Golden Rectangle and Ratio

Golden Rectangle and Ratio
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2017-01-08 09:15
This example demonstrates the golden rectangle and its ratio. A golden rectangle is a special rectangle with a length-to-width ratio of the golden ratio. The core mathematical concepts involved include ratio, the golden ratio, and geometric construction. Using GeoGebra commands such as Segment, OrthogonalLine, Circle, and Intersect, the golden rectangle can be constructed. Suitable for middle school and above students to learn about geometry and ratio.

GeoGebra Commands & Parameters

  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