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多边形周长与几何变换的交互演示

多边形周长与几何变换的交互演示
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2016-12-08 02:38
多边形变换几何作图滑块动画
① 本范例通过GeoGebra动态展示多个多边形（poly1、poly2、poly3等）的周长（PERIMETER）计算，并利用几何变换（如平移、旋转或缩放）生成一系列相似或全等的多边形，直观呈现周长与边长的关系。② 核心数学概念包括多边形周长、几何变换（平移、旋转、缩放）、相似形与全等形，以及周长在变换下的不变性或比例变化。③ 作图要点：使用Polygon命令创建多边形，Point定义顶点，Intersect求交点，PolyLine绘制折线；对象包括A至F、poly1、c至f、G至J、poly2、g至j、K至N、poly3、k至n以及带下标的G_1、H_1等，通过重复构造和变换生成多个多边形，便于对比周长。④ 适合初中至高中阶段学习几何与变换的学生，也可用于教师课堂演示周长概念与几何变换的直观教学。

GeoGebra 命令及参数

  1. Polygon(C, D, E, F) → poly1, c, d, e, f
  2. Polygon(G, H, I, J) → poly2, g, h, i, j
  3. Polygon(K, L, M, N) → poly3, k, l, m, n
  4. Polygon(G_1, H_1, I_1, J_1) → poly2_1, g_1, h_1, i_1, j_1
  5. Polygon(G_2, H_2, I_2, J_2) → poly2_2, g_2, h_2, i_2, j_2
  6. Polygon(G_3, H_3, I_3, J_3) → poly2_3, g_3, h_3, i_3, j_3
  7. Polygon(G_4, H_4, I_4, J_4) → poly2_4, g_4, h_4, i_4, j_4
  8. Polygon(G_5, H_5, I_5, J_5) → poly2_5, g_5, h_5, i_5, j_5
  9. Polygon(G_6, H_6, I_6, J_6) → poly2_6, g_6, h_6, i_6, j_6
  10. Polygon(G_7, H_7, I_7, J_7) → poly2_7, g_7, h_7, i_7, j_7
  11. Polygon(G_8, H_8, I_8, J_8) → poly2_8, g_8, h_8, i_8, j_8
  12. Polygon(G_9, H_9, I_9, J_9) → poly2_9, g_9, h_9, i_9, j_9
  13. Polygon(G_{10}, H_{10}, I_{10}, J_{10}) → poly2_{10}, g_{10}, h_{10}, i_{10}, j_{10}
  14. Polygon(G_{11}, H_{11}, I_{11}, J_{11}) → poly2_{11}, g_{11}, h_{11}, i_{11}, j_{11}
  15. Polygon(G_{12}, H_{12}, I_{12}, J_{12}) → poly2_{12}, g_{12}, h_{12}, i_{12}, j_{12}
  16. Polygon(G_{13}, H_{13}, I_{13}, J_{13}) → poly2_{13}, g_{13}, h_{13}, i_{13}, j_{13}
  17. Polygon(G_{14}, H_{14}, I_{14}, J_{14}) → poly2_{14}, g_{14}, h_{14}, i_{14}, j_{14}
  18. Polygon(G_{15}, H_{15}, I_{15}, J_{15}) → poly2_{15}, g_{15}, h_{15}, i_{15}, j_{15}
  19. Polygon(G_{16}, H_{16}, I_{16}, J_{16}) → poly2_{16}, g_{16}, h_{16}, i_{16}, j_{16}
  20. Polygon(G_{17}, H_{17}, I_{17}, J_{17}) → poly2_{17}, g_{17}, h_{17}, i_{17}, j_{17}
  21. Polygon(G_{18}, H_{18}, I_{18}, J_{18}) → poly2_{18}, g_{18}, h_{18}, i_{18}, j_{18}
  22. Polygon(G_{19}, H_{19}, I_{19}, J_{19}) → poly2_{19}, g_{19}, h_{19}, i_{19}, j_{19}
  23. Polygon(G_{20}, H_{20}, I_{20}, J_{20}) → poly2_{20}, g_{20}, h_{20}, i_{20}, j_{20}
  24. Polygon(G_{21}, H_{21}, I_{21}, J_{21}) → poly2_{21}, g_{21}, h_{21}, i_{21}, j_{21}
  25. Polygon(G_{22}, H_{22}, I_{22}, J_{22}) → poly2_{22}, g_{22}, h_{22}, i_{22}, j_{22}
  26. Polygon(G_{23}, H_{23}, I_{23}, J_{23}) → poly2_{23}, g_{23}, h_{23}, i_{23}, j_{23}
  27. Polygon(G_{24}, H_{24}, I_{24}, J_{24}) → poly2_{24}, g_{24}, h_{24}, i_{24}, j_{24}
  28. Polygon(G_{25}, H_{25}, I_{25}, J_{25}) → poly2_{25}, g_{25}, h_{25}, i_{25}, j_{25}
  29. Polygon(G_{26}, H_{26}, I_{26}, J_{26}) → poly2_{26}, g_{26}, h_{26}, i_{26}, j_{26}
  30. Polygon(G_{27}, H_{27}, I_{27}, J_{27}) → poly2_{27}, g_{27}, h_{27}, i_{27}, j_{27}
  31. Polygon(G_{28}, H_{28}, I_{28}, J_{28}) → poly2_{28}, g_{28}, h_{28}, i_{28}, j_{28}
  32. Point(j_{14}) → O
  33. Point(h_{27}) → Q
  34. Point(j_9) → R
  35. Point(j_{14}) → S
  36. Point(h_{27}) → U
  37. Point(j_9) → V
  38. Intersect(n, j_{17}) → Z
  39. Point(h_{27}) → A_1
  40. Point(j_9) → B_1
  41. Point(j_{14}) → C_1
  42. PolyLine(O, P, A_1, B_1, C_1, Q, R, S, T, U, V, W, Z) → p

AI 绘图提示语参考

绘制多个多边形，展示它们通过平移、旋转或缩放生成的相似或全等多边形，并比较它们的周长。首先创建三个基础多边形，然后通过重复应用变换生成一系列相似或全等多边形，用线条连接特定点形成复杂图形，直观展示周长与边长的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。