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极坐标寻船游戏 by Woogon Chung

极坐标寻船游戏 by Woogon Chung
几何画板及绘图内容加载中，请稍等……
2011-10-22 18:09
解析几何概率统计几何作图
所属专题 Games Portugal is great
本范例通过极坐标系中的点来寻找船只的位置。核心数学概念包括极坐标系、角度计算和条件概率。通过使用GeoGebra命令如Random、Circle、Ray等，可以动态地展示极坐标系中的点和线。适合高中数学教学，特别是解析几何和概率统计的教学。

GeoGebra 命令及参数

  1. Random(4.0, 15.0) → rr
  2. Circle(A, (1.5 * v - 1.0) * rr) → c'
  3. Ray(A, (0.0, 0.0)) → a
  4. OrthogonalLine(A, a) → b
  5. Intersect(c', b) → B, C
  6. Intersect(c', a) → D, T
  7. CircumcircleArc(B, D, C) → d
  8. Midpoint(C, D) → E
  9. Midpoint(B, D) → F_2
  10. Ray(A', E) → e
  11. Ray(A', F_2) → f
  12. Intersect(d, e) → G,
  13. Intersect(d, f) → H,
  14. CircumcircleArc(G, D, H) → g
  15. Circle(I, 1.0) → h
  16. Sequence(Text[If[s < 10.0, " ", ""] + (s), (21.6 + 2.0 * Mod[s - 1.0, 3.0], 7.75 - 2.0 * Div[s - 1.0, 3.0])], s, 1.0, 12.0) → liste3
  17. Circle(J, 1.0) → k
  18. Sequence(Text[If[s ≟ 1.0, " ", If[s < 5.0, " ", ""]] + (30.0 * (s - 1.0)) + "º", (21.25 + 2.0 * Mod[s - 1.0, 3.0], -(6.25) - 2.0 * Div[s - 1.0, 3.0])], s, 1.0, 12.0) → liste4
  19. If(yB > -(5.0), 5.0*°, ((xB - 3.0 * yB) / 2.0 - 19.0 - 1.0) * 30.0°) → ang
  20. If(ang ≟ α ∧ dist ≟ rr, true, false) → raz
  21. Angle((1.0, 0.0), (0.0, 0.0), A) → β
  22. Segment(O, N) → m
  23. Circle(A, (2.0 * v - 1.0) * rr - n) → p
  24. Sequence(Circle[A, (1.5 * v - 1.0) * rr - i], i, 0.0, n, n / 10.0) → liste5
  25. Polygon(P, Q, R, S) → poly1, p_1, q, r_1, s
  26. Angle((1.0, 0.0), (0.0, 0.0), A) → γ
  27. Circle((0.0, 0.0), If[2.0 * v * rr > 12.0, 0.0, 2.0 * v * rr]) → c
  28. Midpoint(K, L) → U
  29. Midpoint(U, L) → V
  30. Midpoint(U, V) → W
  31. Midpoint(V, L) → Z
  32. Segment(K, C_1) → l
  33. Line(A, l) → i
  34. Segment(A, U) → t
  35. Intersect(c, t) → A_1, B_1
  36. Segment(U, A_1) → a_1
  37. Circle(U, W) → c_1
  38. Circle(U, V) → d_1
  39. Circle(U, Z) → e_1
  40. Circle(U, L) → f_1
  41. Rotate(C_1, 6.0 * v, U) → L'
  42. Segment(U, L') → b_1
  43. Mod(v * 100.0, 2.0) → ab
  44. Sequence(Circle[(0.0, 0.0), t], t, 1.0, 15.0) → liste1
  45. Sequence(Segment[(0.0, 0.0), (15.0; 2.0 * 3.141592653589793 * t / 36.0)], t, 0.0, 37.0) → liste2
  46. Segment(O, D_1) → j
  47. Circle(O, C_1) → g_1
  48. Point(g_1) → E_1
  49. Segment(O, E_1) → h_1
  50. Circle(U, C_1) → k_1
  51. Circle(F_1, 8.0 - r / 2.5) → q_1
  52. Line(F_1, l) → i_1
  53. Intersect(q_1, i_1) → G_1, H_1
  54. Line(J_1, r_1) → j_1
  55. Point(j_1) → N_1
  56. Line(N_1, l) → l_1
  57. Line(J_1, l) → m_1
  58. Point(m_1) → O_1
  59. Point(l_1) → P_1
  60. Intersect(l_1, r_1) → M_1
  61. Polygon(M_1, N_1, J_1, F) → poly2, m_2, n_1, j_2, f_2
  62. Point(l_1) → Q_1
  63. Point(m_1) → R_1
  64. Polygon(P_1, Q_1, R_1, O_1) → poly3, p_2, q_2, r_2, o_1
  65. Point(j_1) → S_1
  66. Point(o_1) → T_1
  67. Polygon(S_1, T_1, O_1, J_1) → poly4, s_1, t_1, o_2, j_3
  68. Midpoint(s_1) → V_1
  69. Midpoint(o_2) → W_1
  70. Midpoint(S_1, J_1) → Z_1
  71. Midpoint(t_1) → A_2
  72. Segment(V_1, W_1) → a_2
  73. Segment(Z_1, A_2) → b_2
  74. Intersect(b_2, a_2) → B_2
  75. Circle(B_2, V_1) → c_2