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用三角形拼砌形成图形（P3）

用三角形拼砌形成图形（P3）
几何画板及绘图内容加载中，请稍等……
2021-03-26 17:12
测试改名0多边形变换几何作图
所属专题 P3 3S2 Making Triangles
这个范例演示如何通过三角形的拼砌与镜像对称，逐步构造出更复杂的平面图形结构。核心数学概念包括：几何作图、三角形与多边形的构成、对称变换（镜像/反射）以及向量与参数化曲线思想在几何构造中的表达。作图要点可从构造摘要提炼：使用 Point 创建关键点，Polygon 连接点形成三角形/多边形，Mirror 实现关于直线的对称反射；并用 IndexOf、If 等条件与索引逻辑来选择/更新参与构造的点集。相关对象包括 ShGrid（网格显示）、buttonShowGridC/ buttonShowGridE（控制开关）、Text2InstructionC/ Text3InstructionE（提示文字）以及一系列反射得到的点（ReflectA1、ReflectA2、ReflectA3、ReflectA4、ReflectB1、ReflectB2、ReflectB3、ReflectB4 等）与由此拼出的 A、A1、A2 以及分组点（如 A1P1、A1P2、A1P3 等）。适合中学数学的几何构造教学与分组探究，也适合作为 GeoGebra 几何变换与拼砌活动的课堂示例。

GeoGebra 命令及参数

  1. Point(Circle[A1P1, 3]) → A1P2
  2. Polygon(A1P1, A1P2, A1P3) → A1, c, a, b
  3. Point(Circle[A2P1, 3]) → A2P2
  4. Polygon(A2P1, A2P2, A2P3) → A2, c_1, a_1, b_1
  5. Mirror(A1P1, c) → A1P1'
  6. Mirror(A1P2, c) → A1P2'
  7. Mirror(A1P3, c) → A1P3'
  8. Polygon(A1P1', A1P2', A1P3') → A1', a1p3', a1p1', a1p2'
  9. IndexOf(SelectedElement[ListFig], ListFig) → ReflectFig
  10. If(ShowChi, "選擇要反轉的圖形", "Select a figure to reflect") → TextInstSelect
  11. Mirror(A2P1, c_1) → A2P1'
  12. Mirror(A2P2, c_1) → A2P2'
  13. Mirror(A2P3, c_1) → A2P3'
  14. Polygon(A2P1', A2P2', A2P3') → A2', a2p3', a2p1', a2p2'
  15. Point(Circle[A3P1, 3]) → A3P2
  16. Polygon(A3P1, A3P2, A3P3) → A3, c_2, a_2, b_2
  17. Mirror(A3P1, c_2) → A3P1'
  18. Mirror(A3P2, c_2) → A3P2'
  19. Mirror(A3P3, c_2) → A3P3'
  20. Polygon(A3P1', A3P2', A3P3') → A3', a3p3', a3p1', a3p2'
  21. Point(Circle[A4P1, 3]) → A4P2
  22. Polygon(A4P1, A4P2, A4P3) → A4, c_3, a_3, b_3
  23. Mirror(A4P1, c_3) → A4P1'
  24. Mirror(A4P2, c_3) → A4P2'
  25. Mirror(A4P3, c_3) → A4P3'
  26. Polygon(A4P1', A4P2', A4P3') → A4', c', a4p1', a4p2'
  27. Point(Circle[B1P1, 3]) → B1P2
  28. Polygon(B1P1, B1P2, B1P3) → B1, d, a_4, b_4
  29. Mirror(B1P1, d) → B1P1'
  30. Mirror(B1P2, d) → B1P2'
  31. Mirror(B1P3, d) → B1P3'
  32. Polygon(B1P1', B1P2', B1P3') → B1', b1p3', b1p1', b1p2'
  33. Point(Circle[B2P1, 3]) → B2P2
  34. Polygon(B2P1, B2P2, B2P3) → B2, c_4, a_5, b_5
  35. Mirror(B2P1, c_4) → B2P1'
  36. Mirror(B2P2, c_4) → B2P2'
  37. Mirror(B2P3, c_4) → B2P3'
  38. Polygon(B2P1', B2P2', B2P3') → B2', b2p3', a', b2p2'
  39. Point(Circle[B3P1, 3]) → B3P2
  40. Polygon(B3P1, B3P2, B3P3) → B3, c_5, a_6, b_6
  41. Mirror(B3P1, c_5) → B3P1'
  42. Mirror(B3P2, c_5) → B3P2'
  43. Mirror(B3P3, c_5) → B3P3'
  44. Polygon(B3P1', B3P2', B3P3') → B3', f, b3p1', b3p2'
  45. Point(Circle[B4P1, 3]) → B4P2
  46. Polygon(B4P1, B4P2, B4P3) → B4, d_1, a_7, b_7
  47. Mirror(B4P1, d_1) → B4P1'
  48. Mirror(B4P2, d_1) → B4P2'
  49. Mirror(B4P3, d_1) → B4P3'
  50. Polygon(B4P1', B4P2', B4P3') → B4', b4p3', b4p1', b4p2'
  51. Point(Circle[C1P1, 2]) → C1P2
  52. Polygon(C1P1, C1P2, C1P3) → C1, c_6, a_8, b_8
  53. Polygon(C1P1, C1P2, C1P4) → C1a, c1p4, c1p1, c1p2
  54. Mirror(C1P1, c_6) → C1P1'
  55. Mirror(C1P2, c_6) → C1P2'
  56. Mirror(C1P3, c_6) → C1P3'
  57. Polygon(C1P1', C1P2', C1P3') → C1', c1p3', c1p1', c1p2'
  58. Mirror(C1P1, c_6) → C1P1'_1
  59. Mirror(C1P2, c_6) → C1P2'_1
  60. Mirror(C1P4, c_6) → C1P4'
  61. Polygon(C1P1'_1, C1P2'_1, C1P4') → C1a', c1p4', c1p1'_1, c1p2'_1
  62. Point(Circle[C2P1, 2]) → C2P2
  63. Polygon(C2P1, C2P2, C2P3) → C2, c_7, a_9, b_9
  64. Polygon(C2P1, C2P2, C2P4) → C2a, c2p4, c2p1, c2p2
  65. Mirror(C2P1, c2p4) → C2P1'
  66. Mirror(C2P2, c2p4) → C2P2'
  67. Mirror(C2P4, c2p4) → C2P4'
  68. Polygon(C2P1', C2P2', C2P4') → C2a', c2p4', c2p1', c2p2'
  69. Mirror(C2P1, c2p4) → C2P1'_1
  70. Mirror(C2P2, c2p4) → C2P2'_1
  71. Mirror(C2P3, c2p4) → C2P3'
  72. Polygon(C2P1'_1, C2P2'_1, C2P3') → C2', c2p3', c2p1'_1, c2p2'_1
  73. Point(Circle[C3P1, 2]) → C3P2
  74. Polygon(C3P1, C3P2, C3P3) → C3, c_8, a_{10}, b_{10}
  75. Polygon(C3P1, C3P2, C3P4) → C3a, c3p4, c3p1, c3p2
  76. Mirror(C3P1, c_8) → C3P1'
  77. Mirror(C3P2, c_8) → C3P2'
  78. Mirror(C3P4, c_8) → C3P4'
  79. Polygon(C3P1', C3P2', C3P4') → C3a', c3p4', c3p1', c3p2'
  80. Mirror(C3P1, c_8) → C3P1'_1
  81. Mirror(C3P2, c_8) → C3P2'_1
  82. Mirror(C3P3, c_8) → C3P3'
  83. Polygon(C3P1'_1, C3P2'_1, C3P3') → C3', c3p3', c3p1'_1, c3p2'_1
  84. Point(Circle[C4P1, 2]) → C4P2
  85. Polygon(C4P1, C4P2, C4P3) → C4, c_9, a_{11}, b_{11}
  86. Polygon(C4P1, C4P2, C4P4) → C4a, c4p4, c4p1, c4p2
  87. Mirror(C4P1, c_9) → C4P1'
  88. Mirror(C4P2, c_9) → C4P2'
  89. Mirror(C4P4, c_9) → C4P4'
  90. Polygon(C4P1', C4P2', C4P4') → C4a', c4p4', c4p1', c4p2'
  91. Mirror(C4P1, c_9) → C4P1'_1
  92. Mirror(C4P2, c_9) → C4P2'_1
  93. Mirror(C4P3, c_9) → C4P3'
  94. Polygon(C4P1'_1, C4P2'_1, C4P3') → C4', c4p3', c4p1'_1, c4p2'_1
  95. Point(Circle[D1P1, 4.123105625617661]) → D1P2
  96. Polygon(D1P1, D1P2, D1P3) → D1, c_{10}, a_{12}, b_{12}
  97. Point(Circle[D2P1, 4.123105625617661]) → D2P2
  98. Polygon(D2P1, D2P2, D2P3) → D2, c_{11}, a_{13}, b_{13}
  99. Point(Circle[D3P1, 4.123105625617661]) → D3P2
  100. Polygon(D3P1, D3P2, D3P3) → D3, c_{12}, a_{14}, b_{14}
  101. Point(Circle[D4P1, 4.123105625617661]) → D4P2
  102. Polygon(D4P1, D4P2, D4P3) → D4, c_{13}, a_{15}, b_{15}
  103. Point(Circle[E1P1, 3]) → E1P2
  104. Polygon(E1P1, E1P2, E1P3) → E1, c_{14}, a_{16}, b_{16}
  105. Point(Circle[E2P1, 3]) → E2P2
  106. Polygon(E2P1, E2P2, E2P3) → E2, c_{15}, a_{17}, b_{17}
  107. Point(Circle[E3P1, 3]) → E3P2
  108. Polygon(E3P1, E3P2, E3P3) → E3, c_{16}, a_{18}, b_{18}
  109. Point(Circle[E4P1, 3]) → E4P2
  110. Polygon(E4P1, E4P2, E4P3) → E4, c_{17}, a_{19}, b_{19}
  111. Point(Circle[E5P1, 3]) → E5P2
  112. Polygon(E5P1, E5P2, E5P3) → E5, c_{18}, a_{20}, b_{20}
  113. Point(Circle[E6P1, 3]) → E6P2
  114. Polygon(E6P1, E6P2, E6P3) → E6, c_{19}, a_{21}, b_{21}

AI 绘图提示语参考

请绘制一个由多个三角形通过镜像对称组合而成的复杂多边形图形。首先在网格上放置几个基础三角形，然后使用镜像变换生成每个三角形的反射副本。接着将这些反射副本与原始三角形组合，形成更大的多边形结构。整个过程应逐步构建，确保三角形之间的对称关系清晰可见，适合用于几何教学和探索。
以上提示语为根据原始绘图命令整理而来，仅供参考。