足球3v3 - 位置、角度与缩放

足球3v3 - 位置、角度与缩放
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2020-07-09 21:02
①本范例演示足球比赛中球员位置、角度和缩放关系的几何原理;②涉及核心数学概念包括角度、缩放变换、几何变换、相似性、解析几何;③作图要点运用了Point, Line, Midpoint, Circle, Segment, Distance, Intersect, Polygon等GeoGebra命令与对象;④适合高中阶段数学教学,用于理解体育中的几何应用。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Line(A, B) → f
  3. Point(f) → C
  4. Point(f) → D
  5. Point(f) → E
  6. Point(f) → F
  7. Midpoint(E, F) → Goal
  8. Circle(Goal, OffenseA) → c
  9. Point(Circle[OffenseA, 2]) → K
  10. Segment(OffenseA, K) → h
  11. Midpoint(OffenseA, K) → L
  12. Point(Circle[Goalkeeper, 2]) → N
  13. Segment(Goalkeeper, N) → j
  14. Midpoint(Goalkeeper, N) → M
  15. Distance(L, M) → distanceLM
  16. Distance(L, M) → d
  17. Distance(M, Goal) → distanceMGoal
  18. Point(Circle[OffenseB, 2]) → V
  19. Segment(OffenseB, V) → r
  20. Midpoint(OffenseB, V) → G
  21. Point(Circle[DefenderA, 2]) → S
  22. Segment(DefenderA, S) → t
  23. Midpoint(DefenderA, S) → B_1
  24. Line(V, DefenderA) → p_2
  25. Line(V, S) → q_2
  26. Line(V, Goalkeeper) → a_2
  27. Line(V, N) → b_2
  28. Point(p_2) → O_1
  29. Point(a_2) → U_1
  30. Line(O_1, f) → c_2
  31. Line(U_1, f) → e_2
  32. Intersect(q_2, c_2) → V_1
  33. Intersect(e_2, b_2) → Z_1
  34. Polygon(U_1, Z_1, V) → t8, v_2, u_1, z_1
  35. Polygon(O_1, V_1, V) → t9, v_3, g_3, h_3
  36. Midpoint(O_1, V_1) → H_2
  37. Midpoint(U_1, Z_1) → J_2
  38. Polygon(V, OffenseA, K) → t11, k_3, v_5, offensea
  39. Polygon(V, E, F) → t12, f_4, v_6, e_3
  40. Line(K, DefenderA) → i_3
  41. Line(K, S) → j_3
  42. Line(K, Goalkeeper) → n_3
  43. Line(K, N) → p_3
  44. Point(i_3) → Q
  45. Point(n_3) → R
  46. Line(Q, f) → n
  47. Line(R, f) → q_3
  48. Intersect(n, j_3) → B_2
  49. Intersect(q_3, p_3) → C_2
  50. Intersect(f, i_3) → E_2
  51. Intersect(f, j_3) → F_2
  52. Intersect(f, n_3) → G_2
  53. Intersect(f, p_3) → K_2
  54. Midpoint(Q, B_2) → A_1
  55. Midpoint(R, C_2) → N_2
  56. Polygon(Q, B_2, K) → t14, k_5, q_4, a_3
  57. Polygon(R, C_2, K) → t15, c_3, d_3, g_4
  58. Polygon(K, V, OffenseB) → t17, i_4, k_7, v_7
  59. Polygon(K, E, F) → t18, f_5, k_8, e_4
  60. Point(Circle[OffenseC, 2]) → T
  61. Segment(OffenseC, T) → g
  62. Midpoint(OffenseC, T) → P
  63. Polygon(K, OffenseC, T) → t1, t_1, k, offensec
  64. Polygon(V, OffenseC, T) → t2, t_2, v, i
  65. Point(Circle[DefenderC, 2]) → Z
  66. Segment(DefenderC, Z) → l
  67. Line(K, DefenderC) → m
  68. Line(K, Z) → p
  69. Point(m) → O
  70. Line(O, f) → s
  71. Intersect(s, p) → U
  72. Midpoint(O, U) → D_1
  73. Midpoint(DefenderC, Z) → E_1
  74. Polygon(O, U, K) → t3, k_1, o, u
  75. Intersect(f, m) → F_1
  76. Intersect(f, p) → G_1
  77. Line(V, DefenderC) → a
  78. Line(V, Z) → b
  79. Intersect(f, a) → H_1
  80. Intersect(f, b) → I_1
  81. Point(a) → J_1
  82. Line(J_1, f) → e
  83. Intersect(e, b) → M_1
  84. Midpoint(J_1, M_1) → N_1
  85. Polygon(J_1, M_1, V) → t4, v_1, j_1, m_1
  86. Line(T, DefenderA) → f_1
  87. Line(T, S) → g_1
  88. Line(T, DefenderC) → h_1
  89. Line(T, Z) → i_1
  90. Line(T, Goalkeeper) → l_1
  91. Line(T, N) → n_1
  92. Point(f_1) → W
  93. Point(h_1) → C_1
  94. Point(l_1) → P_1
  95. Line(W, f) → p_1
  96. Line(C_1, f) → q_1
  97. Line(P_1, f) → r_1
  98. Intersect(p_1, g_1) → Q_1
  99. Intersect(q_1, i_1) → R_1
  100. Intersect(n_1, r_1) → S_1
  101. Midpoint(P_1, S_1) → T_1
  102. Midpoint(W, Q_1) → W_1
  103. Midpoint(C_1, R_1) → A_2
  104. Polygon(T, V, OffenseB) → t5, offenseb, t_3, v_4
  105. Polygon(T, OffenseA, K) → t6, k_2, t_4, s_1
  106. Polygon(T, E, F) → t7, f_2, t_5, e_1
  107. Polygon(P_1, S_1, T) → t10, t_6, c_1, d_1
  108. Polygon(C_1, R_1, T) → t13, t_7, g_2, h_2
  109. Polygon(W, Q_1, T) → t16, t_8, w_1, i_2

AI 绘图提示语参考

画一个足球场上的3v3阵型,包含三个进攻球员、一个守门员和三个防守球员。用圆圈表示球员的位置,用线段连接相关点,标出关键角度和距离。先画出一条基线,再确定球门位置和球员位置,然后画出球员之间的距离和角度关系,最后用多边形连接相关点形成区域。
以上提示语为根据原始绘图命令整理而来,仅供参考。