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给定周长和侧边与对角线夹角的矩形

给定周长和侧边与对角线夹角的矩形
几何画板及绘图内容加载中，请稍等……
2017-07-02 04:20
多边形角最值优化几何作图
①本范例演示了如何绘制一个给定周长和侧边与对角线夹角的矩形；②涉及的核心数学概念包括矩形的几何性质、线性规划、角度计算；③作图要点——从下方『构造摘要』提炼用到了Segment, Angle, Ray, Point, Rotate, Circle, Intersect, OrthogonalLine, Polygon, Line等GeoGebra命令/对象；④适合高中数学教学，用于理解几何作图与优化问题。

GeoGebra 命令及参数

  1. Segment(F, G) → T
  2. Segment(N, O) → g
  3. Segment(N, P) → g_1
  4. Angle(P, N, O) → α
  5. Ray(A, B) → i
  6. Point(i) → A_1
  7. Rotate(A_1, α, A) → B'
  8. Angle(B, A, B') → γ
  9. Ray(A, B') → h
  10. Circle(B', A) → c
  11. Intersect(c, h, 2) → D
  12. OrthogonalLine(D, i) → j
  13. Intersect(j, i) → E
  14. Segment(D, E) → n
  15. Segment(A, E) → k
  16. Segment(A, D) → p
  17. Polygon(D, A, E) → poly1, e_1, d_1, a
  18. Line(E, B') → h_1
  19. Intersect(c, h_1, 2) → C
  20. Polygon(D, C, A, E) → poly3, d_2, c_1, a_2, e_2
  21. Angle(D, E, A) → β
  22. Circle(D, E) → d
  23. Intersect(d, h, 2) → H
  24. Segment(D, H) → l
  25. Circle(H, k) → e
  26. Intersect(e, h, 2) → I
  27. Segment(H, I) → m
  28. Circle(A, T) → r
  29. Intersect(r, p, 1) → Z
  30. Intersect(h, p) → Q
  31. Intersect(h, p) → R
  32. Segment(I, E) → i_1
  33. Intersect(h, p) → S
  34. Intersect(h, p) → U
  35. Intersect(h, p) → V
  36. Intersect(h, p) → W
  37. Intersect(r, h) → J,
  38. Segment(J, A) → f
  39. Segment(I, E) → q
  40. Line(J, q) → s
  41. Intersect(s, i) → K
  42. OrthogonalLine(K, k) → t
  43. Intersect(t, h) → L
  44. Line(L, k) → b
  45. OrthogonalLine(A, b) → f_1
  46. Intersect(f_1, b) → M
  47. Polygon(L, M, A, K) → poly2, l_1, m_1, a_1, k_1