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算术分形陀螺

算术分形陀螺
几何画板及绘图内容加载中，请稍等……
2017-06-15 03:16
函数微积分不等式几何作图
所属专题 Algebra 1
①本范例演示一个基于算术运算的分形陀螺图形，通过动态交互展示其构造过程；②涉及核心数学概念包括指数运算、对称性、分段函数、上下和（黎曼和）、不等式等；③作图要点提炼自构造摘要，使用了圆、交点、中点、圆弧、文本框等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解复杂几何图形的生成原理及微积分概念的可视化。

GeoGebra 命令及参数

  1. Circle((0, 0), 1) → u
  2. Circle(P, 1.73) → c
  3. Intersect(c, u) → A, B, ,
  4. Midpoint(A, B) → D
  5. Midpoint(A, P) → E
  6. Midpoint(B, P) → F
  7. Midpoint(D, C) → G
  8. Midpoint(E, C) → H
  9. Midpoint(C, F) → I
  10. Circle(B, 0.25) → d_2
  11. Circle(P, 0.25) → e
  12. Circle(A, 0.25) → g_2
  13. Intersect(d_2, u) → J, K, ,
  14. Intersect(u, g_2) → L, M, ,
  15. Intersect(e, u) → O, Q, ,
  16. CircumcircleArc(M, G, K) → h_2
  17. CircumcircleArc(J, I, Q) → k
  18. CircumcircleArc(O, H, L) → p
  19. Circle(P, 0.4) → q
  20. Circle(B, 0.4) → t
  21. Circle(A, 0.4) → c_1
  22. Circle(N, 1.73) → d_1
  23. Intersect(d_1, u) → R, S, ,
  24. Circle(N, 0.25) → e_1
  25. Circle(S, 0.25) → f_1
  26. Circle(R, 0.25) → g_1
  27. Intersect(u, f_1) → T, U, ,
  28. Intersect(g_1, u) → V, W, ,
  29. Intersect(e_1, u) → Z, A_1, ,
  30. Midpoint(S, R) → B_1
  31. Midpoint(R, N) → C_1
  32. Midpoint(N, S) → D_1
  33. Midpoint(B_1, C) → E_1
  34. Midpoint(C_1, C) → F_1
  35. Midpoint(D_1, C) → G_1
  36. CircumcircleArc(T, E_1, V) → h_1
  37. CircumcircleArc(W, F_1, Z) → k_1
  38. CircumcircleArc(A_1, G_1, U) → p_1
  39. Circle(S, 0.4) → s_1
  40. Circle(R, 0.4) → r_1
  41. Circle(N, 0.4) → q_1
  42. Textfield(g) → InputBox1
  43. Textfield(g) → InputBox2
  44. Textfield(g) → InputBox3
  45. Textfield(g) → InputBox4
  46. Textfield(g) → InputBox5