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Polar Coordinates Boat Game by Woogon Chung (2)

Polar Coordinates Boat Game by Woogon Chung (2)
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2011-10-22 18:09
Coordinate GeometryProbability & StatisticsGeometric Construction
In collections Games Portugal is great
This example uses polar coordinates to find the position of a boat. Key mathematical concepts include polar coordinates, angle calculation, and conditional probability. Using GeoGebra commands such as Random, Circle, Ray, etc., it dynamically demonstrates points and lines in the polar coordinate system. Suitable for high school mathematics education, particularly in coordinate geometry and probability & statistics.

GeoGebra Commands & Parameters

  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