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Triangle to Square Puzzle

Triangle to Square Puzzle
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2018-10-18 07:13
Coordinate GeometryOptimizationGeometric Construction
In collections Elementary Geometry
This example demonstrates the geometric transformation of an arbitrary triangle into a square. It involves core mathematical concepts such as coordinate geometry, geometric construction, transformation, and optimization. Key GeoGebra commands and objects used in the construction include Polygon, Midpoint, Circle, Intersect, OrthogonalLine, Line, Distance, Point, Rotate, Segment, and Angle. Suitable for high school and above mathematics learners to understand geometric transformations and optimization problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Midpoint(A, D) → E
  3. Circle(E, A) → f
  4. Circle(A, E) → g
  5. Intersect(f, g, 1) → G
  6. Circle(G, E) → h
  7. OrthogonalLine(E, d) → i
  8. Intersect(h, i, 2) → J
  9. Polygon(A, G, E) → poly3, e_1, a_2, g_1
  10. Polygon(G, E, J) → poly4, j_1, g_2, e_2
  11. Polygon(B, J, A) → poly2, a_1, b_1, j
  12. Intersect(f, i) → L, M
  13. Line(B, J) → k
  14. Intersect(k, c) → N
  15. Polygon(B, N, C) → poly6, c_1, b_2, n
  16. OrthogonalLine(C, k) → l
  17. OrthogonalLine(M, c) → e
  18. Intersect(e, c) → O
  19. Polygon(O, E, D) → poly5, d_1, o, e_3
  20. Polygon(J, O, E) → poly7, e_4, j_2, o_1
  21. Polygon(J, O, N) → poly8, n_1, j_3, o_2
  22. Polygon(F, H, 3) → poly9, m, p, q, I
  23. Distance(F, H) → distanceFH
  24. Circle(K, r) → s
  25. Point(s) → P
  26. Rotate(P, 119.99999999999999°, K) → P'
  27. Polygon(K, P, P') → poly10, p', k_1, p_1
  28. Circle(Q, r) → t
  29. Point(t) → R
  30. Segment(R, Q) → f_1
  31. OrthogonalLine(Q, f_1) → h_1
  32. Intersect(t, h_1, 2) → S
  33. Polygon(R, Q, S) → poly11, s_1, r_1, q_1
  34. Circle(T, (2 * r)) → t_1
  35. Point(t_1) → U
  36. Rotate(U, 29.999999999999996°, T) → U'
  37. Polygon(T, U, U') → poly12, u', t_2, u
  38. Circle(V, k_1) → c_2
  39. Point(c_2) → W
  40. Segment(V, W) → i_1
  41. Circle(W, q_1) → d_2
  42. Intersect(d_2, i_1, 1) → Z
  43. Rotate(Z, 45°, W) → Z'
  44. Polygon(V, Z', W) → poly13, w, v, z'
  45. Circle(A_1, (2 * r)) → f_2
  46. Point(f_2) → B_1
  47. Segment(A_1, B_1) → l_1
  48. OrthogonalLine(B_1, l_1) → m_1
  49. Rotate(B_1, 14.999999999999998°, A_1) → C_1
  50. Line(A_1, C_1) → h_2
  51. Intersect(m_1, h_2) → D_1
  52. Polygon(A_1, B_1, D_1) → poly14, d_3, a_3, b_3
  53. Circle(E_1, w) → k_2
  54. Point(k_2) → F_1
  55. Angle(J, O, N) → α
  56. Rotate(F_1, α, E_1) → G_1
  57. Angle(N, J, O) → β
  58. Rotate(E_1, (-β), F_1) → H_1
  59. Line(F_1, H_1) → i_2
  60. Line(E_1, G_1) → l_2
  61. Intersect(i_2, l_2) → I_1
  62. Polygon(F_1, I_1, E_1) → poly15, e_5, f_3, i_3

AI Drawing Prompt Reference

Draw an arbitrary triangle and transform it into a square through geometric constructions. Start by finding the midpoint of one side and use it as a center to draw circles. The intersection points of these circles help form new shapes, gradually transforming the triangle into a square. The process involves coordinate geometry, geometric construction, transformation, and optimization.
The prompt above was compiled from the original drawing commands and is for reference only.