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Polar Coordinates in Battleship

Polar Coordinates in Battleship
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2020-02-06 05:37
CircleAngleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the application of polar coordinates in a battleship game, simulating attack trajectories using a polar coordinate system. Key math concepts include polar coordinate representation, angle calculation, distance measurement, and the application of trigonometric functions. Construction highlights involve GeoGebra commands/objects like Random (random number generation), Circle (circle), Ray (ray), OrthogonalLine (perpendicular line), Intersect (intersection), CircumcircleArc (circumcircle arc), Midpoint (midpoint), Sequence (sequence), If (conditional statements), Angle (angle), Segment (segment), Polygon (polygon), Line (line), Rotate (rotation), Mod (modulus operation), and Point (point). Suitable for high school students learning polar coordinates, trigonometry, and analytical geometry, this example can be used in classroom instruction or as homework practice to help students understand the practical applications of polar coordinates.

GeoGebra Commands & Parameters

  1. Random(4, 15) → rr
  2. Circle(A, (((1.5 * v) - 1) * rr)) → c'
  3. Ray(A, (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) → h
  16. Sequence(Text[If[s < 10, " ", ""] + (s), (21.6 + (2 * Mod[s - 1, 3]), 7.75 - (2 * Div[s - 1, 3]))], s, 1, 12) → liste3
  17. Circle(J, 1) → k
  18. 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
  19. If(yB > -5, 5°, ((((xB - (3 * yB)) / 2 - 19 - 1) * 30))°) → ang
  20. If(ang ≟ α ∧ dist ≟ rr, true, false) → raz
  21. Angle((1, 0), (0, 0), A) → β
  22. Segment(O, N) → m
  23. Circle(A, (((2 * v) - 1) * rr) - n) → p
  24. Sequence(Circle[A, (((1.5 * v) - 1) * rr) - i], i, 0, n, n / 10) → liste5
  25. Polygon(P, Q, R, S) → poly1, p_1, q, r_1, s
  26. Angle((1, 0), (0, 0), A) → γ
  27. Circle((0, 0), If[((2 * v) * rr) > 12, 0, ((2 * 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 * v), U) → L'
  42. Segment(U, L') → b_1
  43. Mod((v * 100), 2) → ab
  44. Sequence(Circle[(0, 0), t], t, 1, 15) → liste1
  45. Sequence(Segment[(0, 0), (15; ((2 * 3.141592653589793) * t / 36))], t, 0, 37) → 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 - 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
  76. Polygon(C_2, D_2, E_2, G_2) → poly5, c_3, d_2, e_2, g_2

AI Drawing Prompt Reference

Draw a circle centered at the origin and several rays and arcs starting from the origin. Use random numbers to generate attack trajectories, calculate angles and distances using polar coordinates, and construct a series of intersection points and arcs to form a simulated projectile trajectory diagram. Pay attention to the calculation of angles and distances to ensure correct intersections of rays and arcs.
The prompt above was compiled from the original drawing commands and is for reference only.