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Richard Anuszkiewicz 动画演示

Richard Anuszkiewicz 动画演示
几何画板及绘图内容加载中，请稍等……
2018-04-28 19:23
圆向量三角函数几何作图
所属专题 Homothety, Rotation Symmetry -RO
①本范例演示了Richard Anuszkiewicz相关图形的动态变化过程；②涉及向量、三角函数、内切圆、代数运算等核心概念；③通过GeoGebra命令如Segment（线段）、OrthogonalLine（垂线）、Point（点）、Midpoint（中点）、Intersect（交点）、Polygon（多边形）、PolyLine（多段线）、Line（直线）、Mirror（镜像）等实现几何构造；④适合高中及以上数学学习者，用于理解向量运算、三角函数应用及几何动态演示。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. Point(g) → C
  4. Midpoint(C, B) → J_2
  5. OrthogonalLine(C, g) → h
  6. OrthogonalLine(B, h) → i
  7. Intersect(h, i) → D
  8. Polygon(C, D, B, A) → q1, c_7, d_6, b_4, a_2
  9. Point(d_6) → G_4
  10. Segment(G_4, J_2) → q_1
  11. Segment(C, A) → j
  12. Segment(C, D) → k
  13. Segment(D, B) → l
  14. Segment(C, B) → m
  15. Segment(A, D) → n
  16. PolyLine(A, D, B) → s
  17. Point(q_1) → E
  18. Midpoint(C, E) → D_1
  19. Midpoint(C, D_1) → E_1
  20. Midpoint(C, E_1) → F_1
  21. Midpoint(E_1, D_1) → G_1
  22. Midpoint(D_1, E) → H_1
  23. Midpoint(H_1, E) → I_1
  24. Midpoint(D_1, H_1) → J_1
  25. Midpoint(F_1, E_1) → K_1
  26. Midpoint(E_1, G_1) → L_1
  27. Midpoint(G_1, D_1) → M_1
  28. Midpoint(D_1, J_1) → N_1
  29. Midpoint(J_1, H_1) → O_1
  30. Midpoint(H_1, I_1) → P_1
  31. Midpoint(I_1, E) → Q_1
  32. Midpoint(E, B) → R_1
  33. Midpoint(B, R_1) → S_1
  34. Midpoint(R_1, S_1) → T_1
  35. Midpoint(S_1, B) → U_1
  36. Midpoint(E, R_1) → V_1
  37. Midpoint(E, V_1) → W_1
  38. Midpoint(V_1, W_1) → Z_1
  39. Midpoint(E, W_1) → A_2
  40. Midpoint(V_1, R_1) → B_2
  41. Midpoint(B_2, V_1) → C_2
  42. Midpoint(B_2, R_1) → D_2
  43. Midpoint(R_1, T_1) → E_2
  44. Midpoint(T_1, S_1) → F_2
  45. Midpoint(S_1, U_1) → G_2
  46. Midpoint(U_1, B) → H_2
  47. Midpoint(C, F_1) → I_2
  48. Midpoint(J_2, D) → F
  49. Intersect(n, s) → H, I
  50. Intersect(n, s) → J, K
  51. Intersect(n, s) → L, M
  52. Intersect(n, s) → N, O
  53. Line(I_2, k) → p
  54. Line(F_1, p) → q
  55. Line(K_1, q) → r
  56. Line(E_1, r) → t
  57. Line(L_1, t) → a
  58. Line(G_1, a) → b
  59. Line(M_1, b) → c
  60. Line(D_1, c) → d
  61. Line(N_1, d) → e
  62. Line(J_1, e) → f_1
  63. Line(O_1, f_1) → g_1
  64. Line(H_1, g_1) → h_1
  65. Line(P_1, h_1) → i_1
  66. Line(I_1, i_1) → j_1
  67. Line(Q_1, j_1) → k_1
  68. Line(E, k_1) → l_1
  69. Intersect(p, s) → P, Q
  70. Intersect(q, n) → R
  71. Intersect(n, s) → S, T
  72. Intersect(r, n) → U
  73. Intersect(t, n) → V
  74. Intersect(a, n) → W
  75. Intersect(b, n) → Z
  76. Intersect(c, n) → A_1
  77. Intersect(d, n) → B_1
  78. Intersect(n, s) → Q_3, R_3
  79. Intersect(e, n) → S_3
  80. Intersect(f_1, n) → T_3
  81. Intersect(g_1, n) → U_3
  82. Intersect(h_1, n) → V_3
  83. Intersect(i_1, n) → W_3
  84. Intersect(j_1, n) → Z_3
  85. Intersect(n, s) → A_4, B_4
  86. Polygon(I_2, P, H_2) → t1, h_2, i_2, p_1
  87. Polygon(F_1, R, U_1) → t2, u_1, f_2, r_1
  88. Polygon(K_1, U, G_2) → t3, g_2, k_2, u
  89. Polygon(E_1, V, S_1) → t4, s_1, e_1, v
  90. Polygon(L_1, W, F_2) → t5, f_3, l_2, w
  91. Polygon(G_1, Z, T_1) → t6, t_1, g_3, z_1
  92. Polygon(M_1, A_1, E_2) → t7, e_2, m_1, a_1
  93. Polygon(D_1, B_1, R_1) → t8, r_2, d_1, b_1
  94. Polygon(N_1, S_3, D_2) → t9, d_2, n_1, s_3
  95. Polygon(J_1, T_3, B_2) → t10, b_2, j_2, t_3
  96. Polygon(O_1, U_3, C_2) → t11, c_2, o_1, u_3
  97. Polygon(H_1, V_3, V_1) → t12, v_1, h_3, v_3
  98. Polygon(P_1, W_3, Z_1) → t13, z_2, p_2, w_3
  99. Polygon(W_1, I_1, Z_3) → t14, z_3, w_1, i_3
  100. Mirror(J_1, J_2) → G
  101. Mirror(T_3, J_2) → C_1
  102. Mirror(B_2, J_2) → K_2
  103. Polygon(G, C_1, K_2) → t10', k_3, g_4, c_1
  104. Mirror(I_2, J_2) → L_2
  105. Mirror(P, J_2) → P'
  106. Mirror(H_2, J_2) → M_2
  107. Polygon(L_2, P', M_2) → t1', m_2, l_3, p'
  108. Mirror(F_1, J_2) → N_2
  109. Mirror(R, J_2) → R'
  110. Mirror(U_1, J_2) → O_2
  111. Polygon(N_2, R', O_2) → t2', o_2, n_2, r'
  112. Mirror(K_1, J_2) → P_2
  113. Mirror(U, J_2) → U'
  114. Mirror(G_2, J_2) → Q_2
  115. Polygon(P_2, U', Q_2) → t3', q_2, p_3, u'
  116. Mirror(E_1, J_2) → R_2
  117. Mirror(V, J_2) → V'
  118. Mirror(S_1, J_2) → S_2
  119. Polygon(R_2, V', S_2) → t4', s_2, r_3, v'
  120. Mirror(L_1, J_2) → T_2
  121. Mirror(W, J_2) → W'
  122. Mirror(F_2, J_2) → U_2
  123. Polygon(T_2, W', U_2) → t5', u_2, t_2, w'
  124. Mirror(G_1, J_2) → V_2
  125. Mirror(Z, J_2) → Z'
  126. Mirror(T_1, J_2) → W_2
  127. Polygon(V_2, Z', W_2) → t6', w_2, v_2, z'
  128. Mirror(M_1, J_2) → Z_2
  129. Mirror(A_1, J_2) → A_3
  130. Mirror(E_2, J_2) → B_3
  131. Polygon(Z_2, A_3, B_3) → t7', b_3, z_4, a_3
  132. Mirror(D_1, J_2) → C_3
  133. Mirror(B_1, J_2) → D_3
  134. Mirror(R_1, J_2) → E_3
  135. Polygon(C_3, D_3, E_3) → t8', e_3, c_3, d_3
  136. Mirror(N_1, J_2) → F_3
  137. Mirror(S_3, J_2) → G_3
  138. Mirror(D_2, J_2) → H_3
  139. Polygon(F_3, G_3, H_3) → t9', h_4, f_4, g_5
  140. Mirror(O_1, J_2) → I_3
  141. Mirror(U_3, J_2) → J_3
  142. Mirror(C_2, J_2) → K_3
  143. Polygon(I_3, J_3, K_3) → t11', k_4, i_4, j_3
  144. Mirror(H_1, J_2) → L_3
  145. Mirror(V_3, J_2) → M_3
  146. Mirror(V_1, J_2) → N_3
  147. Polygon(L_3, M_3, N_3) → t12', n_3, l_4, m_3
  148. Mirror(P_1, J_2) → O_3
  149. Mirror(W_3, J_2) → P_3
  150. Mirror(Z_1, J_2) → C_4
  151. Polygon(O_3, P_3, C_4) → t13', c_4, o_3, p_4
  152. Mirror(W_1, J_2) → D_4
  153. Mirror(I_1, J_2) → E_4
  154. Mirror(Z_3, J_2) → F_4
  155. Polygon(D_4, E_4, F_4) → t14', f_5, d_4, e_4
  156. Polygon(I_3, J_3, K_3) → t15, k_5, i_5, j_4
  157. Polygon(K_2, C_1, G) → t16, g_6, k_6, c_5
  158. Polygon(K_3, M_3, L_3) → t17, l_5, k_7, m_4
  159. Polygon(K_3, J_3, I_3) → t18, i_6, k_8, j_5
  160. Polygon(N_3, M_3, L_3) → t19, l_6, n_4, m_5
  161. Polygon(C_4, P_3, O_3) → t20, o_4, c_6, p_5
  162. Polygon(D_4, F_4, E_4) → t21, e_5, d_5, f_6