音符组合的数学表示

音符组合的数学表示
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2020-11-09 04:27
①本范例通过 GeoGebra 展示了音乐理论中音符组合的几何表示;②涉及的核心数学概念包括集合论、坐标几何、几何作图和函数图像;③作图要点提炼自构造摘要,使用了 Circle(圆)、Intersect(交点)、Polygon(多边形)、Point(点)、Area(面积)、PointIn(点在对象内)等命令和对象;④适合高中及以上学生或数学爱好者用于理解音乐与数学的交叉应用。

GeoGebra 命令及参数

  1. Circle((0, 0), A) → a
  2. Circle((0, 0), Bb) → bb
  3. Circle((0, 0), B) → b
  4. Circle((0, 0), C) → c
  5. Circle((0, 0), Db) → db
  6. Circle((0, 0), D) → d
  7. Circle((0, 0), Eb) → eb
  8. Circle((0, 0), E) → e
  9. Circle((0, 0), F) → f
  10. Circle((0, 0), Gb) → gb
  11. Circle((0, 0), G) → g
  12. Circle((0, 0), Ab) → ab
  13. Intersect(a, yAxis, 2) → H
  14. Intersect(a, xAxis, 1) → I
  15. Intersect(a, yAxis, 1) → J
  16. Polygon(A, H, I, J) → q1, a_1, h, i, j
  17. Intersect(bb, yAxis, 1) → K
  18. Intersect(bb, yAxis, 2) → L
  19. Intersect(bb, xAxis, 1) → M
  20. Polygon(K, Bb, L, M) → q2, k, l, l_1, m
  21. Point(yAxis) → N
  22. Intersect(b, yAxis, 2) → O
  23. Intersect(b, xAxis, 1) → P
  24. Polygon(N, B, O, P) → q3, n, b_1, o, p
  25. Intersect(c, xAxis, 1) → R
  26. Point(yAxis) → S
  27. Polygon(C, Q, R, S) → q4, c_1, q, r, s
  28. Intersect(db, yAxis, 2) → T
  29. Intersect(db, xAxis, 1) → U
  30. Intersect(db, yAxis, 1) → V
  31. Polygon(Db, T, U, V) → q5, t, t_1, u, v
  32. Intersect(d, yAxis, 1) → W
  33. Intersect(d, yAxis, 2) → Z
  34. Intersect(d, xAxis, 1) → A_1
  35. Polygon(W, D, Z, A_1) → q6, w, d_1, z_1, f_1
  36. Point(eb) → B_1
  37. Intersect(eb, yAxis, 2) → C_1
  38. Intersect(eb, xAxis, 1) → D_1
  39. Polygon(B_1, Eb, C_1, D_1) → q7, g_1, h_1, i_1, j_1
  40. Point(e) → F_1
  41. Intersect(e, xAxis, 1) → G_1
  42. Polygon(E_1, E, F_1, G_1) → q8, e_1, e_2, k_1, m_1
  43. Intersect(f, yAxis, 1) → H_1
  44. Intersect(f, yAxis, 2) → I_1
  45. Intersect(f, xAxis, 1) → J_1
  46. Polygon(H_1, F, I_1, J_1) → q9, n_1, f_2, p_1, q_1
  47. Intersect(gb, yAxis, 1) → K_1
  48. Intersect(gb, yAxis, 2) → L_1
  49. Intersect(gb, xAxis, 1) → M_1
  50. Polygon(K_1, Gb, L_1, M_1) → q10, r_1, s_1, g_2, h_2
  51. Intersect(g, yAxis, 1) → N_1
  52. Intersect(g, yAxis, 2) → O_1
  53. Intersect(g, xAxis, 1) → P_1
  54. Polygon(N_1, G, O_1, P_1) → q11, i_2, g_3, o_1, j_2
  55. Intersect(ab, yAxis, 2) → Q_1
  56. Intersect(ab, xAxis, 1) → R_1
  57. Intersect(ab, yAxis, 1) → S_1
  58. Polygon(Ab, Q_1, R_1, S_1) → q12, k_2, l_2, m_2, n_2
  59. Area(ab) → u_1
  60. PointIn(ab) → Pointab
  61. Area(g) → v_1
  62. PointIn(g) → Pointg
  63. Area(gb) → w_1
  64. PointIn(gb) → Pointgb
  65. Area(f) → a_2
  66. PointIn(f) → Pointf
  67. Area(e) → b_2
  68. PointIn(e) → Pointe
  69. Area(eb) → c_2
  70. PointIn(eb) → Pointeb
  71. Area(d) → d_2
  72. PointIn(d) → Pointd
  73. Area(db) → o_2
  74. PointIn(db) → Pointdb
  75. Area(c) → p_2
  76. PointIn(c) → Pointc_{1}
  77. PointIn(q12) → Pointq12_{1}
  78. PointIn(q12) → Pointq12_{2}
  79. Area(a) → q_2
  80. PointIn(a) → Pointa
  81. Area(bb) → r_2
  82. PointIn(bb) → Pointbb
  83. Area(b) → s_2
  84. PointIn(b) → Pointb
  85. PointIn(q12) → Pointq12
  86. Area(c) → t_2
  87. PointIn(c) → Pointc

AI 绘图提示语参考

绘制以原点为中心的12个音符的圆,每个圆代表一个音符,然后通过这些圆与坐标轴的交点,构造9个四边形,每个四边形代表一个音符的组合。
以上提示语为根据原始绘图命令整理而来,仅供参考。