积极 AI Logo 积极 AI

动态几何问题示例

动态几何问题示例
几何画板及绘图内容加载中，请稍等……
2019-01-21 23:20
角变换几何作图
这是一个动态可修改的几何问题示例，基于Ed Southall在Twitter上发布的问题。该示例展示了角度、几何图形、正方形等核心数学概念。通过使用GeoGebra命令如Polygon、Ray、Segment等，可以动态调整图形，帮助理解几何变换和作图要点。适合初中及以上学生和教师使用。

GeoGebra 命令及参数

  1. Polygon(A, B, 12) → poly1, f, p, q, r, C, D, E, F, G, H, I, g, J, K, L, h, i, j, k, l, m, n
  2. Polygon(J, I, 6) → poly2, s, P, t, a, b, c, d, M, N, O
  3. Polygon(I, H, 4) → poly3, e, f_1, g_1, h_1, Q, R
  4. Polygon(E, D, 6) → poly4, i_1, V, j_1, k_1, l_1, m_1, n_1, S, T, U
  5. Ray(Q, N) → p_1
  6. Ray(Q, S) → q_1
  7. Segment(A, B) → r_1
  8. Segment(B, C) → s_1
  9. Segment(C, D) → t_1
  10. Segment(D, E) → a_1
  11. Segment(E, F) → b_1
  12. Segment(F, G) → c_1
  13. Segment(G, H) → d_1
  14. Segment(H, I) → e_1
  15. Segment(I, J) → f_2
  16. Segment(J, K) → g_2
  17. Segment(K, L) → h_2
  18. Segment(L, A) → i_2
  19. Segment(H, Q) → j_2
  20. Segment(Q, R) → k_2
  21. Segment(R, I) → l_2
  22. Segment(R, N) → m_2
  23. Segment(N, O) → n_2
  24. Segment(O, P) → p_2
  25. Segment(P, J) → q_2
  26. Segment(D, S) → r_2
  27. Segment(S, T) → s_2
  28. Segment(T, U) → t_2
  29. Segment(U, V) → a_2
  30. Segment(V, E) → b_2
  31. Semicircle(U, Q) → c_2
  32. Dilate(Q, If[0 < o ≤ 1, 1 - o, 0], N) → Q'
  33. Dilate(Q, If[0 < o ≤ 1, 1 - o, 0], S) → Q'_1
  34. Segment(Q, Q') → d_2
  35. Segment(Q, Q'_1) → e_2
  36. Rotate(V, If[1 < o ≤ 2, (((o - 1) * 2) * π / 3), (2 * π / 3)], U) → V'
  37. Circle(U, (0.5 * a_2)) → c_3
  38. Ray(U, V') → f_3
  39. Intersect(c_3, f_3, 1) → W
  40. Intersect(c_3, a_2, 1) → Z
  41. CircleSector(U, Z, W) → d_3
  42. Rotate(U, If[2.5 < o ≤ 3.5, ((-(o - 2.5)) * π), (-π)], Midpoint[Q, U]) → U'
  43. Vector(U, U') → u
  44. Line(U, d_2) → g_3
  45. Point(g_3) → A_1
  46. Translate(d_3, u) → e_3
  47. Point(g_3) → B_1
  48. Rotate(e_3, If[2.5 < o ≤ 3.5, (((-(o - 2.5)) * 7) * π / 4), (-7 * π / 4)], U') → h_3