  41. Point(h') → N_1
  42. Polygon(K_1, L_1, M_1, N_1) → poly6, k_1, l_1, m_1, n_1
  43. Point(h) → O_1
  44. Point(f) → P_1
  45. Point(h') → R_1
  46. Polygon(O_1, P_1, Q_1, R_1) → poly7, o_1, p_1, q_1, r_1
  47. Point(h) → S_1
  48. Point(f) → T_1
  49. Point(f') → U_1
  50. Point(h') → V_1
  51. Polygon(S_1, T_1, U_1, V_1) → poly8, s_1, t_1, u_2, v_1
  52. Intersect(g', h') → W_1
  53. Point(g) → Z_1
  54. Segment(W_1, Z_1) → j
  55. Point(o) → A_2
  56. Segment(Z_1, A_2) → c_1
  57. Segment(W_1, A_2) → d_1
  58. Segment(Z_1, B_2) → e_1
  59. Point(g) → C_2
  60. Intersect(t_1, d_1) → D_2
  61. Segment(C_2, D_2) → f_1
  62. Point(f) → L_2
  63. Segment(K_2, L_2) → g_1
  64. Vector(M_2, N_2) → w_1
  65. Translate(Z_1, w_1) → O_2
  66. Translate(A_2, w_1) → P_2
  67. Segment(O_2, P_2) → h_1
  68. Vector(Q_2, R_2) → i_1
  69. Translate(W_1, i_1) → S_2
  70. Translate(Z_1, i_1) → T_2
  71. Segment(S_2, T_2) → j'
  72. Vector(U_2, V_2) → j_1
  73. Translate(Z_1, j_1) → W_2
  74. Translate(B_2, j_1) → Z_2
  75. Segment(W_2, Z_2) → a_2
  76. Vector(A_3, B_3) → v_2
  77. Translate(C_2, v_2) → C_3
  78. Translate(D_2, v_2) → D_3
  79. Segment(C_3, D_3) → b_2
  80. Vector(E_3, F_3) → w_2
  81. Translate(K_2, w_2) → G_3
  82. Translate(L_2, w_2) → H_3
  83. Segment(G_3, H_3) → c_2
  84. Point(e) → I_3
  85. Point(o) → J_3
  86. Segment(I_3, J_3) → d_2
  87. Point(e) → K_3
  88. Intersect(t_1, f_1) → L_3
  89. Segment(K_3, L_3) → e_2
  90. Point(e) → M_3
  91. Point(f) → N_3
  92. Segment(M_3, N_3) → f_2
  93. Point(e) → O_3
  94. Point(e_1) → P_3
  95. Segment(O_3, P_3) → g_2
  96. Point(e) → Q_3
  97. Intersect(g', h') → R_3
  98. Segment(Q_3, R_3) → h_2
  99. Intersect(e, h) → S_3
  100. Segment(S_3, T_3) → i_2
  101. Intersect(g, h) → U_3
  102. Segment(U_3, V_3) → j_2
  103. Intersect(e', f') → W_3
  104. Segment(W_3, Z_3) → k_2
  105. Intersect(e', h') → A_4
  106. Segment(A_4, B_4) → l_2
  107. Intersect(e', h') → C_4
  108. Point(i_2) → E_4
  109. Point(j_2) → F_4
  110. Segment(E_4, F_4) → n_2
  111. Intersect(f', g') → G_4
  112. Segment(G_4, H_4) → p_2
  113. Point(f') → I_4
  114. Segment(I_4, J_4) → q_2
  115. Point(f') → K_4
  116. Segment(K_4, L_4) → r_2
  117. Intersect(e', f') → M_4
  118. Segment(M_4, N_4) → s_2
  119. Point(f') → O_4
  120. Segment(O_4, P_4) → t_2
  121. Point(i_2) → Q_4
  122. Vector(Q_4, R_4) → u_3
  123. Intersect(e, h) → S_4
  124. Vector(S_4, T_4) → v_3
  125. Point(h') → U_4
  126. Segment(U_4, V_4) → a_3
  127. Intersect(e', h') → W_4
  128. Segment(W_4, Z_4) → b_3
  129. Point(a_3) → A_5
  130. Point(b_3) → B_5
  131. Segment(A_5, B_5) → c_3
  132. Point(h') → C_5
  133. Segment(C_5, D_5) → d_3
  134. Point(q) → E_5
  135. Segment(E_5, F_5) → e_3
  136. Intersect(a_3, c_3) → G_5
  137. Point(e_3) → H_5
  138. Segment(G_5, H_5) → f_3
  139. Intersect(c_1, d_1) → K_5
  140. Intersect(e', h') → L_5
  141. Segment(K_5, L_5) → h_3
  142. Intersect(t_1, d_1) → M_5
  143. Point(b_2) → N_5
  144. Segment(M_5, N_5) → i_3
  145. Point(f) → O_5
  146. Point(e') → P_5
  147. Segment(O_5, P_5) → j_3
  148. Intersect(e_1, g_2) → Q_5
  149. Point(a_2) → R_5
  150. Segment(Q_5, R_5) → k_3
  151. Point(g) → S_5
  152. Segment(L_5, S_5) → l_3
  153. Point(b_2) → T_5
  154. Circle(T_5, U_5) → p_3
  155. Vector(V_5, W_5) → w_3
  156. Translate(p_3, w_3) → q_3
  157. Point(e) → Z_5
  158. Segment(U_5, Z_5) → m_3
  159. Intersect(p_3, m_1, 1) → A_6
  160. Segment(A_6, Z_5) → n_3
  161. Point(p_3) → B_6
  162. Segment(B_6, Z_5) → r_3
  163. Point(p_3) → C_6
  164. Segment(C_6, Z_5) → s_3
  165. Segment(C_6, Z_5) → t_3
  166. Angle(p_1, t_2) → α
  167. Point(l_2) → D_6
  168. Segment(D_6, E_6) → a_4
  169. Point(b_3) → F_6
  170. Segment(E_6, F_6) → b_4
  171. Segment(G_6, H_6) → c_4
  172. Segment(K_6, L_6) → d_4
  173. Segment(K_6, M_6) → e_4
  174. Segment(K_6, N_6) → f_4
  175. Point(d_4) → O_6
  176. Point(e_4) → P_6
  177. Segment(O_6, P_6) → h_4
  178. Point(f_4) → Q_6
  179. Segment(P_6, Q_6) → i_4
  180. Segment(Q_6, O_6) → j_4
  181. Segment(R_7, T_7) → g_4
  182. Intersect(e', h') → U_6
  183. Vector(U_6, V_6) → u_4
  184. Segment(W_6, Z_6) → m_2
  185. Segment(A_7, B_7) → g_3
  186. Point(b_3) → C_7
  187. Segment(C_7, D_7) → k_4
  188. Segment(E_7, F_7) → l_4
  189. Segment(G_7, H_7) → m_4
  190. Point(k_4) → I_7
  191. Vector(I_7, J_7) → v_4
  192. Point(v_4) → K_7
  193. Segment(K_7, L_7) → n_4
  194. Segment(I_7, M_7) → p_4
  195. Point(f') → N_7
  196. Segment(N_7, O_7) → q_4
  197. Intersect(e', f') → P_7
  198. Segment(P_7, Q_7) → r_4

AI 绘图提示语参考

绘制一个四维复数线的几何表示。首先,创建两条垂直于y轴的直线a和b,两条垂直于x轴的直线c和d。接着,找到这些直线的交点E、F、G、H,然后用这些点构造一个四边形。接着,通过平移和旋转这些点,构造一系列新的四边形。最后,通过这些新的四边形,进一步构造出更复杂的几何图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。