创建数学模型

创建数学模型
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2017-08-09 00:24
①本范例演示如何使用 GeoGebra 创建和操作数学模型,包括多边形、线段、函数图像等;②涉及的核心数学概念有函数、解析几何、优化问题、概率统计等;③作图要点提炼自构造摘要,使用了 Polygon(多边形)、Line(线)、Midpoint(中点)、Segment(线段)、FitPoly(拟合多项式)等命令和对象;④适合高中及以上学生学习和教师教学使用。

GeoGebra 命令及参数

  1. Polygon(A, E, D) → poly1, d_4, a_4, e_{16}
  2. Polygon(C, E, B) → poly2, b_4, c_2, e_1
  3. Polygon(I, E, F) → poly3, f_9, i_9, e_2
  4. Polygon(G, E, H) → poly4, h_4, g_4, e_3
  5. Polygon(A, B, E) → poly5, e_4, a_1, b_1
  6. Polygon(C, F, E) → poly6, e_5, c_1, f_6
  7. Polygon(I, H, E) → poly7, e_6, i_6, h_1
  8. Polygon(G, D, E) → poly8, e_7, g_1, d_1
  9. Polygon(A, D, E) → poly9, e_8, a_2, d_2
  10. Polygon(C, B, E) → poly10, e_9, c_3, b_2
  11. Polygon(I, F, E) → poly11, e_{10}, i_7, f_7
  12. Polygon(G, H, E) → poly12, e_{11}, g_2, h_2
  13. Polygon(A, B, E) → poly13, e_{12}, a_3, b_3
  14. Polygon(F, C, E) → poly14, e_{13}, f_8, c_4
  15. Polygon(H, I, E) → poly15, e_{14}, h_3, i_8
  16. Polygon(D, G, E) → poly16, e_{15}, d_3, g_3
  17. Textfield(a) → InputBox1
  18. Line(L, M) → c_{answer}
  19. Line(J, K) → b_{answer}
  20. Textfield(b) → InputBox2
  21. Textfield(c) → InputBox3
  22. Textfield(d_{a1}) → InputBox4
  23. Textfield(d_{b1}) → InputBox5
  24. Textfield(d_{c1}) → InputBox6
  25. Polygon(W_1, W_2, W_3, W_4) → poly17, w_1, w_2, w_3, w_4
  26. Midpoint(W_1, W_2) → N
  27. Midpoint(W_3, W_2) → O
  28. Midpoint(W_3, W_4) → P
  29. Midpoint(W_1, W_4) → Q
  30. Segment(O, Q) → j
  31. Midpoint(W_1, N) → R
  32. Midpoint(N, W_2) → S
  33. Midpoint(W_3, P) → T
  34. Midpoint(W_4, P) → U
  35. Segment(R, U) → k
  36. Segment(N, P) → l
  37. Segment(S, T) → m
  38. FitPoly(list11, 2) → q
  39. Textfield(e) → InputBox7
  40. Textfield(f) → InputBox8
  41. Textfield(g) → InputBox9
  42. Textfield(h) → InputBox10
  43. Polygon(A_1, C_1, B_1, D_1) → poly18, a_5, c_6, b_5, d_5
  44. Line(A_1, C_1) → i_{line3}
  45. Line(A_1, D_1) → i_{line4}
  46. Line(B_1, C_1) → i_{line1}
  47. Line(B_1, D_1) → i_{line2}
  48. Textfield(i_{answer1}) → InputBox11
  49. Textfield(i_{answer2}) → InputBox12
  50. Textfield(i_{answer3}) → InputBox13
  51. Textfield(i_{answer4}) → InputBox14
  52. Segment(A_1, C_1) → i
  53. Segment(A_1, D_1) → s
  54. Segment(B_1, C_1) → t
  55. Segment(B_1, D_1) → j_1

AI 绘图提示语参考

画多个多边形,它们共享一个公共顶点,并按顺序连接顶点形成封闭形状。再画几条线段连接多边形的顶点,并标出线段的中点。最后,用一条曲线拟合这些中点,展示函数与统计的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。