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Shree Yanthra 几何构造

Shree Yanthra 几何构造
几何画板及绘图内容加载中，请稍等……
2019-12-15 17:30
圆多边形三角函数变换几何作图
①本范例演示了Shree Yanthra的几何构造过程，涉及多边形、圆与三角函数的综合应用；②核心数学概念包括多边形构造、外接圆、余弦定理、旋转与反射等；③作图要点提炼自GeoGebra命令：点、圆、垂线、交点、旋转、角度、射线、镜像、线段、多边形等；④适合高中及以上数学学习者，用于理解几何作图与变换的原理。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Circle(A, Radius) → c
  3. OrthogonalLine(A, xAxis) → f
  4. Intersect(c, xAxis) → B, C
  5. Intersect(c, f) → D, E
  6. Rotate(A, DnAngle / 2, E) → A'
  7. Angle(A, E, A') → α
  8. Ray(E, A') → g
  9. Mirror(E, f) → E'
  10. Mirror(A', f) → A''
  11. Ray(E', A'') → g'
  12. Rotate(A, UpAngle / 2, D) → A'_1
  13. Angle(A, D, A'_1) → β
  14. Ray(D, A'_1) → h
  15. Mirror(D, f) → D'
  16. Mirror(A'_1, f) → F
  17. Ray(D', F) → h'
  18. Intersect(c, h) → G, H
  19. Intersect(c, h') → I, J
  20. Intersect(c, g') → K, L
  21. Intersect(c, g) → M, N
  22. Segment(L, N) → i
  23. Segment(N, E) → j
  24. Segment(E, L) → k
  25. Segment(D, J) → l
  26. Segment(J, H) → m
  27. Segment(H, D) → n
  28. Intersect(m, f) → O
  29. Circle(B, A) → d
  30. Circle(C, A) → e
  31. Intersect(c, d) → P, Q, ,
  32. Intersect(e, c) → R, S, ,
  33. Rotate(D, Dn2Angle / 2, O) → D'_1
  34. Angle(D, O, D'_1) → γ
  35. Ray(O, D'_1) → p
  36. Mirror(O, f) → O'
  37. Mirror(D'_1, f) → T
  38. Ray(O', T) → p'
  39. Intersect(m, g') → U
  40. Intersect(m, g) → V
  41. Intersect(h', l) → W
  42. Intersect(p, h') → Z
  43. Intersect(p', i) → A_1
  44. Intersect(p, i) → B_1
  45. Line(V, B_1) → q
  46. Line(U, A_1) → r
  47. Intersect(q, r) → C_1
  48. OrthogonalLine(C_1, f) → s
  49. Intersect(s, p') → D_1
  50. Intersect(p, s) → E_1
  51. Segment(D_1, E_1) → t
  52. Segment(E_1, O) → a
  53. Segment(O, D_1) → b
  54. Rotate(C, SlashAngle, A) → C'
  55. Angle(C, A, C') → δ
  56. Ray(A, C') → f_1
  57. Intersect(p, a) → F_1
  58. Intersect(f_1, p) → G_1
  59. Circle(A, G_1) → c_1
  60. Intersect(c_1, f) → H_1, I_1
  61. Ray(H_1, G_1) → g_1
  62. Mirror(H_1, f) → J_1
  63. Mirror(G_1, f) → K_1
  64. Ray(J_1, K_1) → h_1
  65. Intersect(i, h) → L_1
  66. Intersect(h', l) → M_1
  67. Intersect(h', l) → N_1
  68. Intersect(h', l) → O_1
  69. Intersect(i, h') → P_1
  70. Intersect(m, h_1) → Q_1
  71. Intersect(m, g_1) → R_1
  72. Intersect(g', k) → S_1
  73. Intersect(h_1, g') → T_1
  74. Intersect(g_1, g) → U_1
  75. Line(T_1, U_1) → i_1
  76. Intersect(r, i_1) → V_1
  77. Intersect(q, i_1) → W_1
  78. Segment(C_1, W_1) → j_1
  79. Segment(W_1, V_1) → k_1
  80. Segment(V_1, C_1) → l_1
  81. Line(L_1, Q_1) → m_1
  82. Line(R_1, P_1) → n_1
  83. Intersect(m_1, n_1) → Z_1
  84. Intersect(m_1, r) → A_2
  85. Intersect(n_1, q) → B_2
  86. Intersect(h, n) → C_2
  87. Intersect(p', b) → D_2
  88. Intersect(h, n) → E_2
  89. Intersect(h, n) → F_2
  90. Intersect(h, n) → G_2
  91. Intersect(h, n) → H_2
  92. Intersect(p', b) → I_2
  93. Intersect(p', b) → J_2
  94. Intersect(h, n) → K_2
  95. Intersect(h, n) → L_2
  96. Intersect(p', h) → M_2
  97. Line(M_2, Z) → p_1
  98. Intersect(m_1, p_1) → N_2
  99. Intersect(n_1, p_1) → O_2
  100. Line(Z_1, xAxis) → q_1
  101. Intersect(h_1, q_1) → P_2
  102. Intersect(g_1, q_1) → Q_2
  103. Segment(H_1, Q_2) → r_1
  104. Segment(Q_2, P_2) → s_1
  105. Segment(P_2, H_1) → t_1
  106. Segment(Z_1, N_2) → a_1
  107. Segment(N_2, O_2) → b_1
  108. Segment(O_2, Z_1) → d_1
  109. Intersect(g', k) → R_2
  110. Intersect(h, n) → S_2
  111. Intersect(h, g') → T_2
  112. Intersect(h', g) → U_2
  113. Intersect(g', k) → V_2
  114. Intersect(q_1, s_1) → W_2
  115. Intersect(q_1, g') → Z_2
  116. Intersect(q_1, g) → A_3
  117. Intersect(n_1, i_1) → B_3
  118. Intersect(m_1, i_1) → C_3
  119. Intersect(s, h) → D_3
  120. Intersect(s, h') → E_3
  121. Intersect(q, p_1) → F_3
  122. Intersect(r, p_1) → G_3
  123. Intersect(i_1, f) → H_3
  124. Intersect(f, i) → I_3
  125. Line(H_1, xAxis) → f_5
  126. Intersect(f_5, r) → J_3
  127. Intersect(q, f_5) → K_3
  128. Segment(J_3, K_3) → g_5
  129. Segment(K_3, H_3) → h_5
  130. Segment(H_3, J_3) → i_5
  131. Intersect(f_5, p) → L_3
  132. Intersect(f_5, p') → M_3
  133. Intersect(p_1, f) → N_3
  134. Ray(N_3, M_3) → j_5
  135. Ray(N_3, L_3) → k_5
  136. Intersect(m_1, j_5) → O_3
  137. Intersect(k_5, n_1) → P_3
  138. Segment(N_3, P_3) → l_5
  139. Segment(P_3, O_3) → m_5
  140. Segment(O_3, N_3) → n_5
  141. Intersect(i_5, m) → Q_3
  142. Intersect(d, h_5) → R_3,
  143. Intersect(m, h_5) → S_3
  144. Intersect(i_5, h_1) → T_3
  145. Intersect(g_1, r_1) → U_3
  146. Intersect(h_5, g_1) → V_3
  147. Intersect(p, a) → W_3
  148. Intersect(m_5, p) → Z_3
  149. Intersect(p', b) → A_4
  150. Intersect(m_5, p') → B_4
  151. Intersect(i_5, n_5) → C_4
  152. Intersect(h_5, l_5) → D_4
  153. Intersect(i, n_5) → E_4
  154. Intersect(l_5, i) → F_4
  155. Line(K_1, G_1) → e_1
  156. Intersect(i_5, e_1) → G_4
  157. Intersect(e_1, h_5) → H_4
  158. Segment(G_4, I_3) → f_2
  159. Segment(I_3, H_4) → g_2
  160. Segment(H_4, G_4) → h_2
  161. Polygon(H, D, J) → t1, j_2, h_3, d_2
  162. Polygon(V_1, C_1, W_1) → t2, w_1, v_1, i_2
  163. Polygon(P_2, H_1, Q_2) → t3, q_2, p_2, k_2
  164. Polygon(O_3, N_3, P_3) → t4, p_3, o_3, n_3
  165. Polygon(G_4, I_3, H_4) → t5, h_4, g_4, i_3
  166. Polygon(O_3, N_3, P_3) → t6, l_2, m_2, n_2
  167. Polygon(E, L, N) → t7, n_4, e_2, l_3
  168. Polygon(Z_1, N_2, O_2) → t8, o_2, z_1, r_2
  169. Polygon(O, D_1, E_1) → t9, s_2, o, t_2
  170. Polygon(H_3, J_3, K_3) → t10, k_3, a_2, j_3
  171. Polygon(K_1, H_1, G_1) → t11, b_2, c_2, f_3