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4除以5/4的GeoGebra演示

4除以5/4的GeoGebra演示
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2015-01-29 01:53
向量解析几何几何作图
①这个范例演示了4除以5/4的几何计算过程，源自1896年印第安纳州重新定义π的尝试；②涉及的核心数学概念包括分数运算、除法、向量、几何图形构造；③作图要点——从下方『构造摘要』提炼用到了Segment（线段）、Point（点）、Polygon（多边形）、Vector（向量）、Translate（平移）等GeoGebra命令/对象；④适合高中数学教学，用于理解分数除法与几何表示的关联。

GeoGebra 命令及参数

  1. Segment(B1, B17) → a
  2. Segment(B1, C1) → b
  3. Segment(B2, C2) → c
  4. Segment(B3, C3) → d
  5. Segment(B4, C4) → e
  6. Segment(B5, C5) → f
  7. Segment(B6, C6) → g
  8. Segment(B7, C7) → h
  9. Segment(B8, C8) → i
  10. Segment(B9, C9) → j
  11. Segment(B10, C10) → k
  12. Segment(B11, C11) → l
  13. Segment(B12, C12) → m
  14. Segment(B13, C13) → n
  15. Segment(B14, C14) → p
  16. Segment(B15, C15) → q
  17. Segment(B16, C16) → r
  18. Segment(B17, C17) → s
  19. Segment(C1, C17) → t
  20. Point(yAxis) → A
  21. Point(yAxis) → B
  22. Segment(A, L) → a_1
  23. Segment(L, G) → b_1
  24. Segment(B, G) → c_1
  25. Segment(A, B) → d_1
  26. Segment(K, F) → e_1
  27. Segment(J, E) → f_1
  28. Segment(I, D) → g_1
  29. Segment(H, C) → h_1
  30. Polygon(L, A, B, G) → poly1, l_1, a_2, b_2, g_2
  31. Vector((1, -8), (1, -8 + o)) → u
  32. Translate(L, u) → L'
  33. Translate(A, u) → A'
  34. Translate(B, u) → B'
  35. Translate(G, u) → G'
  36. Polygon(L', A', B', G') → poly1', l', a', b', g'
  37. Vector(A, (v * x(B6), -1 + v * 2)) → w
  38. Translate(L, w) → L'_1
  39. Translate(A, w) → A'_1
  40. Translate(B, w) → B'_1
  41. Translate(G, w) → G'_1
  42. Polygon(L'_1, A'_1, B'_1, G'_1) → poly1'_1, l'_1, a'_1, b'_1, g'_1
  43. Vector(A, (z * x(B11), -1 + z * 2)) → u_1
  44. Translate(L, u_1) → L'_2
  45. Translate(A, u_1) → A'_2
  46. Translate(B, u_1) → B'_2
  47. Translate(G, u_1) → G'_2
  48. Polygon(L'_2, A'_2, B'_2, G'_2) → poly1'_2, l'_2, a'_2, b'_2, g'_2
  49. Segment(B5, C5) → i_1
  50. Segment(B9, C9) → j_1
  51. Segment(B13, C13) → k_1
  52. Segment(B16, C16) → m_1
  53. Segment(K, F) → n_1