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黄金矩形与比例

黄金矩形与比例
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2017-01-08 09:15
函数几何作图
这个范例演示了黄金矩形及其比例。黄金矩形是一种特殊的矩形，其长宽比为黄金比例。本例涉及的核心数学概念包括比例、黄金比例和几何作图。通过使用GeoGebra命令如Segment、OrthogonalLine、Circle、Intersect等，可以构造黄金矩形。适合初中及以上学生学习几何和比例相关知识。

GeoGebra 命令及参数

  1. Segment(B, A) → f
  2. OrthogonalLine(A, f) → g
  3. Circle(A, a) → c
  4. Intersect(c, g, 2) → D
  5. OrthogonalLine(D, g) → h
  6. OrthogonalLine(B, h) → i
  7. Intersect(h, i) → C
  8. Segment(C, B) → j
  9. Segment(A, D) → k
  10. Segment(D, C) → l
  11. Rotate(C, ((-π)) / 2, B) → F
  12. OrthogonalLine(F, f) → m
  13. Intersect(m, l) → E
  14. Segment(E, F) → n
  15. Segment(C, E) → p
  16. Segment(E, F) → q
  17. Segment(F, B) → r
  18. Segment(B, C) → s
  19. Segment(D, A) → t
  20. Vector(C, B) → u
  21. Vector(B, A) → w
  22. Segment(K, J) → f_1
  23. Translate(H, w) → H'
  24. Translate(K, w) → K'
  25. Translate(J, w) → J'
  26. Segment(K', J') → g_1
  27. Segment(H, H') → h_1
  28. Segment(M, L) → i_1
  29. Translate(I, Vector[(-u)]) → I'
  30. Translate(M, Vector[(-u)]) → M'
  31. Translate(L, Vector[(-u)]) → L'
  32. Segment(M', L') → j_1
  33. Segment(I, I') → k_1
  34. Midpoint(h_1) → N
  35. Midpoint(k_1) → O
  36. Angle(B, C, D) → α
  37. Angle(C, D, A) → β
  38. Angle(D, A, B) → γ
  39. Angle(A, B, C) → δ
  40. Segment(D, E) → l_1
  41. Midpoint(l_1) → P
  42. Midpoint(p) → Q
  43. Angle(F, E, D) → ε
  44. Angle(A, F, E) → ζ
  45. Polygon(F, B, C, E) → poly1, f_2, b_1, c_1, e_1
  46. Polygon(A, F, E, D) → poly2, a_1, f_3, e_2, d_1
  47. Segment(R, S) → m_1
  48. Segment(T, U) → n_1
  49. Polygon(A, D, C, B) → poly3, a_2, d, c_2, b_2