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元素G的几何变换

元素G的几何变换
几何画板及绘图内容加载中，请稍等……
2020-05-14 00:40
解析几何变换几何作图
①本范例演示了通过旋转、相交、镜像等变换构造几何图形G的过程；②涉及核心数学概念包括几何变换、解析几何、相似三角形、函数图像等；③构造过程中运用了Rotate（旋转）、Intersect（相交）、Mirror（镜像）、Line（直线）、Circle（圆）等GeoGebra命令；④适合高中数学教学，用于理解几何变换与坐标几何的综合应用。

GeoGebra 命令及参数

  1. Rotate(B, 67.5°, A) → B'
  2. Ray(A, B') → f
  3. Intersect(f, yAxis) → C
  4. Segment(C, A) → g
  5. Segment(C, B) → h
  6. Circle(C, 0.35) → c
  7. Intersect(c, g, 1) → D
  8. Intersect(c, h, 1) → E
  9. Line(A, yAxis) → i
  10. Line(B, yAxis) → j
  11. Line(D, E) → k
  12. Intersect(i, k) → F
  13. Intersect(k, j) → G
  14. Distance(F, A) → af1
  15. Mirror(F, H) → F'
  16. Segment(F, F') → l
  17. Mirror(F', yAxis) → F''
  18. Mirror(H, yAxis) → H'
  19. Segment(F, G) → m
  20. Segment(F', F'') → n
  21. Segment(G, F'') → p
  22. CircleArc(M, Q, I) → d
  23. CircleArc(M, O, Q) → e
  24. CircleArc(N, P, R) → r
  25. CircleArc(N, R, J) → q
  26. Line(A, zAxis) → s
  27. Intersect(s, d) → S,
  28. Line(B, zAxis) → t
  29. Intersect(t, q) → T,
  30. Segment(S, T) → a
  31. Segment(S, A) → b
  32. Segment(T, B) → f_1
  33. Plane(D, A, K) → p_1
  34. Surface(l, (straal * cos(t)) + y(H), (straal * sin(t)) + z(ver), l, ((-v2)) / 2, v2 / 2, t, 0°, 180°) → o
  35. PointIn(p_1) → V
  36. PointIn(p_1) → W
  37. PointIn(p_1) → Z
  38. PointIn(p_1) → A_1
  39. PointIn(p_1) → B_1
  40. Segment(C, A) → g_1
  41. Segment(E_1, C_1) → h_1
  42. Segment(E_1, D_1) → i_1
  43. Segment(E_1, C) → j_1
  44. Segment(U, D) → k_1
  45. Polygon(G_1, A_1, Z, H_1) → vierhoek1, l_1, a_1, z_1, m_1
  46. Polygon(F_1, U, A_1, G_1) → vierhoek2, n_1, u, q_1, r_1
  47. Polygon(H_1, Z, W, I_1) → vierhoek3, s_1, z_2, w, t_1
  48. Polygon(I_1, W, V, J_1) → vierhoek4, b_1, w_1, v, c_1
  49. Polygon(J_1, V, B_1, K_1) → vierhoek5, d_1, v_1, e_1, f_2
  50. Polygon(K_1, B_1, S, L_1) → vierhoek6, g_2, h_2, s_2, i_2
  51. Polygon(L_1, S, C_1, E_1) → vierhoek7, j_2, s_3, k_2, l_2
  52. Polygon(C, D, U, F_1) → vierhoek8, c_2, d_2, u_1, m_2
  53. Plane(C, (-C), C + ver) → sym
  54. Mirror(vierhoek1, sym) → vierhoek1'
  55. Mirror(vierhoek2, sym) → vierhoek2'
  56. Mirror(vierhoek3, sym) → vierhoek3'
  57. Mirror(vierhoek4, sym) → vierhoek4'
  58. Mirror(vierhoek5, sym) → vierhoek5'
  59. Mirror(vierhoek6, sym) → vierhoek6'
  60. Mirror(vierhoek7, sym) → vierhoek7'
  61. Mirror(vierhoek8, sym) → vierhoek8'
  62. Mirror(vierhoek1, sym2) → vierhoek1'_1
  63. Mirror(vierhoek2, sym2) → vierhoek2'_1
  64. Mirror(vierhoek3, sym2) → vierhoek3'_1
  65. Mirror(vierhoek4, sym2) → vierhoek4'_1
  66. Mirror(vierhoek5, sym2) → vierhoek5'_1
  67. Mirror(vierhoek6, sym2) → vierhoek6'_1
  68. Mirror(vierhoek7, sym2) → vierhoek7'_1
  69. Mirror(vierhoek8, sym2) → vierhoek8'_1
  70. Mirror(vierhoek1', sym2) → vierhoek1''
  71. Mirror(vierhoek2', sym2) → vierhoek2''
  72. Mirror(vierhoek3', sym2) → vierhoek3''
  73. Mirror(vierhoek4', sym2) → vierhoek4''
  74. Mirror(vierhoek5', sym2) → vierhoek5''
  75. Mirror(vierhoek6', sym2) → vierhoek6''
  76. Mirror(vierhoek7', sym2) → vierhoek7''
  77. Mirror(vierhoek8', sym2) → vierhoek8''
  78. Segment(U, A_1) → n_2
  79. Segment(A_1, Z) → p_2
  80. Segment(Z, W) → q_2
  81. Segment(W, V) → r_2
  82. Segment(V, B_1) → t_2
  83. Segment(B_1, S) → b_2
  84. Segment(C_1, S) → e_2
  85. Polygon(S, T, D_1, C_1) → vierhoek9, s_4, t_3, f_3, g_3
  86. Mirror(B_1, sym) → M_1
  87. Mirror(V, sym) → V'
  88. Mirror(W, sym) → W'
  89. Mirror(Z, sym) → Z'
  90. Mirror(A_1, sym) → N_1
  91. Mirror(U, sym) → U'
  92. Polygon(D, E, U', U) → vierhoek10, d_3, e_3, u', u_2
  93. Polygon(B_1, M_1, T, S) → vierhoek11, h_3, i_3, t_4, s_5
  94. Polygon(B_1, V, V', M_1) → vierhoek12, j_3, v_2, v', k_3
  95. Polygon(V, W, W', V') → vierhoek13, v_3, w_2, w', l_3
  96. Polygon(W, Z, Z', W') → vierhoek14, w_3, z_3, z', m_3
  97. Polygon(Z, A_1, N_1, Z') → vierhoek15, z_4, n_3, p_3, q_3
  98. Point(p_3) → O_1
  99. Polygon(A_1, U, U', N_1) → vierhoek16, r_3, a_3, b_3, c_3
  100. Segment(T, M_1) → f_4
  101. Segment(M_1, V') → g_4
  102. Segment(V', W') → h_4
  103. Segment(W', Z') → i_4
  104. Segment(Z', O_1) → j_4
  105. Segment(O_1, U') → k_4
  106. Mirror(vierhoek11, sym2) → vierhoek11'
  107. Mirror(vierhoek12, sym2) → vierhoek12'
  108. Mirror(vierhoek13, sym2) → vierhoek13'
  109. Mirror(vierhoek14, sym2) → vierhoek14'
  110. Mirror(vierhoek15, sym2) → vierhoek15'
  111. Mirror(vierhoek16, sym2) → vierhoek16'
  112. Mirror(vierhoek10, sym2) → vierhoek10'
  113. Mirror(U, sym2) → U'_1
  114. Mirror(D, sym2) → D'
  115. Segment(U'_1, D') → l_4
  116. Mirror(B_1, sym2) → P_1
  117. Mirror(V, sym2) → V'_1
  118. Mirror(W, sym2) → W'_1
  119. Mirror(Z, sym2) → Z'_1
  120. Mirror(A_1, sym2) → Q_1
  121. Mirror(Z', sym2) → Z''
  122. Mirror(O_1, sym2) → R_1
  123. Mirror(U', sym2) → U''
  124. Mirror(E, sym2) → E'
  125. Mirror(C, sym2) → C'
  126. Mirror(E_1, sym2) → S_1
  127. Mirror(W', sym2) → W''
  128. Mirror(V', sym2) → V''
  129. Mirror(M_1, sym2) → T_1
  130. Segment(T, T_1) → m_4
  131. Segment(T_1, V'') → n_4
  132. Segment(V'', W'') → p_4
  133. Segment(W'', Z'') → q_4
  134. Segment(Z'', R_1) → r_4
  135. Segment(R_1, U'') → a_4
  136. Segment(U'', E') → b_4
  137. Segment(S_1, C') → c_4
  138. Segment(S_1, D_1) → d_4
  139. Segment(S_1, C_1) → e_4
  140. Segment(S, P_1) → f_5
  141. Segment(P_1, V'_1) → g_5
  142. Segment(V'_1, W'_1) → h_5
  143. Segment(W'_1, Z'_1) → i_5
  144. Segment(Z'_1, Q_1) → j_5
  145. Segment(Q_1, U'_1) → k_5
  146. Segment(D', C') → l_5
  147. Segment(C', E') → m_5
  148. Polygon(D_1, E_1, C_1) → driehoek1, n_5, p_5, q_5
  149. Polygon(D_1, C_1, S_1) → driehoek2, r_5, t_5, a_5
  150. Segment(C, D) → b_5
  151. Segment(D, E) → c_5
  152. Segment(E, C) → d_5

AI 绘图提示语参考

画一个几何图形，通过旋转、交点和镜像等变换构造。首先旋转一个点，然后创建射线与y轴交点，连接交点和原点形成线段。以交点为圆心画圆，与线段交点再连接形成新线段。接着画垂直线，交点连接形成新线段。再镜像点，连接镜像点和原点形成线段。最后画圆弧和四边形，展示几何变换和坐标几何的融合。
以上提示语为根据原始绘图命令整理而来，仅供参考。