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梯形台球桌反弹角度演示

梯形台球桌反弹角度演示
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2013-12-15 17:11
多边形角向量三角函数几何作图
①本范例演示在梯形台球桌上的反弹角度计算与可视化；②涉及核心数学概念包括角度、反射定律、三角函数和向量运算；③构造过程中运用了 Rotate（旋转）、Line（直线）、Point（点）、Segment（线段）、OrthogonalLine（垂线）、Angle（角度）、Mirror（镜像）、Intersect（交点）、Vector（向量）、Polygon（多边形）等 GeoGebra 命令/对象；④适合高中数学教学，用于理解几何变换、反射原理及三角函数应用。

GeoGebra 命令及参数

  1. Rotate(B, -o - 90°, A) → C'
  2. Line(A, C') → k_2
  3. Point(k_2) → D
  4. Segment(A, B) → a_1
  5. Segment(A, C_1) → b_1
  6. Line(C_1, a_1) → a
  7. OrthogonalLine(B, a) → b
  8. Point(b_1) → D_1
  9. Point(a_1) → E
  10. Segment(D_1, E) → e
  11. Angle(A, E, D_1) → α
  12. OrthogonalLine(E, a_1) → f
  13. Mirror(D_1, f) → D'
  14. Angle(D', E, B) → β
  15. Line(E, D') → g
  16. Intersect(a, b) → C
  17. Segment(B, C) → h
  18. Segment(C, C_1) → j
  19. Line(E, D') → i
  20. Line(A, B) → c
  21. Line(A, C_1) → d
  22. Line(E, D') → k
  23. Intersect(k, h) → H
  24. Intersect(k, j) → F
  25. Segment(E, H) → l
  26. Segment(E, F) → m
  27. OrthogonalLine(H, h) → n
  28. Mirror(E, n) → E'
  29. Mirror(H, n) → H'
  30. Segment(E', H') → l'
  31. Line(H, E') → p
  32. Intersect(p, j) → I
  33. Intersect(p, b_1) → J
  34. Segment(J, H) → q
  35. Segment(I, H) → r
  36. OrthogonalLine(F, j) → s
  37. Mirror(E, s) → E'_1
  38. Mirror(F, s) → F'
  39. Segment(E'_1, F') → m'
  40. Line(F, E'_1) → t
  41. Intersect(t, h) → K
  42. Segment(F, K) → c_1
  43. OrthogonalLine(K, h) → d_1
  44. Mirror(F, d_1) → F'_1
  45. Mirror(K, d_1) → K'
  46. Segment(F'_1, K') → e_1
  47. Line(K, F'_1) → f_1
  48. Intersect(f_1, a_1) → L
  49. Segment(K, L) → g_1
  50. OrthogonalLine(I, j) → h_1
  51. Mirror(I, h_1) → I'
  52. Mirror(H, h_1) → H'_1
  53. Segment(I', H'_1) → r'
  54. Line(I, H'_1) → i_1
  55. Intersect(i_1, b_1) → M
  56. Segment(I, M) → j_1
  57. OrthogonalLine(L, a_1) → k_1
  58. Mirror(K, k_1) → K'_1
  59. Mirror(L, k_1) → L'
  60. Segment(K'_1, L') → l_1
  61. Line(L, K'_1) → m_1
  62. Intersect(m_1, j) → N
  63. OrthogonalLine(N, j) → n_1
  64. Mirror(m_1, n_1) → p_1
  65. Intersect(p_1, b_1) → O
  66. Segment(L, N) → q_1
  67. Segment(N, O) → r_1
  68. OrthogonalLine(I, j) → s_1
  69. Mirror(I, s_1) → I'_1
  70. Mirror(H, s_1) → H'_2
  71. Segment(I'_1, H'_2) → r'_1
  72. Line(I, H'_2) → t_1
  73. Intersect(t_1, a_1) → P
  74. Segment(P, I) → a_2
  75. OrthogonalLine(P, a_1) → b_2
  76. Mirror(P, b_2) → P'
  77. Mirror(I, b_2) → I'_2
  78. Segment(P', I'_2) → c_2
  79. Line(P, I'_2) → d_2
  80. Intersect(d_2, b_1) → Q
  81. Segment(P, Q) → e_2
  82. OrthogonalLine(L, a_1) → f_2
  83. Mirror(K, f_2) → K'_2
  84. Mirror(L, f_2) → L'_1
  85. Segment(K'_2, L'_1) → g_2
  86. Line(L, K'_2) → h_2
  87. Intersect(h_2, b_1) → R
  88. Segment(L, R) → i_2
  89. Segment(A, C') → j_2
  90. Angle(H, C, I) → δ
  91. Angle(A, B, C) → ε
  92. Angle(C, I, H) → ζ
  93. Angle(M, I, D) → η
  94. Angle(E, D_1, A) → θ
  95. OrthogonalLine(F', j) → l_2
  96. Mirror(E, l_2) → E'_2
  97. Mirror(F, l_2) → F'_2
  98. Segment(E'_2, F'_2) → m'_1
  99. Line(F', E'_2) → m_2
  100. Intersect(m_2, a_1) → G
  101. Segment(G, F') → n_2
  102. OrthogonalLine(G, a_1) → p_2
  103. Mirror(G, p_2) → G'
  104. Mirror(F', p_2) → F''
  105. Segment(G', F'') → q_2
  106. Line(F'', G) → r_2
  107. Intersect(r_2, h) → S
  108. Segment(G, S) → s_2
  109. OrthogonalLine(S, h) → t_2
  110. Mirror(G, t_2) → G'_1
  111. Mirror(S, t_2) → S'
  112. Segment(G'_1, S') → a_3
  113. Line(S, G'_1) → b_3
  114. Intersect(j, b_3) → T
  115. Segment(S, T) → c_3
  116. OrthogonalLine(T, j) → d_3
  117. Mirror(S, d_3) → S'_1
  118. Mirror(T, d_3) → T'
  119. Segment(S'_1, T') → e_3
  120. Line(T, S'_1) → f_3
  121. Intersect(f_3, a_1) → U
  122. Segment(U, T) → g_3
  123. OrthogonalLine(U, a_1) → h_3
  124. Mirror(U, h_3) → U'
  125. Mirror(T, h_3) → T'_1
  126. Segment(U', T'_1) → i_3
  127. Line(U, T'_1) → j_3
  128. Intersect(j_3, j) → V
  129. OrthogonalLine(V, j) → k_3
  130. Mirror(j_3, k_3) → l_3
  131. Intersect(l_3, b_1) → W
  132. Segment(W, V) → m_3
  133. Segment(V, U) → n_3
  134. OrthogonalLine(V, j) → p_3
  135. Mirror(V, p_3) → V'
  136. Mirror(U, p_3) → U'_1
  137. Segment(V', U'_1) → q_3
  138. Line(V, U'_1) → r_3
  139. Intersect(r_3, b_1) → Z
  140. Segment(Z, V) → s_3
  141. OrthogonalLine(N, j) → t_3
  142. Mirror(L, t_3) → L'_2
  143. Mirror(N, t_3) → N'
  144. Segment(L'_2, N') → a_4
  145. Line(N, L'_2) → b_4
  146. Intersect(b_4, a_1) → A_1
  147. OrthogonalLine(A_1, a_1) → c_4
  148. Segment(A_1, N) → d_4
  149. Mirror(A_1, c_4) → B_1
  150. Mirror(N, c_4) → N'_1
  151. Segment(B_1, N'_1) → e_4
  152. Line(N'_1, A_1) → f_4
  153. Intersect(f_4, b_1) → E_1
  154. Segment(A_1, E_1) → g_4
  155. OrthogonalLine(U, a_1) → h_4
  156. Mirror(U, h_4) → U'_2
  157. Mirror(T, h_4) → T'_2
  158. Segment(U'_2, T'_2) → i_4
  159. Line(U, T'_2) → j_4
  160. Intersect(j_4, b_1) → F_1
  161. Segment(U, F_1) → k_4
  162. OrthogonalLine(V, j) → l_4
  163. Mirror(V, l_4) → V'_1
  164. Mirror(U, l_4) → U'_3
  165. Segment(V'_1, U'_3) → m_4
  166. Line(U'_3, V) → n_4
  167. Intersect(n_4, a_1) → G_1
  168. OrthogonalLine(G_1, a_1) → p_4
  169. Mirror(n_4, p_4) → q_4
  170. Intersect(q_4, b_1) → H_1
  171. Segment(H_1, G_1) → r_4
  172. Segment(G_1, V) → s_4
  173. OrthogonalLine(G, a_1) → t_4
  174. Mirror(G, t_4) → G'_2
  175. Mirror(F', t_4) → F''_1
  176. Segment(G'_2, F''_1) → a_5
  177. Line(G, F''_1) → b_5
  178. Intersect(b_5, j) → I_1
  179. OrthogonalLine(I_1, j) → c_5
  180. Mirror(b_5, c_5) → d_5
  181. Intersect(d_5, h) → J_1
  182. OrthogonalLine(J_1, h) → e_5
  183. Mirror(d_5, e_5) → f_5
  184. Intersect(f_5, a_1) → K_1
  185. OrthogonalLine(K_1, a_1) → g_5
  186. Mirror(f_5, g_5) → h_5
  187. Intersect(h_5, j) → L_1
  188. OrthogonalLine(L_1, j) → i_5
  189. Segment(G, I_1) → j_5
  190. Segment(I_1, J_1) → k_5
  191. Segment(J_1, K_1) → l_5
  192. Segment(K_1, L_1) → m_5
  193. Mirror(h_5, i_5) → n_5
  194. Intersect(n_5, a_1) → M_1
  195. OrthogonalLine(M_1, a_1) → p_5
  196. Mirror(n_5, p_5) → q_5
  197. Intersect(q_5, j) → N_1
  198. OrthogonalLine(N_1, j) → r_5
  199. Mirror(q_5, r_5) → s_5
  200. Intersect(s_5, b_1) → O_1
  201. Segment(O_1, N_1) → t_5
  202. Segment(N_1, M_1) → a_6
  203. Segment(M_1, L_1) → b_6
  204. Angle(C, D, A) → ι
  205. Vector(D_1, E) → u
  206. Polygon(A, B, C, D) → poly1, a_7, b_7, c_6, d_6

AI 绘图提示语参考

绘制一个梯形台球桌，桌面由四个顶点构成，其中一条底边水平。从左上顶点向底边引一条射线，与底边相交后形成入射路径。在底边上取一点作为击球点，从该点向桌内画一条线段，表示球的运动方向。根据反射定律，在击球点处作底边的垂线，将入射线段关于该垂线镜像，得到反射路径。反射路径继续延伸，与桌子的另一条边相交，再次作该边的垂线并镜像，得到第二次反射路径。重复此过程，在每条边上依次反射，形成一条折线轨迹。同时，标注入射角与反射角，并用虚线表示法线。整个图形展示球在梯形桌面上多次反弹的完整路径。
以上提示语为根据原始绘图命令整理而来，仅供参考。