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费曼路径反射演示

费曼路径反射演示
几何画板及绘图内容加载中，请稍等……
2014-12-09 01:28
概率统计几何作图
①本范例演示了费曼路径在几何反射中的多路径特性；②涉及核心数学概念包括反射、统计特性、乘法、实数、体积、集合论；③作图要点提炼自构造摘要，使用了Point, Intersect, PointIn, Segment, Mirror, Midpoint, Circle, Vector, OrthogonalLine等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解复杂几何变换与概率统计应用。

GeoGebra 命令及参数

  1. Point(xAxis) → F
  2. Point(xAxis) → G
  3. Point(xAxis) → H
  4. Point(xAxis) → I
  5. Point(xAxis) → J
  6. Point(xAxis) → K
  7. Point(xAxis) → L
  8. Point(xAxis) → M
  9. Intersect(xAxis, yAxis) → N
  10. Point(xAxis) → O
  11. Point(xAxis) → P
  12. Point(xAxis) → Q
  13. Point(xAxis) → R
  14. Point(xAxis) → S
  15. Point(xAxis) → T
  16. Point(xAxis) → U
  17. Point(xAxis) → V
  18. PointIn(y ≥ 0) → D
  19. Segment(D, F) → a
  20. PointIn(y ≥ 0) → E
  21. Segment(F, E) → b
  22. Segment(D, G) → d
  23. Segment(G, E) → e
  24. Segment(D, H) → f
  25. Segment(H, E) → g
  26. Point(a) → W
  27. Point(b) → Z
  28. Mirror(A_1, yAxis) → B_1
  29. Midpoint(A_1, B_1) → C_1
  30. Midpoint(A_1, C_1) → D_1
  31. Midpoint(C_1, B_1) → E_1
  32. Midpoint(B_1, E_1) → F_1
  33. Midpoint(E_1, C_1) → G_1
  34. Midpoint(C_1, D_1) → H_1
  35. Midpoint(D_1, A_1) → I_1
  36. Midpoint(A_1, I_1) → J_1
  37. Midpoint(I_1, D_1) → K_1
  38. Midpoint(D_1, H_1) → L_1
  39. Midpoint(H_1, C_1) → M_1
  40. Midpoint(C_1, G_1) → N_1
  41. Midpoint(G_1, E_1) → O_1
  42. Midpoint(E_1, F_1) → P_1
  43. Midpoint(F_1, B_1) → Q_1
  44. Circle(A_1, 0.5) → h
  45. Circle(J_1, 0.5) → k_3
  46. Circle(I_1, 0.5) → p
  47. Circle(K_1, 0.5) → q
  48. Circle(D_1, 0.5) → r
  49. Point(h) → R_1
  50. Point(k_3) → S_1
  51. Point(p) → T_1
  52. Point(q) → U_1
  53. Point(r) → V_1
  54. Vector(A_1, R_1) → v
  55. Vector(J_1, S_1) → w
  56. Vector(I_1, T_1) → i
  57. Vector(K_1, U_1) → j
  58. Vector(D_1, V_1) → l
  59. Point(e) → W_1
  60. Point(g) → Z_1
  61. Point(d) → A_2
  62. Point(f) → B_2
  63. Circle(L_1, 0.5) → s
  64. Circle(H_1, 0.5) → t
  65. Circle(M_1, 0.5) → c_1
  66. Circle(C_1, 0.5) → d_1
  67. Circle(N_1, 0.5) → e_1
  68. Circle(G_1, 0.5) → f_1
  69. Circle(O_1, 0.5) → g_1
  70. Circle(E_1, 0.5) → h_1
  71. Circle(P_1, 0.5) → k_1
  72. Circle(F_1, 0.5) → p_1
  73. Circle(Q_1, 0.5) → q_1
  74. Circle(B_1, 0.5) → r_1
  75. Point(s) → C_2
  76. Point(t) → D_2
  77. Point(c_1) → E_2
  78. Point(d_1) → F_2
  79. Point(e_1) → G_2
  80. Point(f_1) → H_2
  81. Point(g_1) → I_2
  82. Point(h_1) → J_2
  83. Point(k_1) → K_2
  84. Point(q_1) → M_2
  85. Point(r_1) → N_2
  86. Point(p_1) → L_2
  87. Segment(D, I) → m
  88. Segment(I, E) → n
  89. Point(m) → O_2
  90. Point(n) → P_2
  91. Segment(D, J) → a_1
  92. Segment(J, E) → b_1
  93. Segment(D, K) → i_1
  94. Segment(K, E) → j_1
  95. Segment(D, L) → l_1
  96. Segment(L, E) → m_1
  97. Segment(D, M) → n_1
  98. Segment(M, E) → s_1
  99. Segment(D, N) → t_1
  100. Segment(N, E) → a_2
  101. Segment(D, O) → b_2
  102. Segment(O, E) → c_2
  103. Segment(D, P) → d_2
  104. Segment(P, E) → e_2
  105. Segment(D, Q) → f_2
  106. Segment(Q, E) → g_2
  107. Segment(D, R) → h_2
  108. Segment(R, E) → i_2
  109. Segment(D, S) → j_2
  110. Segment(S, E) → k_2
  111. Segment(D, T) → l_2
  112. Segment(T, E) → m_2
  113. Segment(D, U) → n_2
  114. Segment(U, E) → p_2
  115. Segment(D, V) → q_2
  116. Segment(V, E) → r_2
  117. Point(a_1) → Q_2
  118. Point(b_1) → R_2
  119. Point(i_1) → S_2
  120. Point(j_1) → T_2
  121. Point(l_1) → U_2
  122. Point(m_1) → V_2
  123. Point(n_1) → W_2
  124. Point(s_1) → Z_2
  125. Point(t_1) → A_3
  126. Point(a_2) → B_3
  127. Point(b_2) → C_3
  128. Point(c_2) → D_3
  129. Point(d_2) → E_3
  130. Point(e_2) → F_3
  131. Point(f_2) → G_3
  132. Point(g_2) → H_3
  133. Point(h_2) → I_3
  134. Point(i_2) → J_3
  135. Point(j_2) → K_3
  136. Point(k_2) → L_3
  137. Point(l_2) → M_3
  138. Point(m_2) → N_3
  139. Point(n_2) → O_3
  140. Point(p_2) → P_3
  141. Point(q_2) → Q_3
  142. Point(r_2) → R_3
  143. Vector(L_1, C_2) → u_1
  144. Vector(H_1, D_2) → v_1
  145. Vector(M_1, E_2) → w_1
  146. Vector(C_1, F_2) → u_2
  147. Vector(N_1, G_2) → v_2
  148. Vector(G_1, H_2) → w_2
  149. Vector(O_1, I_2) → s_2
  150. Vector(E_1, J_2) → t_2
  151. Vector(F_1, L_2) → u_3
  152. Vector(Q_1, M_2) → v_3
  153. Vector(B_1, N_2) → w_3
  154. Vector(P_1, K_2) → a_3
  155. Mirror(E, xAxis) → E'
  156. Segment(D, E') → c
  157. Intersect(c, xAxis) → A
  158. Segment(D, A) → b_3
  159. Segment(A, E) → c_3
  160. OrthogonalLine(A, xAxis) → d_3
  161. Circle(A, 6) → e_3
  162. Intersect(e_3, d_3) → C, T_3
  163. Segment(T_3, C) → f_3
  164. OrthogonalLine(A_1, xAxis) → g_3
  165. OrthogonalLine(J_1, xAxis) → h_3
  166. OrthogonalLine(I_1, xAxis) → i_3
  167. OrthogonalLine(K_1, xAxis) → j_3
  168. OrthogonalLine(D_1, xAxis) → l_3
  169. Point(yAxis) → S_3
  170. OrthogonalLine(S_3, yAxis) → m_3
  171. Point(yAxis) → U_3
  172. OrthogonalLine(U_3, yAxis) → n_3
  173. Intersect(m_3, l_3) → V_3
  174. Intersect(m_3, j_3) → W_3
  175. Intersect(m_3, i_3) → Z_3
  176. Intersect(m_3, h_3) → A_4
  177. Intersect(m_3, g_3) → B_4
  178. Intersect(n_3, l_3) → C_4
  179. Intersect(n_3, j_3) → D_4
  180. Intersect(n_3, i_3) → E_4
  181. Intersect(n_3, h_3) → F_4
  182. Intersect(n_3, g_3) → G_4
  183. Segment(G_4, B_4) → p_3
  184. Segment(F_4, A_4) → q_3
  185. Segment(E_4, Z_3) → r_3
  186. Segment(D_4, W_3) → s_3
  187. Segment(C_4, V_3) → t_3
  188. Point(p_3) → H_4
  189. Point(q_3) → I_4
  190. Point(r_3) → J_4
  191. Point(s_3) → K_4
  192. Point(t_3) → L_4
  193. Mirror(D_4, t_3) → M_4
  194. Mirror(W_3, t_3) → N_4
  195. Segment(M_4, N_4) → a_4
  196. Mirror(C_4, a_4) → O_4
  197. Mirror(V_3, a_4) → P_4
  198. Segment(O_4, P_4) → b_4
  199. Mirror(M_4, b_4) → Q_4
  200. Mirror(N_4, b_4) → R_4
  201. Segment(Q_4, R_4) → c_4
  202. Mirror(O_4, c_4) → S_4
  203. Mirror(P_4, c_4) → T_4
  204. Segment(S_4, T_4) → d_4
  205. Mirror(Q_4, d_4) → U_4
  206. Mirror(R_4, d_4) → V_4
  207. Segment(U_4, V_4) → e_4
  208. Mirror(S_4, e_4) → W_4
  209. Mirror(T_4, e_4) → Z_4
  210. Segment(W_4, Z_4) → f_4
  211. Mirror(U_4, f_4) → A_5
  212. Mirror(V_4, f_4) → B_5
  213. Segment(A_5, B_5) → g_4
  214. Mirror(W_4, g_4) → C_5
  215. Mirror(Z_4, g_4) → D_5
  216. Segment(C_5, D_5) → h_4
  217. Mirror(A_5, h_4) → E_5
  218. Mirror(B_5, h_4) → F_5
  219. Segment(E_5, F_5) → i_4
  220. Mirror(C_5, i_4) → G_5
  221. Mirror(D_5, i_4) → H_5
  222. Segment(G_5, H_5) → j_4
  223. Mirror(E_5, j_4) → I_5
  224. Mirror(F_5, j_4) → J_5
  225. Segment(I_5, J_5) → k_4
  226. Mirror(G_5, k_4) → K_5
  227. Mirror(H_5, k_4) → L_5
  228. Segment(K_5, L_5) → l_4
  229. Point(a_4) → M_5
  230. Point(b_4) → N_5
  231. Point(c_4) → O_5
  232. Point(d_4) → P_5
  233. Point(e_4) → Q_5
  234. Point(f_4) → R_5
  235. Point(g_4) → S_5
  236. Point(h_4) → T_5
  237. Point(i_4) → U_5
  238. Point(j_4) → V_5
  239. Point(k_4) → W_5
  240. Point(l_4) → Z_5
  241. Vector(A_6, B_6) → u
  242. Vector(B_6, C_6) → u_4
  243. Vector(C_6, D_6) → v_4
  244. Vector(D_6, E_6) → w_4
  245. Vector(E_6, F_6) → m_4
  246. Vector(F_6, G_6) → n_4
  247. Vector(G_6, H_6) → p_4
  248. Vector(H_6, I_6) → q_4
  249. Vector(I_6, J_6) → r_4
  250. Vector(J_6, K_6) → s_4
  251. Vector(K_6, L_6) → t_4
  252. Vector(L_6, M_6) → u_5
  253. Vector(M_6, N_6) → v_5
  254. Vector(N_6, O_6) → w_5
  255. Vector(O_6, P_6) → a_5
  256. Vector(P_6, Q_6) → b_5
  257. Vector(Q_6, R_6) → c_5
  258. Segment(F, V) → d_5
  259. Vector(S_6, T_6) → e_5

AI 绘图提示语参考

在横轴上依次创建多个点，并选择一个位于非负半轴的点。连接该点与横轴上的两个相邻点形成线段。对每条线段进行镜像操作，并依次计算各线段中点、中点中点等，形成一系列点。以其中一个点为圆心画圆，并以其他点为中点画多个圆。最后连接特定点形成路径，展示几何反射的多路径特性。
以上提示语为根据原始绘图命令整理而来，仅供参考。