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3.4.5 Museo de Onda: Azulejo 5 - Geometric Construction and Function Graphing

3.4.5 Museo de Onda: Azulejo 5 - Geometric Construction and Function Graphing
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2023-03-22 21:46
TriangleFunctionGeometric Construction
In collections geometriadinamica.es
This example demonstrates constructing function graphs through geometric methods. Key mathematical concepts include triangles, function graphing, and geometric transformations. Construction involves GeoGebra commands like Line, Point, OrthogonalLine, etc. Suitable for high school students or college freshmen learning geometry and function applications.

GeoGebra Commands & Parameters

  1. Line(A, B) → b
  2. Line(G, b) → e
  3. Point(e) → J
  4. OrthogonalLine(J, e) → h
  5. OrthogonalLine(G, e) → f
  6. Point(f) → H
  7. OrthogonalLine(H, f) → g
  8. Intersect(g, h) → E
  9. Midpoint(E, H) → I
  10. Midpoint(I, E) → B_1
  11. Midpoint(G, J) → D
  12. Midpoint(J, E) → F
  13. Midpoint(H, G) → K
  14. Midpoint(D, I) → L
  15. Midpoint(K, L) → M
  16. Midpoint(L, F) → N
  17. Midpoint(F, J) → O
  18. Midpoint(J, D) → P
  19. Midpoint(G, D) → Q
  20. Midpoint(K, G) → R
  21. Midpoint(Q, M) → S
  22. Midpoint(L, D) → T
  23. Midpoint(P, N) → U
  24. Midpoint(F, E) → V
  25. Midpoint(K, H) → W
  26. Midpoint(W, V) → Z
  27. Midpoint(H, I) → A_1
  28. Midpoint(N, B_1) → C_1
  29. Midpoint(Z, W) → D_1
  30. Mirror(B_1, h) → A_2
  31. Point(b) → A1
  32. Min(90, ((a - 1) * 90)) → r1
  33. Rotate(U, ((-r1))°, T) → U'_3
  34. Rotate(T, ((-r1))°, T) → T'_8
  35. Rotate(T, ((-r1))°, T'_8) → T'_9
  36. Rotate(L, ((-r1))°, T) → L'_2
  37. Midpoint(C_1, E) → K_{20}
  38. Min(180, ((a - 1) * 180)) → r2
  39. Min(270, ((a - 1) * 270)) → r3
  40. Rotate(T, r1°, T) → T'_4
  41. Rotate(T, r2°, T) → T'_5
  42. Rotate(T, r3°, T) → T'_6
  43. Rotate(L, r1°, T) → L'_1
  44. Rotate(L, r2°, T) → L'_3
  45. Rotate(L, r3°, T) → L'_4
  46. Min(180, ((a - 5.5) * 180)) → r4
  47. Vector(N, U) → z
  48. Vector(N, F) → u_1
  49. Translate(pic1, z) → pic1'
  50. Translate(pic1', z) → pic1''
  51. Translate(pic1'', z) → pic1'''
  52. Translate(pic1''', z) → pic2
  53. Translate(pic2, u_1) → pic2'
  54. Translate(pic2', u_1) → pic2''
  55. Translate(pic2'', u_1) → pic2'''
  56. Translate(pic2''', u_1) → pic3
  57. Translate(pic1, u_1) → pic1'_1
  58. Translate(pic1'_1, u_1) → pic4
  59. Translate(pic4, u_1) → pic4'
  60. Translate(pic4', u_1) → pic4''
  61. Translate(pic1', u_1) → pic1''_1
  62. Translate(pic1''_1, z) → pic5
  63. Translate(pic5, z) → pic5'
  64. Translate(pic5', u_1) → pic5''
  65. Translate(pic5'', u_1) → pic5'''
  66. Translate(pic5''', u_1) → pic6
  67. Translate(pic5, u_1) → pic5'_1
  68. Translate(pic1''_1, u_1) → pic7
  69. Translate(pic7, u_1) → pic7'
  70. Translate(pic7', u_1) → pic7''
  71. Translate(pic7', z) → pic7''_1
  72. Translate(pic7'', z) → pic7'''
  73. Line(D_1, J) → d
  74. Line(P, M) → i
  75. Line(S, D) → j
  76. Line(Z, O) → k
  77. Line(C_1, F) → l
  78. OrthogonalLine(D, j) → m
  79. Intersect(i, m) → C
  80. Intersect(k, m) → E_1
  81. Midpoint(D, C) → F_1
  82. Midpoint(C, U) → G_1
  83. Midpoint(U, E_1) → H_1
  84. Midpoint(E_1, F) → I_1
  85. OrthogonalLine(F_1, m) → n
  86. OrthogonalLine(G_1, m) → p
  87. OrthogonalLine(H_1, m) → q
  88. OrthogonalLine(I_1, m) → r

AI Drawing Prompt Reference

Draw a geometric construction based on a base line b and a given point G in the plane. Start by using b to define a point J on the line, then construct two perpendicular lines: one through J perpendicular to b, and another through G perpendicular to the corresponding line e. Intersect these auxiliary perpendicular lines to obtain a key intersection point E. From E and other already constructed points (including H, J, and G), repeatedly take midpoints to build a multi-stage internal subdivision, producing a central point U and additional midpoint-defined points. Then perform chained rotations around the pivot T: rotate U about T by an angle derived from a parameter a, rotate T about itself by the first angle, rotate T again using the rotated position, and rotate another key point L about T by three related angles. The resulting figure should show a symmetric, tiling-like geometric arrangement, with direction cues consistent with vectors from N toward U and F.
The prompt above was compiled from the original drawing commands and is for reference only.