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寻潜艇坐标游戏

寻潜艇坐标游戏
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2019-03-22 11:50
圆函数三角函数解析几何概率统计
这个范例通过寻潜艇游戏演示坐标系的运用。核心数学概念包括坐标确定位置、等边三角形、圆、指数函数、随机实验和积分计算。作图要点运用了Random、Circle、Ray、OrthogonalLine、Intersect、CircumcircleArc、Midpoint、Sequence、If、Segment、Polygon、Line、Rotate、Mod、Point等GeoGebra命令和对象。适合初中及以上学生用于坐标学习和实践。

GeoGebra 命令及参数

  1. Random(-10, 10) → bb
  2. Random(-10, 10) → aa
  3. Random(-10, 10) → cc
  4. Random(4, 15) → rr
  5. Circle(A, (1.5 * v - 1) * rr) → c'
  6. Ray(A, (0, 0)) → a
  7. OrthogonalLine(A, a) → b
  8. Intersect(c', b) → B, C
  9. Intersect(c', a) → D, T
  10. CircumcircleArc(B, D, C) → d
  11. Midpoint(C, D) → E
  12. Midpoint(B, D) → F_2
  13. Ray(A', E) → e
  14. Ray(A', F_2) → f
  15. Intersect(d, e) → G,
  16. Intersect(d, f) → H,
  17. CircumcircleArc(G, D, H) → g
  18. Circle(I, 1) → h
  19. Sequence(Text[If[s < 10, " ", ""] + (s), (21.6 + 2 * Mod[s - 1, 3], 7.75 - 2 * Div[s - 1, 3])], s, 1, 12) → liste3
  20. Circle(J, 1) → k
  21. Sequence(Text[If[s ≟ 1, " ", If[s < 5, " ", ""]] + (30 * (s - 1)) + "º", (21.25 + 2 * Mod[s - 1, 3], -6.25 - 2 * Div[s - 1, 3])], s, 1, 12) → liste4
  22. If(yB > -5, 5*°, (((xB - 3 * yB) / 2 - 19 - 1) * 30)°) → ang
  23. If(ang ≟ α ∧ dist ≟ rr, true, false) → raz
  24. Segment(O, N) → m
  25. Circle(A, (2 * v - 1) * rr - n) → p
  26. Sequence(Circle[A, (1.5 * v - 1) * rr - i], i, 0, n, n / 10) → liste5
  27. Polygon(P, Q, R, S) → poly1, p_1, q, r_1, s
  28. Circle((0, 0), If[2 * v * rr > 12, 0, 2 * v * rr]) → c
  29. Midpoint(K, L) → U
  30. Midpoint(U, L) → V
  31. Midpoint(U, V) → W
  32. Midpoint(V, L) → Z
  33. Segment(K, C_1) → l
  34. Line(A, l) → i
  35. Segment(A, U) → t
  36. Intersect(c, t) → A_1, B_1
  37. Segment(U, A_1) → a_1
  38. Rotate(C_1, 6 * v, U) → L'
  39. Segment(U, L') → b_1
  40. Mod(v * 100, 2) → ab
  41. Segment(O, D_1) → j
  42. Circle(O, C_1) → g_1
  43. Point(g_1) → E_1
  44. Segment(O, E_1) → h_1
  45. Circle(F_1, 6.5 - abs(r / 4.5)) → q_1
  46. Line(F_1, l) → i_1
  47. Intersect(q_1, i_1) → G_1, H_1
  48. Line(J_1, r_1) → j_1
  49. Point(j_1) → N_1
  50. Line(N_1, l) → l_1
  51. Line(J_1, l) → m_1
  52. Point(m_1) → O_1
  53. Point(l_1) → P_1
  54. Intersect(l_1, r_1) → M_1
  55. Polygon(M_1, N_1, J_1, F) → poly2, m_2, n_1, j_2, f_2
  56. Point(l_1) → Q_1
  57. Point(m_1) → R_1
  58. Polygon(P_1, Q_1, R_1, O_1) → poly3, p_2, q_2, r_2, o_1
  59. Point(j_1) → S_1
  60. Polygon(S_1, T_1, O_1, J_1) → poly4, s_1, t_1, o_2, j_3
  61. Midpoint(s_1) → V_1
  62. Midpoint(o_2) → W_1
  63. Midpoint(S_1, J_1) → Z_1
  64. Midpoint(t_1) → A_2
  65. Segment(V_1, W_1) → a_2
  66. Segment(Z_1, A_2) → b_2
  67. Intersect(b_2, a_2) → B_2
  68. Circle(B_2, V_1) → c_2
  69. Sequence((x(O) + i, y(D_1)), i, -11, 11, 1) → liste1
  70. Sequence((x(N) + i, y(N)), i, -11, 11, 1) → liste6
  71. Sequence((x(C_1), y(C_1) + i), i, -11, 11, 1) → liste7
  72. Sequence((x(E_1), y(E_1) + i), i, -11, 11, 1) → liste8
  73. Ray(M_1, T_1) → c_1
  74. Sequence(Segment[Element[liste8, i], Element[liste7, i]], i, 0, 22) → liste10
  75. Sequence((x(D_1) + i, 0), i, -11, 11) → liste2
  76. Sequence(Segment[Element[liste1, i], Element[liste6, i]], i, 0, 22) → liste9
  77. Line(S, P) → d_1
  78. Line(J_1, S_1) → e_1
  79. Line(Q_1, e_1) → f_1
  80. Intersect(d_1, s) → M
  81. Intersect(d_1, f_1) → C_2
  82. Line(R, d_1) → k_1
  83. Intersect(e_1, k_1) → D_2
  84. Polygon(S, C_2, Q_1, S_1, D_2, R) → poly5, s_2, c_3, q_3, s_3, d_2, r_3
  85. Point(d_1) → E_2
  86. Line(E_2, p_1) → e_2
  87. Intersect(k_1, e_2) → G_2
  88. Polygon(E_2, P, Q, G_2) → poly6, e_3, p_3, q_4, g_2
  89. Sequence(O + (i, 0), i, -10, 10) → liste11
  90. Sequence(O + (0, i), i, -10, 10) → liste12
  91. Sequence(i, i, -10, 10) → liste13
  92. Sequence(Text[Element[liste13, i], (x(Element[liste11, i] - 0.42), y(Element[liste11, i] - 0.85))], i, 1, Length[liste13], 2) → liste14
  93. Sequence(Text[Element[liste13, i], (x(Element[liste12, i] - 1), y(Element[liste12, i] - 0.31))], i, 1, Length[liste13], 2) → liste15