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Rectangle with given perimeter sum and angle

Rectangle with given perimeter sum and angle
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2017-07-02 04:20
PolygonAngleOptimizationGeometric Construction
This example demonstrates how to construct a rectangle with a specified sum of its sides and the angle between a side and its diagonal. It involves core mathematical concepts such as rectangle geometry, linear programming, and angle calculations. The construction uses GeoGebra commands like Segment, Angle, Ray, Point, Rotate, Circle, Intersect, OrthogonalLine, Polygon, and Line. Suitable for high school mathematics education, helping students understand geometric constructions and optimization problems.

GeoGebra Commands & Parameters

  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