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圆顶结构模型

圆顶结构模型
几何画板及绘图内容加载中，请稍等……
2020-05-22 16:59
圆三角函数几何作图
该范例演示了一个圆顶结构的几何模型。涉及的核心数学概念包括圆、线段、三角函数和相似三角形。通过使用GeoGebra命令如Point、Rotate、CircleArc、Intersect等，构建了一个复杂的几何图形。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(yAxis) → M
  2. Point(yAxis) → N
  3. Rotate(G, (-(90°)), yAxis) → G'
  4. CircleArc(M, G, G') → c
  5. CircleArc(M, G', L) → d
  6. CircleArc(N, H, O) → e
  7. CircleArc(N, O, K) → f
  8. Point(xAxis) → P
  9. CircleArc(P, I, Q) → g
  10. CircleArc(P, Q, F) → h
  11. CircleArc(R, E, S) → k
  12. CircleArc(R, S, J) → p
  13. Intersect(h, c, 2) → T
  14. Point(h) → U
  15. Point(h) → V
  16. Point(h) → W
  17. Point(h) → Z
  18. Segment(A, B) → i
  19. Line(T, i) → j
  20. Line(U, i) → l
  21. Line(V, i) → m
  22. Line(W, i) → n
  23. Line(Z, i) → q
  24. Intersect(j, d, 2) → A_1
  25. Rotate(j, 90°, zAxis) → j'
  26. Rotate(l, 90°, zAxis) → l'
  27. Rotate(m, 90°, zAxis) → m'
  28. Rotate(n, 90°, zAxis) → n'
  29. Rotate(q, 90°, zAxis) → q'
  30. Intersect(q, q') → B_1
  31. Intersect(n, n') → C_1
  32. Intersect(m, m') → D_1
  33. Intersect(l, l') → E_1
  34. Rotate(E_1, (-(90°)), zAxis) → F_1
  35. Rotate(D_1, (-(90°)), zAxis) → G_1
  36. Rotate(C_1, (-(90°)), zAxis) → H_1
  37. Rotate(B_1, (-(90°)), zAxis) → I_1
  38. Polygon(F_1, E_1, T, A_1) → vierhoek1, f_1, e_1, t, a_1
  39. Polygon(F_1, G_1, D_1, E_1) → vierhoek2, r, g_1, d_1, s
  40. Polygon(G_1, H_1, C_1, D_1) → vierhoek3, a, h_1, c_1, b
  41. Polygon(H_1, I_1, B_1, C_1) → vierhoek4, i_1, j_1, b_1, k_1
  42. Polygon(I_1, A, B, B_1) → vierhoek5, l_1, a_2, b_2, m_1
  43. Polygon(T, J_1, A_1) → driehoek1, n_1, t_1, p_1
  44. Sequence(Rotate[driehoek1, (nn * 90°), zAxis], nn, 1, 4) → l2
  45. Sequence(Rotate[vierhoek1, (nn * 90°), zAxis], nn, 1, 4) → l1
  46. Sequence(Rotate[vierhoek2, (nn * 90°), zAxis], nn, 1, 4) → l3
  47. Sequence(Rotate[vierhoek3, (nn * 90°), zAxis], nn, 1, 4) → l4
  48. Sequence(Rotate[vierhoek4, (nn * 90°), zAxis], nn, 1, 4) → l5
  49. Sequence(Rotate[vierhoek5, (nn * 90°), zAxis], nn, 1, 4) → l6
  50. CircleArc(P, T, F) → q_1
  51. Rotate(q_1, 90°, zAxis) → r_1
  52. Rotate(q_1, 180°, zAxis) → s_1
  53. Rotate(q_1, 270°, zAxis) → c_2
  54. Mirror(q_1, vgl1) → d_2
  55. Rotate(d_2, 90°, zAxis) → e_2
  56. Rotate(d_2, 180°, zAxis) → f_2
  57. Rotate(d_2, 270°, zAxis) → g_2
  58. Segment(A_1, T) → h_2
  59. Rotate(A_1, 90°, zAxis) → K_1
  60. Rotate(T, 90°, zAxis) → T'
  61. Segment(K_1, T') → i_2
  62. Rotate(A_1, 180°, zAxis) → L_1
  63. Rotate(T, 180°, zAxis) → T'_1
  64. Segment(L_1, T'_1) → j_2
  65. Rotate(A_1, 270°, zAxis) → M_1
  66. Rotate(T, 270°, zAxis) → T'_2
  67. Segment(M_1, T'_2) → k_2
  68. Rotate(driehoek1, 90°, zAxis) → driehoek1'
  69. Rotate(driehoek1, 180°, zAxis) → driehoek1'_1
  70. Rotate(driehoek1, 270°, zAxis) → driehoek1'_2
  71. Polygon(N_1, A, B, O_1) → vierhoek6, l_2, a_3, b_3, o_1
  72. Polygon(P_1, N_1, O_1, Q_1) → vierhoek7, m_2, n_2, p_2, q_2
  73. Polygon(R_1, P_1, Q_1, S_1) → vierhoek8, r_2, s_2, t_2, f_3
  74. Polygon(T_1, R_1, S_1, U_1) → vierhoek9, g_3, h_3, i_3, u_1
  75. Polygon(V_1, T_1, U_1, W_1) → vierhoek10, v_1, j_3, k_3, w_1
  76. Polygon(Z_1, V_1, W_1) → driehoek2, l_3, z_1, m_3
  77. Segment(F, A_2) → n_3
  78. Segment(A_2, B_2) → p_3
  79. Segment(B_2, C_2) → q_3
  80. Segment(C_2, D_2) → r_3
  81. Segment(D_2, W_1) → s_3
  82. Mirror(F, vgl1) → F'
  83. Mirror(A_2, vgl1) → E_2
  84. Segment(F', E_2) → t_3
  85. Mirror(A_2, vgl1) → F_2
  86. Mirror(B_2, vgl1) → G_2
  87. Segment(F_2, G_2) → c_3
  88. Mirror(B_2, vgl1) → H_2
  89. Mirror(C_2, vgl1) → I_2
  90. Segment(H_2, I_2) → d_3
  91. Mirror(C_2, vgl1) → J_2
  92. Mirror(D_2, vgl1) → K_2
  93. Segment(J_2, K_2) → e_3
  94. Mirror(D_2, vgl1) → L_2
  95. Mirror(W_1, vgl1) → M_2
  96. Segment(L_2, M_2) → f_4
  97. Mirror(L_2, vlaky) → N_2
  98. Mirror(M_2, vlaky) → O_2
  99. Segment(N_2, O_2) → g_4
  100. Mirror(J_2, vlaky) → P_2
  101. Mirror(K_2, vlaky) → Q_2
  102. Segment(P_2, Q_2) → h_4
  103. Mirror(H_2, vlaky) → R_2
  104. Mirror(I_2, vlaky) → S_2
  105. Segment(R_2, S_2) → i_4
  106. Mirror(F_2, vlaky) → T_2
  107. Mirror(G_2, vlaky) → U_2
  108. Segment(T_2, U_2) → j_4
  109. Mirror(F', vlaky) → F''
  110. Mirror(E_2, vlaky) → V_2
  111. Segment(F'', V_2) → k_4
  112. Mirror(D_2, vlaky) → W_2
  113. Mirror(W_1, vlaky) → Z_2
  114. Segment(W_2, Z_2) → l_4
  115. Mirror(C_2, vlaky) → A_3
  116. Mirror(D_2, vlaky) → B_3
  117. Segment(A_3, B_3) → m_4
  118. Mirror(B_2, vlaky) → C_3
  119. Mirror(C_2, vlaky) → D_3
  120. Segment(C_3, D_3) → n_4
  121. Mirror(A_2, vlaky) → E_3
  122. Mirror(B_2, vlaky) → F_3
  123. Segment(E_3, F_3) → p_4
  124. Mirror(F, vlaky) → F'_1
  125. Mirror(A_2, vlaky) → G_3
  126. Segment(F'_1, G_3) → q_4
  127. Rotate(F'_1, 90°, zAxis) → H_3
  128. Rotate(G_3, 90°, zAxis) → I_3
  129. Segment(H_3, I_3) → r_4
  130. Rotate(E_3, 90°, zAxis) → J_3
  131. Rotate(F_3, 90°, zAxis) → K_3
  132. Segment(J_3, K_3) → s_4
  133. Rotate(C_3, 90°, zAxis) → L_3
  134. Rotate(D_3, 90°, zAxis) → M_3
  135. Segment(L_3, M_3) → t_4
  136. Rotate(A_3, 90°, zAxis) → N_3
  137. Rotate(B_3, 90°, zAxis) → O_3
  138. Segment(N_3, O_3) → a_4
  139. Rotate(W_2, 90°, zAxis) → P_3
  140. Rotate(Z_2, 90°, zAxis) → Q_3
  141. Segment(P_3, Q_3) → b_4
  142. Rotate(F'', 90°, zAxis) → F'''
  143. Rotate(V_2, 90°, zAxis) → R_3
  144. Segment(F''', R_3) → c_4
  145. Rotate(T_2, 90°, zAxis) → S_3
  146. Rotate(U_2, 90°, zAxis) → T_3
  147. Segment(S_3, T_3) → d_4
  148. Rotate(R_2, 90°, zAxis) → U_3
  149. Rotate(S_2, 90°, zAxis) → V_3
  150. Segment(U_3, V_3) → e_4
  151. Rotate(P_2, 90°, zAxis) → W_3
  152. Rotate(Q_2, 90°, zAxis) → Z_3
  153. Segment(W_3, Z_3) → f_5
  154. Rotate(N_2, 90°, zAxis) → A_4
  155. Rotate(O_2, 90°, zAxis) → B_4
  156. Segment(A_4, B_4) → g_5
  157. Rotate(L_2, 90°, zAxis) → C_4
  158. Rotate(M_2, 90°, zAxis) → D_4
  159. Segment(C_4, D_4) → h_5
  160. Rotate(J_2, 90°, zAxis) → E_4
  161. Rotate(K_2, 90°, zAxis) → F_4
  162. Segment(E_4, F_4) → i_5
  163. Rotate(H_2, 90°, zAxis) → G_4
  164. Rotate(I_2, 90°, zAxis) → H_4
  165. Segment(G_4, H_4) → j_5
  166. Rotate(F_2, 90°, zAxis) → I_4
  167. Rotate(G_2, 90°, zAxis) → J_4
  168. Segment(I_4, J_4) → k_5
  169. Rotate(F', 90°, zAxis) → F''_1
  170. Rotate(E_2, 90°, zAxis) → K_4
  171. Segment(F''_1, K_4) → l_5
  172. Rotate(D_2, 90°, zAxis) → L_4
  173. Rotate(W_1, 90°, zAxis) → M_4
  174. Segment(L_4, M_4) → m_5
  175. Rotate(C_2, 90°, zAxis) → N_4
  176. Rotate(D_2, 90°, zAxis) → O_4
  177. Segment(N_4, O_4) → n_5
  178. Rotate(B_2, 90°, zAxis) → P_4
  179. Rotate(C_2, 90°, zAxis) → Q_4
  180. Segment(P_4, Q_4) → p_5
  181. Rotate(A_2, 90°, zAxis) → R_4
  182. Rotate(B_2, 90°, zAxis) → S_4
  183. Segment(R_4, S_4) → q_5
  184. Rotate(F, 90°, zAxis) → F'_2
  185. Rotate(A_2, 90°, zAxis) → T_4
  186. Segment(F'_2, T_4) → r_5
  187. Segment(B_4, W_1) → s_5
  188. Segment(W_1, Z_2) → t_5
  189. Segment(Z_2, Q_3) → a_5
  190. Segment(Q_3, B_4) → b_5
  191. Rotate(driehoek2, 90°, zAxis) → driehoek2'
  192. Rotate(driehoek2, 180°, zAxis) → driehoek2'_1
  193. Rotate(driehoek2, 270°, zAxis) → driehoek2'_2
  194. Segment(B, O_1) → c_5
  195. Segment(O_1, Q_1) → d_5
  196. Segment(Q_1, S_1) → e_5
  197. Segment(S_1, U_1) → f_6
  198. Segment(U_1, W_1) → g_6
  199. Segment(A, N_1) → h_6
  200. Segment(N_1, P_1) → i_6
  201. Segment(P_1, R_1) → j_6
  202. Segment(R_1, T_1) → k_6
  203. Segment(T_1, B_4) → l_6
  204. Sequence(Rotate[vierhoek6, (nn * 90°), zAxis], nn, 1, 4) → l7
  205. Sequence(Rotate[vierhoek7, (nn * 90°), zAxis], nn, 1, 4) → l8
  206. Sequence(Rotate[vierhoek8, (nn * 90°), zAxis], nn, 1, 4) → l9
  207. Sequence(Rotate[vierhoek9, (nn * 90°), zAxis], nn, 1, 4) → l10
  208. Sequence(Rotate[vierhoek10, (nn * 90°), zAxis], nn, 1, 4) → l11
  209. Segment(Z_1, W_1) → m_6
  210. Segment(Z_1, B_4) → n_6
  211. Segment(Z_1, Q_3) → p_6
  212. Segment(Z_1, Z_2) → q_6
  213. Sequence(Segment[Rotate[U_1, (nn * 90°), zAxis], Rotate[W_1, (nn * 90°), zAxis]], nn, 1, 2) → l12
  214. Sequence(Segment[Rotate[S_1, (nn * 90°), zAxis], Rotate[U_1, (nn * 90°), zAxis]], nn, 1, 2) → l13
  215. Sequence(Segment[Rotate[Q_1, (nn * 90°), zAxis], Rotate[S_1, (nn * 90°), zAxis]], nn, 1, 2) → l14
  216. Sequence(Segment[Rotate[O_1, (nn * 90°), zAxis], Rotate[Q_1, (nn * 90°), zAxis]], nn, 1, 2) → l15
  217. Sequence(Segment[Rotate[B, (nn * 90°), zAxis], Rotate[O_1, (nn * 90°), zAxis]], nn, 1, 2) → l16
  218. Segment(B, C) → r_6
  219. Segment(C, D) → s_6
  220. Segment(D, A) → t_6
  221. Segment(K, H) → a_6
  222. Segment(J, E) → b_6
  223. Segment(I, F) → c_6
  224. Segment(L, G) → d_6
  225. Segment(E, J) → e_6
  226. Segment(F, I) → f_7
  227. Segment(K, H) → g_7
  228. Segment(L, G) → h_7
  229. Segment(L, F) → i_7
  230. Segment(F, H) → j_7
  231. Segment(H, J) → k_7
  232. Segment(J, L) → l_7
  233. Plane(L, F, L + (0, 0, 1)) → p_7
  234. PointIn(vierhoek6) → U_4
  235. PointIn(p_7) → W_4
  236. PointIn(vierhoek8) → V_4
  237. PointIn(p_7) → Z_4
  238. PointIn(p_7) → A_5
  239. PointIn(p_7) → B_5
  240. PointIn(p_7) → C_5
  241. Segment(L, C_5) → m_7
  242. Segment(L, C_5) → n_7
  243. Segment(C_5, B_5) → q_7
  244. Segment(B_5, A_5) → r_7
  245. Segment(A_5, Z_4) → s_7
  246. Segment(Z_4, W_4) → t_7
  247. Segment(W_4, V_4) → a_7
  248. Segment(V_4, U_4) → b_7
  249. Segment(U_4, F) → c_7
  250. Sequence(Rotate[l17, (nn * 90°), zAxis], nn, 1, 3) → l18
  251. Mirror(l17, vgl2) → l17'
  252. Sequence(Rotate[l17', (nn * 90°), zAxis], nn, 1, 3) → l19
  253. Mirror(J, yAxis) → J'
  254. Mirror(L, yAxis) → L'
  255. Segment(J', L') → d_7
  256. Mirror(H, yAxis) → H'
  257. Mirror(J, yAxis) → J'_1
  258. Segment(H', J'_1) → e_7
  259. Mirror(L, yAxis) → L'_1
  260. Mirror(F, yAxis) → F'_3
  261. Segment(L'_1, F'_3) → f_8
  262. Mirror(F, yAxis) → F'_4
  263. Mirror(H, yAxis) → H'_1
  264. Segment(F'_4, H'_1) → g_8
  265. Midpoint(D_4, O_2) → E_5
  266. Midpoint(Z_2, B_4) → D_5
  267. Line(Z_2, B_4) → h_8
  268. Rotate(Q_3, (-(90°)), h_8) → F_5
  269. CircleArc(D_5, Q_3, F_5) → c_8
  270. Point(c_8) → G_5
  271. Point(c_8) → H_5
  272. Point(c_8) → I_5
  273. Point(c_8) → J_5
  274. Mirror(L_5, vgl1) → P_5
  275. Mirror(M_5, vgl1) → Q_5
  276. Mirror(N_5, vgl1) → R_5
  277. Mirror(O_5, vgl1) → S_5
  278. Polygon(K_5, P_5, L_5) → driehoek3, i_8, j_8, k_8
  279. Polygon(P_5, Q_5, M_5, L_5) → vierhoek11, l_8, m_8, n_8, p_8
  280. Polygon(Q_5, R_5, N_5, M_5) → vierhoek12, q_8, r_8, s_8, t_8
  281. Polygon(R_5, S_5, O_5, N_5) → vierhoek13, a_8, b_8, o_5, d_8
  282. Polygon(S_5, Z_2, Q_3, O_5) → vierhoek14, e_8, z_2, f_9, g_9
  283. Segment(Z_2, S_5) → h_9
  284. Segment(S_5, R_5) → i_9
  285. Segment(R_5, Q_5) → j_9
  286. Segment(Q_5, P_5) → k_9
  287. Segment(P_5, K_5) → l_9
  288. Sequence(Rotate[l20, (nn * 90°), zAxis], nn, 1, 3) → l22
  289. Sequence(Rotate[l21, (nn * 90°), zAxis], nn, 1, 3) → l23
  290. Segment(K_5, L_5) → m_9
  291. Segment(L_5, M_5) → n_9
  292. Segment(M_5, N_5) → p_9
  293. Segment(N_5, O_5) → q_9
  294. Segment(O_5, Q_3) → r_9
  295. Segment(Q_3, B_4) → s_9
  296. Sequence(Rotate[l24, (nn * 90°), zAxis], nn, 1, 3) → l25