分数计算与生日蛋糕问题

分数计算与生日蛋糕问题
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2013-07-05 20:00
①本范例通过生日蛋糕分割问题演示分数计算与几何图形的关联;②涉及核心数学概念包括分数运算、几何作图、等边三角形性质及实数应用;③构造过程中运用了Circle(圆)、Point(点)、Line(线)、OrthogonalLine(垂线)、Intersect(交点)、Segment(线段)、Midpoint(中点)、CircleSector(圆扇形)等GeoGebra命令与对象;④适合初中及以上数学学习者,用于理解分数运算在几何问题中的应用与可视化。

GeoGebra 命令及参数

  1. Circle(A, 4) → c
  2. Point(c) → B
  3. Line(A, B) → a_7
  4. OrthogonalLine(A, a_7) → b
  5. Intersect(c, a_7) → C, D
  6. Intersect(c, b) → E, F
  7. Segment(B, F) → d
  8. Midpoint(d) → G
  9. OrthogonalLine(G, d) → e
  10. Intersect(c, e) → H, I
  11. CircleSector(A, B, H) → f
  12. Circle(J, 4) → g
  13. Point(g) → K
  14. Segment(J, K) → h
  15. OrthogonalLine(J, h) → i
  16. Intersect(g, i) → L, M
  17. Segment(K, M) → j
  18. Midpoint(j) → N
  19. OrthogonalLine(N, j) → k
  20. Intersect(g, k) → O, P
  21. CircleSector(J, K, O) → p
  22. Circle(A_1, 4) → c_1
  23. Point(c_1) → B_1
  24. Line(A_1, B_1) → a_1
  25. OrthogonalLine(A_1, a_1) → b_1
  26. Intersect(c_1, a_1) → C_1, D_1
  27. Intersect(c_1, b_1) → E_1, F_1
  28. Segment(B_1, F_1) → d_1
  29. Midpoint(d_1) → G_1
  30. OrthogonalLine(G_1, d_1) → e_1
  31. Intersect(c_1, e_1) → H_1, I_1
  32. CircleSector(A_1, B_1, H_1) → f_1
  33. Circle(A_2, 4) → c_2
  34. Point(c_2) → B_2
  35. Line(A_2, B_2) → a_2
  36. OrthogonalLine(A_2, a_2) → b_2
  37. Intersect(c_2, a_2) → C_2, D_2
  38. Intersect(c_2, b_2) → E_2, F_2
  39. Segment(B_2, F_2) → d_2
  40. Midpoint(d_2) → G_2
  41. OrthogonalLine(G_2, d_2) → e_2
  42. Intersect(c_2, e_2) → H_2, I_2
  43. CircleSector(A_2, B_2, H_2) → f_2
  44. Circle(A_3, 4) → c_3
  45. Point(c_3) → B_3
  46. Line(A_3, B_3) → a_3
  47. OrthogonalLine(A_3, a_3) → b_3
  48. Intersect(c_3, a_3) → C_3, D_3
  49. Intersect(c_3, b_3) → E_3, F_3
  50. Segment(B_3, F_3) → d_3
  51. Midpoint(d_3) → G_3
  52. OrthogonalLine(G_3, d_3) → e_3
  53. Intersect(c_3, e_3) → H_3, I_3
  54. CircleSector(A_3, B_3, H_3) → f_3
  55. Circle(A_4, 4) → c_4
  56. Point(c_4) → B_4
  57. Line(A_4, B_4) → a_4
  58. OrthogonalLine(A_4, a_4) → b_4
  59. Intersect(c_4, a_4) → C_4, D_4
  60. Intersect(c_4, b_4) → E_4, F_4
  61. Segment(B_4, F_4) → d_4
  62. Midpoint(d_4) → G_4
  63. OrthogonalLine(G_4, d_4) → e_4
  64. Intersect(c_4, e_4) → H_4, I_4
  65. CircleSector(A_4, B_4, H_4) → f_4
  66. Circle(A_5, 4) → c_5
  67. Point(c_5) → B_5
  68. Line(A_5, B_5) → a_5
  69. OrthogonalLine(A_5, a_5) → b_5
  70. Intersect(c_5, a_5) → C_5, D_5
  71. Intersect(c_5, b_5) → E_5, F_5
  72. Segment(B_5, F_5) → d_5
  73. Midpoint(d_5) → G_5
  74. OrthogonalLine(G_5, d_5) → e_5
  75. Intersect(c_5, e_5) → H_5, I_5
  76. CircleSector(A_5, B_5, H_5) → f_5
  77. Circle(A_6, 4) → c_6
  78. Point(c_6) → B_6
  79. Line(A_6, B_6) → a_6
  80. OrthogonalLine(A_6, a_6) → b_6
  81. Intersect(c_6, a_6) → C_6, D_6
  82. Intersect(c_6, b_6) → E_6, F_6
  83. Segment(B_6, F_6) → d_6
  84. Midpoint(d_6) → G_6
  85. OrthogonalLine(G_6, d_6) → e_6
  86. Intersect(c_6, e_6) → H_6, I_6
  87. CircleSector(A_6, B_6, H_6) → f_6
  88. Circle(Q, 4) → q
  89. Point(q) → R
  90. Line(Q, R) → l
  91. OrthogonalLine(Q, l) → m
  92. Intersect(q, m) → S, T
  93. Intersect(q, l) → U, V
  94. Segment(T, R) → n
  95. Segment(S, R) → r
  96. Midpoint(n) → W
  97. Midpoint(r) → Z
  98. OrthogonalLine(W, n) → s
  99. OrthogonalLine(Z, r) → t
  100. Intersect(q, t) → J_1, K_1
  101. Intersect(q, s) → L_1, M_1
  102. CircleSector(Q, M_1, T) → g_1
  103. CircleSector(Q, T, K_1) → h_1
  104. CircleSector(Q, K_1, V) → k_1
  105. CircleSector(Q, V, L_1) → p_1
  106. CircleSector(Q, L_1, S) → q_1
  107. CircleSector(Q, S, J_1) → r_1
  108. CircleSector(Q, J_1, R) → s_1
  109. CircleSector(Q, R, M_1) → t_1

AI 绘图提示语参考

画一个圆形,在其上找到圆心并画出一条直径,然后画出垂直于直径的两条线,这两条线与圆相交得到四个点。连接圆心与其中一个交点,并画出垂直于这条线段的中垂线,它与圆相交得到另外两个点。以圆心和其中一个交点为圆心,分别画出两个扇形。重复以上步骤画出三个相同的图形,每个图形都包含一个圆形、两条垂直线、一条直径、一条中垂线、两个扇形和一个线段。
以上提示语为根据原始绘图命令整理而来,仅供参考。