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斯里扬特拉的分步几何构造

斯里扬特拉的分步几何构造
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2020-09-15 18:53
圆多边形角变换几何作图
该范例演示如何在平面上用一组严格的几何作图步骤构造“斯里扬特拉”（Sri-Yantra）图案的关键对称结构。核心数学概念包括：线段与射线/直线的构造、圆与弧（含半圆）生成、对称与镜像、角平分线、线段中点、垂线/正交线、交点确定新顶点，以及由这些点拼接出多重线框多边形网络。作图要点：利用 GeoGebra 的 Intersect 求交点；用 Point、Line、Ray、Segment、Midpoint 生成与定位基础几何要素；通过 Semicircle、Circle、Parabola 提供曲线构型的中间约束（例如以圆/弧确定层次边界）；借助 OrthogonalLine 构造垂直关系；用 Mirror、LineBisector、AngularBisector 实现对称与角平分；最终采用 Polygon 组织成目标图案的多边形/线网结构。适合用于中学竞赛几何、数学兴趣小组的几何作图课，以及函数与几何结合的可视化教学或学生自主探究（强调“从基本作图命令到复杂对称图案”的建模过程）。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Semicircle(B, A) → c_6
  4. Semicircle(A, B) → d_3
  5. Line(B, A) → f
  6. OrthogonalLine(C, f) → g
  7. OrthogonalLine(E, f) → h
  8. Intersect(c_6, g, 1) → G
  9. Intersect(c_6, h, 1) → H
  10. Line(B, H) → i
  11. Line(A, G) → j
  12. Intersect(d_3, g, 1) → I
  13. Line(A, I) → k
  14. Intersect(d_3, h, 1) → J
  15. Line(B, J) → l
  16. Intersect(g, i) → K
  17. OrthogonalLine(D, f) → q
  18. Intersect(h, j) → Q
  19. Intersect(f, yAxis) → Q_1
  20. Ray(F, K) → m
  21. Intersect(h, m) → L
  22. Ray(C, L) → n
  23. Intersect(j, n) → M
  24. OrthogonalLine(M, f) → p
  25. Intersect(f, p) → N
  26. Intersect(q, n) → O
  27. Ray(N, O) → r
  28. Segment(D, K) → s
  29. Intersect(q, m) → P
  30. Segment(P, C) → t
  31. Intersect(s, t) → R
  32. Ray(B, R) → a_7
  33. Intersect(g, a_7) → S
  34. Intersect(g, r) → T
  35. Line(D, a_7) → f_1
  36. Line(Q, r) → g_1
  37. Intersect(f_1, g) → U
  38. Intersect(g_1, g) → V
  39. Midpoint(D, C) → W
  40. OrthogonalLine(Q, g) → b_7
  41. Intersect(g, b_7) → Z
  42. Midpoint(Z, Q) → A_1
  43. OrthogonalLine(A_1, b_7) → e
  44. OrthogonalLine(W, f) → h_1
  45. OrthogonalLine(U, g) → i_1
  46. OrthogonalLine(V, g) → j_1
  47. Midpoint(U, T) → B_1
  48. Midpoint(S, V) → C_1
  49. OrthogonalLine(B_1, g) → k_1
  50. OrthogonalLine(C_1, g) → l_1
  51. Intersect(k_1, h_1) → F_1
  52. Intersect(l_1, e) → G_1
  53. Segment(G_1, V) → m_1
  54. Segment(U, F_1) → n_1
  55. Midpoint(U, F_1) → H_1
  56. Midpoint(G_1, V) → I_1
  57. OrthogonalLine(I_1, m_1) → p_1
  58. OrthogonalLine(H_1, n_1) → q_1
  59. Intersect(k_1, q_1) → J_1
  60. Intersect(p_1, l_1) → K_1
  61. Intersect(p_1, j_1) → L_1
  62. Intersect(i_1, q_1) → M_1
  63. Intersect(e, j_1) → E_1
  64. Circle(V, L_1) → c_1
  65. Intersect(c_1, j_1) → D_1, N_1
  66. Intersect(g, f_1) → O_1
  67. Circle(U, M_1) → d_1
  68. Intersect(d_1, i_1) → P_1, R_1
  69. OrthogonalLine(R_1, i_1) → r_1
  70. OrthogonalLine(N_1, j_1) → s_1
  71. Parabola(K_1, s_1) → e_1
  72. Parabola(J_1, r_1) → t_1
  73. Intersect(t_1, e_1) → S_1, T_1, ,
  74. OrthogonalLine(S_1, g) → a_1
  75. Intersect(a_1, g) → U_1
  76. OrthogonalLine(T_1, h_1) → b_1
  77. Intersect(k_1, r_1) → V_1
  78. Intersect(k_1, s_1) → W_1
  79. Line(V_1, K_1) → f_2
  80. Line(W_1, f_2) → g_2
  81. Intersect(l_1, g_2) → Z_1
  82. Circle(K_1, Z_1) → c_2
  83. Intersect(c_2, l_1) → A_2, B_2
  84. Segment(J_1, Z_1) → h_2
  85. Line(J_1, B_2) → i_2
  86. Intersect(l_1, r_1) → C_2
  87. Circle(J_1, Z_1, C_2) → d_2
  88. Intersect(d_2, i_2) → D_2, E_2
  89. Intersect(c_2, d_2) → F_2, G_2, ,
  90. Line(Z_1, G_2) → j_2
  91. Intersect(j_2, i_2) → H_2
  92. Semicircle(K_1, H_2) → e_2
  93. Semicircle(H_2, K_1) → k_2
  94. Intersect(c_2, k_2) → I_2, M_3, ,
  95. Circle(J_1, E_2, I_2) → p_2
  96. Ray(D, U_1) → l_2
  97. Intersect(i, l_2) → J_2
  98. OrthogonalLine(J_2, f) → m_2
  99. Intersect(m_2, f) → K_2
  100. Segment(K_2, P) → n_2
  101. Intersect(l_2, a_7) → L_2
  102. OrthogonalLine(L_2, f) → q_2
  103. Intersect(j_2, r) → M_2
  104. Intersect(r, q_2) → N_2
  105. Ray(Q, N_2) → r_2
  106. Intersect(l_2, r_2) → O_2
  107. Intersect(r_2, f) → P_2
  108. OrthogonalLine(P_2, f) → s_2
  109. Intersect(i, s_2) → Q_2
  110. Intersect(s_2, l_2) → R_2
  111. OrthogonalLine(F, f) → t_2
  112. Line(P_2, Q) → a_2
  113. Intersect(p, a_2) → S_2
  114. Intersect(t_2, n) → T_2
  115. Intersect(j, t_2) → U_2
  116. Intersect(i, j) → V_2
  117. Intersect(m, m_2) → W_2
  118. Intersect(n, l_2) → Z_2
  119. OrthogonalLine(Z_2, f) → b_2
  120. Intersect(n_2, b_2) → A_3
  121. Mirror(T_2, f) → B_3
  122. Mirror(S_2, f) → C_3
  123. Mirror(W_2, f) → D_3
  124. Mirror(R_2, f) → E_3
  125. Mirror(A_3, f) → F_3
  126. Mirror(L_2, f) → G_3
  127. Mirror(N_2, f) → H_3
  128. Mirror(P, f) → P'
  129. Midpoint(D, Z_2) → I_3
  130. LineBisector(D, Z_2) → l_7
  131. Intersect(l_7, f) → J_3
  132. AngularBisector(b_2, l_2) → g_3, h_3
  133. Intersect(g_3, f) → K_3
  134. Segment(A_3, E) → i_3
  135. Segment(E, H) → j_3
  136. Segment(H, B) → k_3
  137. Semicircle(B, A) → c_3
  138. Segment(A, G) → l_3
  139. Segment(G, C) → m_3
  140. Segment(C, T_2) → n_3
  141. Segment(T_2, F) → p_3
  142. Segment(F, W_2) → q_3
  143. Segment(W_2, K_2) → r_3
  144. Segment(K_2, P) → s_3
  145. Segment(P, D) → t_3
  146. Segment(D, R_2) → a_3
  147. Segment(R_2, P_2) → b_3
  148. Segment(P_2, S_2) → f_4
  149. Segment(S_2, N) → g_4
  150. Segment(N, N_2) → h_4
  151. Segment(N_2, H_3) → i_4
  152. Segment(H_3, N) → j_4
  153. Segment(N, C_3) → k_4
  154. Segment(C_3, P_2) → l_4
  155. Segment(P_2, E_3) → m_4
  156. Segment(E_3, D) → n_4
  157. Segment(D, P') → p_4
  158. Segment(P', K_2) → q_4
  159. Segment(K_2, D_3) → r_4
  160. Segment(D_3, F) → s_4
  161. Segment(F, B_3) → t_4
  162. Segment(B_3, C) → a_4
  163. Segment(C, I) → b_4
  164. Segment(I, A) → c_4
  165. Semicircle(A, B) → d_4
  166. Segment(B, J) → e_4
  167. Segment(J, E) → f_5
  168. Segment(E, F_3) → g_5
  169. Segment(F_3, A_3) → h_5
  170. Polygon(F_3, E, A_3) → t2, i_5, j_5, e_5
  171. Polygon(K_2, P', P) → t3, p_5, k_5, p'
  172. Polygon(H_3, N_2, N) → t4, n_5, l_5, m_5
  173. Polygon(C, B_3, T_2) → t5, q_5, c_5, r_5
  174. Polygon(E_3, D, R_2) → t6, s_5, t_5, d_5
  175. Polygon(P_2, C_3, S_2) → t7, a_5, b_5, f_6
  176. Polygon(D_3, F, W_2) → t8, w_2, g_6, f_7
  177. Polygon(B, J, H) → t9, h_6, b_6, j_6
  178. Polygon(I, G, A) → t10, a_6, i_6, g_7
  179. Intersect(g_3, f) → L_3

AI 绘图提示语参考

请绘制一个对称的几何图形，包含两个圆弧和一条直线。圆弧的端点是直线的交点。直线与圆弧相交后，通过垂直线与圆弧的交点连接，形成新的点。然后用这些点连接成线段，并用垂直线与直线相交。最后，用这些线段和垂直线形成一个封闭的图形。图形应保持对称性，线条清晰。
以上提示语为根据原始绘图命令整理而来，仅供参考。