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正九边形动态演示

正九边形动态演示
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2019-05-13 19:20
多边形几何作图
①本范例动态演示正九边形的几何构造与性质；②涉及核心数学概念包括多边形、正多边形构造、旋转与缩放变换；③构造要点：使用Polygon、Line、Segment、Circle、Intersect、Rotate、Dilate等GeoGebra命令进行正九边形的精确绘制与变换；④适合高中数学教学，用于展示正多边形的对称性与变换特性。

GeoGebra 命令及参数

  1. Polygon(A, B, 9) → poly1, f, C, D, E, F, G, H, I, g, h, i, j, k, l, m, n
  2. Line(F, D) → p
  3. Line(F, B) → q
  4. Line(D, B) → r
  5. Segment(F, E) → s
  6. Circle(F, E) → c
  7. Intersect(c, q, 2) → J
  8. Line(E, I) → t
  9. Segment(F, G) → a
  10. Segment(G, H) → b
  11. Segment(H, I) → d
  12. Segment(I, A) → e
  13. Segment(A, B) → f_1
  14. Segment(B, C) → g_1
  15. Segment(C, D) → h_1
  16. Segment(D, E) → i_1
  17. Rotate(B, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → B'
  18. Rotate(C, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → C'
  19. Segment(B', C') → j_1
  20. Rotate(C, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → C'_1
  21. Rotate(D, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → D'
  22. Segment(C'_1, D') → k_1
  23. Rotate(D, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → D'_1
  24. Rotate(E, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → E'
  25. Segment(D'_1, E') → l_1
  26. Rotate(F, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → F'
  27. Rotate(E, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → E'_1
  28. Segment(F', E'_1) → s'
  29. Rotate(F, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → F'_1
  30. Rotate(G, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → G'
  31. Segment(F'_1, G') → a'
  32. Rotate(G, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → G'_1
  33. Rotate(H, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → H'
  34. Segment(G'_1, H') → b'
  35. Rotate(H, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → H'_1
  36. Rotate(I, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → I'
  37. Segment(H'_1, I') → d'
  38. Rotate(I, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → I'_1
  39. Rotate(A, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → A'
  40. Segment(I'_1, A') → e'
  41. Rotate(A, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → A'_1
  42. Rotate(B, If[0 < o ≤ 1, ((o * 2) * π / 9), (2 * π / 9)], Center[Circle[D, E, F]]) → B'_1
  43. Segment(A'_1, B'_1) → n_1
  44. Rotate(poly1, If[1.5 < o ≤ 2.5, (((o - 1.5) * 2) * π / 9), (2 * π / 9)], Center[Circle[A, B, C]]) → poly1'
  45. Dilate(E'_1, If[3 < o ≤ 4, 4 - o, 0], J) → K
  46. Segment(E', K) → m_1
  47. Dilate(J, If[4 < o ≤ 5, 5 - o, 0], A'_1) → J'
  48. Segment(J, J') → p_1
  49. Dilate(C'_1, If[5 < o ≤ 6, 6 - o, 0], A'_1) → L
  50. Segment(C'_1, L) → q_1
  51. Rotate(D'_1, If[7 < o ≤ 8, ((-(o - 7)) * π / 3), ((-π)) / 3], E'_1) → M
  52. Rotate(E', If[7 < o ≤ 8, ((-(o - 7)) * π / 3), ((-π)) / 3], E'_1) → E''
  53. Segment(M, E'') → r_1
  54. Rotate(C'_1, If[8 < o ≤ 9, (((o - 8) * 2) * π / 9), (2 * π / 9)], A'_1) → N
  55. Rotate(L, If[8 < o ≤ 9, (((o - 8) * 2) * π / 9), (2 * π / 9)], A'_1) → L'
  56. Segment(N, L') → s_1

AI 绘图提示语参考

画一个动态的规则九边形，展示其几何构造和对称性。中心绘制一个九边形，然后从其中一个顶点出发，依次连接相邻顶点形成线段。以某条边的中点为圆心画圆，与相邻边相交得到新点。通过旋转和缩放这些点，动态演示九边形的对称性和变换性质。
以上提示语为根据原始绘图命令整理而来，仅供参考。