角侦探

角侦探
几何画板及绘图内容加载中,请稍等……
2021-06-13 07:35
这个范例通过一个有趣的侦探游戏,演示了菱形的性质。核心数学概念包括角的性质和几何变换。通过使用GeoGebra命令如Point、Angle、Segment等,可以动态地探索菱形的角和对称性。适合初中及以上学生学习几何变换和菱形的性质。

GeoGebra 命令及参数

  1. Point(Circle[A, (2.5 * zr)]) → C'
  2. Angle(C, A, C') → ang
  3. Segment(F, E) → l
  4. Segment(A, C') → a
  5. CircleSector(A, F, Rotate[F, t1, A]) → c
  6. Circle(B, arr) → e
  7. Polygon(F + v_1 / 5, F + h / 10, F - h / 10) → fth, b, f, g
  8. Polygon(E + v_1 / 5, E + h / 10, E - h / 10) → bth, i, j, k
  9. Sequence(Rotate[fth, t1 + ((i * 2) * pi / freq), A], i, 1, freq) → liste3
  10. Sequence(Rotate[bth, t2 + ((i * 2) * pi / rap), B], i, 1, rap) → liste4
  11. Segment(Mirror[F, A], Mirror[E, B]) → m
  12. Vector(E, F) → w
  13. Mirror(F, A) → F'
  14. CircleSector(B, E, Rotate[E, t2, B]) → d
  15. Mirror(E, B) → E'
  16. Vector(F', E') → u
  17. PolyLine(A, B, G, A, H, G) → n
  18. Translate(e, Vector[B, I]) → e'
  19. Sequence(Segment[Rotate[D, t2 + ((i * 2) * pi / av), B], Rotate[E, t2 + ((i * 2) * pi / av), B]], i, 1, av) → liste1
  20. Sequence(Segment[I, Rotate[J, t2 + ((i * 2) * pi / av), I]], i, 1, av) → liste2
  21. Polygon(G + (0.1 * v_1) + h, G + (0.9 * v_1) + h, G + (0.5 * v_1) - (2 * h)) → poly1, q, r, s
  22. Circle(M, (5 * zr)) → d_1
  23. Circle(K, (6 * zr)) → c_1
  24. Intersect(c_1, d_1, 2) → L
  25. Polygon(C' + (0.5 * h) + (0.25 * v_1), C' + (0.5 * h) - (0.25 * v_1), C' - (0.5 * h) - (0.25 * v_1), C' - (0.5 * h) + (0.25 * v_1)) → poly2, b_1, e_1, f_1, g_1
  26. PolyLine(K, L, M) → a_1
  27. Mirror(C', A) → C''
  28. Mirror(poly2, A) → poly2'
  29. Circle(N, (5 * zr)) → h_1
  30. Intersect(c_1, h_1, 2) → O
  31. PolyLine(K, O, N) → i_1
  32. Segment(A, C'') → j_1
  33. Circle(A, r1) → k_1
  34. Circle(B, r2) → p_1
  35. Sequence(Arc[k_1, Rotate[F, Min[3.141592653589793, Max[0, (((chaine * i) + posass) / cc1 * pi)]], A], Rotate[F, Max[0, Min[3.141592653589793, (((chaine * i) + posass + chaine / 2) / cc1 * pi)]], A]], i, 0, round(cc1 / chaine)) → liste5
  36. Sequence(Arc[p_1, Rotate[E', Min[3.141592653589793, Max[0, (((chaine * i) + posdr) / cc2 * pi)]], B], Rotate[E', Max[0, Min[3.141592653589793, (((chaine * i) + posdr + chaine / 2) / cc2 * pi)]], B]], i, 0, round(cc2 / chaine)) → liste7
  37. Sequence(Segment[F' + (u * Min[1, Max[0, ((chaine * i) + posdeb) / l]]), F' + (u * Min[1, Max[0, ((chaine * i) + posdeb + chaine / 2) / l]])], i, 0, If[(chaine * lien) + posdeb > l, lien - 1, lien]) → liste6
  38. Sequence(Segment[E + (w * Min[1, Max[0, ((chaine * i) + poslet) / l]]), E + (w * Min[1, Max[0, ((chaine * i) + poslet + chaine / 2) / l]])], i, 0, If[(chaine * lien) + posdeb > l, lien - 1, lien]) → liste8
  39. Element(liste1, Length[liste1]) → l_1
  40. CircumcircleArc(H, H - v_1, I) → p
  41. Point(n) → Q
  42. Segment(P, Q) → m_1
  43. Point(a_1) → T
  44. Segment(S, A_1) → r_1
  45. Segment(R, S) → q_1
  46. Circle(U, 1.32) → s_1
  47. Segment(R, V) → t_1
  48. Segment(R, K) → n_1
  49. CircumcircleArc(H, Z, P) → c_2
  50. Point(s_1) → C_1
  51. Point(s_1) → D_1
  52. Segment(F_1, C_1) → b_2
  53. CircleArc(U, D_1, C_1) → d_2
  54. Segment(R, U) → e_2
  55. Segment(A_1 + (-0.15, 0.5), V) → a_2
  56. Segment(H_1, I_1) → f_2
  57. Sequence(K_1 + ((10 * i), 0), i, 0, 12) → liste9
  58. Vector(K_1, L_1) → z
  59. Sequence(Translate[image5, Vector[(i * z)]], i, -2, 12) → liste10
  60. Line(J_1, xAxis) → g_2
  61. Polygon(J_1, J_1 + (120, 0), J_1 + (120, -30), J_1 + (0, -30)) → poly3, j_2, h_2, i_2, k_2

AI 绘图提示语参考

绘制一个以菱形为核心的几何侦探主题图形。菱形由两条对角线分割,顶点处有旋转的扇形和圆弧,周围分布着多个小三角形和多边形,形成对称的装饰图案。从菱形中心向外延伸出若干条线段和向量,连接着圆、圆弧和交点。图形中包含多个圆,其中两个较大的圆相交,交点与菱形顶点相连。整体构图强调角度关系、对称性和几何变换,适合用于探索菱形性质的互动教学场景。
以上提示语为根据原始绘图命令整理而来,仅供参考。