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圆弧与穹顶构造

圆弧与穹顶构造
几何画板及绘图内容加载中，请稍等……
2020-05-23 15:45
圆多边形三角函数几何作图
①本范例演示了如何通过圆弧和穹顶构造几何图形；②涉及的核心数学概念包括圆、三角形、多边形、几何变换等；③作图要点提炼自构造摘要，使用了Intersect（交点）、Circle（圆）、Rotate（旋转）、Mirror（镜像）、Segment（线段）、Line（直线）、LineBisector（角平分线）、Sequence（序列）、Polygon（多边形）、Point（点）、Midpoint（中点）、Plane（平面）、OrthogonalLine（垂线）等GeoGebra命令和对象；④适合高中阶段学习几何作图的学生或教师使用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. ConstructionStep() → stap
  3. Circle(A, 4) → c
  4. Intersect(c, xAxis, 2) → B
  5. Rotate(B, 90°) → C
  6. Mirror(C, A) → D
  7. Segment(A, C) → f
  8. Circle(A, 1) → d
  9. Intersect(d, f, 1) → E
  10. Circle(A, 2) → e
  11. Intersect(e, f, 1) → F
  12. Circle(A, 3) → g
  13. Intersect(g, f, 1) → G
  14. Circle(A, 3.5) → h
  15. Intersect(h, f, 1) → H
  16. Circle(A, 3.85) → k
  17. Intersect(k, f, 1) → I
  18. Mirror(K, zAxis) → K'
  19. Mirror(L, zAxis) → L'
  20. Mirror(M, zAxis) → M'
  21. Mirror(N, zAxis) → N'
  22. Mirror(O, zAxis) → O'
  23. Segment(J, K) → i
  24. Segment(K, L) → j
  25. Segment(L, M) → l
  26. Segment(M, N) → m
  27. Segment(N, O) → n
  28. Segment(O, C) → p
  29. Segment(J, K') → q
  30. Segment(K', L') → r
  31. Segment(L', M') → s
  32. Segment(M', N') → t
  33. Segment(N', O') → a
  34. Segment(O', D) → b
  35. Line(C, zAxis) → as
  36. Rotate(O, 45°, as) → O'_1
  37. Rotate(N, 45°, as) → N'_1
  38. Rotate(M, 45°, as) → M'_1
  39. Rotate(L, 45°, as) → L'_1
  40. Rotate(K, 45°, as) → K'_1
  41. Rotate(J, 45°, as) → J'
  42. Rotate(K', 45°, as) → K''
  43. Rotate(L', 45°, as) → L''
  44. Rotate(M', 45°, as) → M''
  45. Rotate(N', 45°, as) → N''
  46. Rotate(O', 45°, as) → O''
  47. Rotate(D, 45°, as) → D'
  48. Segment(C, D) → m_{10}
  49. Segment(O'', D') → f_1
  50. Segment(O'', N'') → g_1
  51. Segment(N'', M'') → h_1
  52. Segment(M'', L'') → i_1
  53. Segment(L'', K'') → j_1
  54. Segment(K'', J') → k_1
  55. Segment(J', K'_1) → l_1
  56. Segment(K'_1, L'_1) → m_1
  57. Segment(L'_1, M'_1) → n_1
  58. Segment(M'_1, N'_1) → p_1
  59. Segment(N'_1, O'_1) → q_1
  60. Segment(C, O'_1) → r_1
  61. LineBisector(C, D', xOyPlane) → s_1
  62. LineBisector(C, D) → t_1
  63. Intersect(s_1, t_1) → P
  64. Line(P, zAxis) → rotas
  65. Sequence(Rotate[l1, (nn * 90°), rotas], nn, 1, 7) → l2
  66. Sequence(Rotate[l3, (nn * 90°), rotas], nn, 1, 7) → l4
  67. Rotate(J, (360°) / 8, rotas) → J'_1
  68. Polygon(J, J'_1, 8, xOyPlane) → veelhoek1, a_1, R, S, T, U, V, b_1, c_1, d_1, e_1, f_2, g_2, h_2, Q
  69. Point(rotas) → W
  70. Rotate(C, (360°) / 8, rotas) → C'
  71. Midpoint(C, C') → Z
  72. Plane(Z, P, P + (0, 0, 1)) → spieg
  73. Mirror(L, spieg) → L'_2
  74. Mirror(M, spieg) → M'_2
  75. Mirror(N, spieg) → N'_2
  76. Mirror(O, spieg) → O'_2
  77. Intersect(j, spieg) → C_1
  78. Midpoint(L'_1, L) → A_1
  79. Midpoint(M'_1, M) → B_1
  80. Midpoint(N'_1, N) → D_1
  81. Plane(A_1, B_1, D_1) → p_2
  82. Midpoint(K'_1, K) → E_1
  83. Rotate(spieg, (360°) / 16, rotas) → spieg'
  84. Intersect(spieg', i) → F_1
  85. Mirror(K, spieg) → K'_2
  86. Mirror(F_1, spieg) → G_1
  87. Segment(P, C') → s_2
  88. Segment(P, C) → t_2
  89. OrthogonalLine(C, t_2, xOyPlane) → a_2
  90. OrthogonalLine(C', s_2, xOyPlane) → b_2
  91. Intersect(a_2, b_2) → H_1
  92. Line(O, a_2) → c_2
  93. Line(O'_2, b_2) → f_3
  94. Line(N, a_2) → g_3
  95. Line(N'_2, b_2) → h_3
  96. Line(M, a_2) → i_3
  97. Line(M'_2, b_2) → l_3
  98. Circle(rotas, V) → c_9
  99. Circle(rotas, G_1) → d_9
  100. Circle(rotas, K'_2) → e_9
  101. Circle(rotas, C_1) → p_9
  102. Circle(rotas, L) → q_9
  103. Circle(rotas, M) → r_9
  104. Circle(rotas, N) → s_9
  105. Circle(rotas, O) → t_9
  106. Circle(rotas, C) → c_{10}
  107. Rotate(H_1, (360°) / 8, rotas) → P_2
  108. Polygon(H_1, P_2, 8, xOyPlane) → veelhoek4, n_9, R_2, S_2, T_2, U_2, V_2, a_9, b_9, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, Q_2
  109. Sequence(Segment[Rotate[P, (nn * (360°) / 8), P], Rotate[C, (nn * (360°) / 8), P]], nn, 1, 7) → l15
  110. Segment(C, D) → k_{10}
  111. Rotate(D, 90°, P) → D'_1
  112. Segment(C, D'_1) → l_{10}
  113. Sequence(Segment[Rotate[C, (nn * 45°), P], Rotate[D, (nn * 45°), P]], nn, 1, 7) → l16
  114. Line(L, a_2) → m_3
  115. Line(L'_2, b_2) → n_3
  116. Intersect(c_2, f_3) → I_1
  117. Intersect(g_3, h_3) → J_1
  118. Intersect(i_3, l_3) → K_1
  119. Intersect(m_3, n_3) → L_1
  120. Polygon(C_1, L, L_1) → driehoek1, i_2, j_2, l_2
  121. Polygon(L, M, K_1, L_1) → vierhoek1, l_4, m_2, k_2, n_2
  122. Polygon(M, N, J_1, K_1) → vierhoek2, m_4, n_4, q_2, d_2
  123. Polygon(N, O, I_1, J_1) → vierhoek3, n_5, o, e_2, j_3
  124. Polygon(O, C, H_1, I_1) → vierhoek4, o_1, c_3, k_3, p_3
  125. Polygon(H_1, C', O'_2, I_1) → vierhoek5, q_3, c', o'_2, r_3
  126. Polygon(I_1, O'_2, N'_2, J_1) → vierhoek6, s_3, t_3, n'_2, a_3
  127. Polygon(J_1, N'_2, M'_2, K_1) → vierhoek7, b_3, d_3, m'_2, e_3
  128. Polygon(K_1, M'_2, L'_2, L_1) → vierhoek8, f_4, g_4, l'_2, h_4
  129. Polygon(L_1, L'_2, C_1) → driehoek2, i_4, j_4, k_4
  130. Segment(W, F_1) → q_4
  131. Segment(W, V) → r_4
  132. Segment(V, C_1) → s_4
  133. Rotate(b_2, (360°) / 8, zAxis) → t_4
  134. Mirror(L'_2, spieg') → M_1
  135. Mirror(M'_2, spieg') → N_1
  136. Mirror(N'_2, spieg') → O_1
  137. Mirror(O'_2, spieg') → P_1
  138. Mirror(C_1, spieg') → Q_1
  139. Line(C', rotas) → a_4
  140. Rotate(b_2, (360°) / 32, a_4) → b_4
  141. Polygon(F_1, C_1, Q_1) → driehoek3, c_4, d_4, e_4
  142. Polygon(C_1, L_1, M_1, Q_1) → vierhoek9, f_5, g_5, h_5, i_5
  143. Polygon(L'_2, M'_2, N_1, M_1) → vierhoek10, j_5, k_5, l_5, m_5
  144. Polygon(M'_2, N'_2, O_1, N_1) → vierhoek11, p_5, q_5, r_5, s_5
  145. Line(K'_2, a_2) → t_5
  146. Line(K, b_2) → a_5
  147. Intersect(t_5, a_5) → S_1
  148. Polygon(K'_2, C_1, S_1) → driehoek4, b_5, k'_2, c_5
  149. Polygon(G_1, K'_2, S_1, V) → vierhoek12, d_5, e_5, f_6, v
  150. Polygon(V, S_1, K, F_1) → vierhoek13, v_1, g_6, k_6, h_6
  151. Polygon(S_1, C_1, K) → driehoek5, k_7, i_6, j_6
  152. Segment(C', C) → l_6
  153. Line(H_1, l_6) → m_6
  154. Rotate(M, (360°) / 8, rotas) → M'_3
  155. Rotate(K_1, (360°) / 8, rotas) → R_1
  156. Segment(M'_3, R_1) → n_6
  157. Rotate(m_6, (360°) / 8, rotas) → p_6
  158. Line(C_1, m_6) → q_6
  159. Line(Q_1, p_6) → r_6
  160. Intersect(r_6, q_6) → T_1
  161. Line(L'_2, m_6) → s_6
  162. Line(M'_2, m_6) → t_6
  163. Line(N'_2, m_6) → a_6
  164. Line(O'_2, m_6) → b_6
  165. Plane(W, F_1, C') → p_7
  166. Intersect(s_6, p_7) → U_1
  167. Intersect(t_6, p_7) → V_1
  168. Intersect(a_6, p_7) → W_1
  169. Intersect(b_6, p_7) → Z_1
  170. Segment(F_1, T_1) → c_6
  171. Segment(T_1, U_1) → d_6
  172. Segment(U_1, V_1) → e_6
  173. Segment(V_1, W_1) → f_7
  174. Segment(O'_2, Z_1) → g_7
  175. Segment(Z_1, W_1) → h_7
  176. Segment(Z_1, C') → i_7
  177. Polygon(F_1, C_1, T_1) → driehoek6, j_7, l_7, m_7
  178. Polygon(C_1, L'_2, U_1, T_1) → vierhoek14, n_7, q_7, u_1, r_7
  179. Polygon(L'_2, M'_2, V_1, U_1) → vierhoek15, s_7, t_7, a_7, b_7
  180. Polygon(M'_2, N'_2, W_1, V_1) → vierhoek16, c_7, d_7, w_1, e_7
  181. Polygon(N'_2, O'_2, Z_1, W_1) → vierhoek17, f_8, g_8, z_1, h_8
  182. Polygon(Z_1, O'_2, C') → driehoek7, i_8, j_8, k_8
  183. Segment(B_2, C_2) → p_4
  184. Sequence(Rotate[l5, (nn * (360°) / 8), rotas], nn, 1, 7) → l6
  185. Mirror(l7, spieg') → l7'
  186. Sequence(Rotate[l7, (nn * (360°) / 8), rotas], nn, 1, 7) → l8
  187. Sequence(Rotate[l7', (nn * (360°) / 8), rotas], nn, 1, 7) → l9
  188. Sequence(Rotate[l10, (nn * (360°) / 8), rotas], nn, 1, 7) → l11
  189. Polygon(V, J, 8, xOyPlane) → veelhoek2, l_8, E_2, F_2, G_2, H_2, I_2, m_8, n_8, p_8, q_8, r_8, s_8, t_8, D_2
  190. Polygon(C_2, B_2, 8, xOyPlane) → veelhoek3, a_8, K_2, L_2, M_2, N_2, O_2, b_8, c_8, d_8, e_8, f_9, g_9, h_9, J_2
  191. Polygon(G_1, V, C_2) → driehoek8, i_9, j_9, v_2
  192. Polygon(V, F_1, B_2) → driehoek9, k_9, v_3, l_9
  193. Sequence(Rotate[driehoek8, (nn * (360°) / 8), rotas], nn, 1, 7) → l12
  194. Sequence(Rotate[driehoek9, (nn * (360°) / 8), rotas], nn, 1, 7) → l13
  195. Polygon(W, O_2, C_2) → driehoek10, m_9, w, o_2
  196. Sequence(Rotate[driehoek10, (nn * (360°) / 8), rotas], nn, 1, 7) → l14

AI 绘图提示语参考

画一个由多个圆弧和拱形组成的几何图形，以x轴和y轴的交点为中心，先画一个半径为4的圆，再通过旋转和镜像操作生成多个三角形和四边形，最后用线段连接这些多边形的顶点，形成复杂的几何结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。