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3.4.3 Museo de Onda: Tile 3 - Parallelogram and Cylinder via Vectors

3.4.3 Museo de Onda: Tile 3 - Parallelogram and Cylinder via Vectors
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2023-03-22 21:36
VectorSolid GeometryTransformationGeometric Construction
In collections geometriadinamica.es
This GeoGebra example demonstrates the construction of a composite figure involving a parallelogram, a cylinder, and vector addition/subtraction, set in the context of the Museo de Onda tile pattern. The core mathematical concepts include properties of parallelograms, vector addition and subtraction, translation transformations, and the geometric representation of a cylinder. The construction uses commands such as Line, Point, OrthogonalLine, Intersect, Midpoint, Mirror, Min, Vector, and Translate, with numerous objects (A, B, b, G, e, J, h, f, H, g, E, I, B_1, a, vp, vg, dif, c, vs, vr, vt, v, vd, gr, D, F, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z) to build complex relationships via vector differences (dif) and multiple translation vectors (vs, vr, vt, etc.). It is suitable for high school or early college students learning coordinate geometry, vector operations, and geometric construction, and can be used in lessons integrating mathematics with cultural heritage.

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. Midpoint(D, U) → E_1
  31. Midpoint(U, J) → F_1
  32. Midpoint(T, Q) → G_1
  33. Midpoint(S, G) → H_1
  34. Midpoint(S, K) → I_1
  35. Midpoint(M, T) → J_1
  36. Midpoint(T, N) → K_1
  37. Midpoint(N, O) → L_1
  38. Midpoint(F, C_1) → M_1
  39. Midpoint(C_1, L) → N_1
  40. Midpoint(L, D_1) → O_1
  41. Midpoint(D_1, K) → P_1
  42. Midpoint(H, D_1) → Q_1
  43. Midpoint(D_1, I) → R_1
  44. Midpoint(I, C_1) → S_1
  45. Midpoint(C_1, E) → T_1
  46. Mirror(F_1, h) → U_1
  47. Mirror(L_1, h) → V_1
  48. Mirror(M_1, h) → W_1
  49. Mirror(T_1, h) → Z_1
  50. Mirror(B_1, h) → A_2
  51. Line(Q, A_2) → d
  52. Line(F, d) → i
  53. Line(C_1, d) → k
  54. Line(S_1, k) → l
  55. Line(R_1, L_1) → j
  56. Line(D_1, j) → m
  57. Line(M, j) → n
  58. Line(I, j) → p
  59. Line(S, A_1) → t
  60. Line(I, T) → a_1
  61. Line(U, B_1) → b_1
  62. Line(E_1, N_1) → c_1
  63. Line(F_1, M_1) → d_1
  64. Line(G_1, R_1) → e_1
  65. Line(W_1, P_1) → g_1
  66. Line(Q_1, Z_1) → h_1
  67. Point(a_1) → F_2
  68. Mirror(F_2, m) → L_2
  69. Mirror(F_2, m) → M_2
  70. Point(b) → A1
  71. Min(90, ((a - 1) * 90)) → r1
  72. Line(G_1, O_1) → l_1
  73. OrthogonalLine(G_1, l_1) → m_1
  74. OrthogonalLine(J_1, l_1) → q_1
  75. OrthogonalLine(O_1, l_1) → r_1
  76. OrthogonalLine(R_1, l_1) → s_1
  77. OrthogonalLine(E_1, m_1) → t_1
  78. OrthogonalLine(F_1, m_1) → a_2
  79. Point(a_1) → C
  80. OrthogonalLine(F_2, d) → i_1
  81. OrthogonalLine(C, d) → j_1
  82. Min(180, ((a - 1) * 180)) → r2
  83. Min(270, ((a - 1) * 270)) → r3
  84. Min(180, ((a - 5.5) * 180)) → r4
  85. Vector(R, S) → z_1
  86. Vector(R, G) → u_2
  87. Vector(L_1, F_1) → u
  88. Vector(L_1, V_1) → w
  89. Translate(pic1, u) → pic1'
  90. Translate(pic1', u) → pic1''
  91. Translate(pic1'', u) → pic1'''
  92. Translate(pic1''', u) → pic2
  93. Translate(pic2, w) → pic2'
  94. Translate(pic1''', w) → pic3
  95. Translate(pic1'', w) → pic1'''_1
  96. Translate(pic1', w) → pic1''_1
  97. Translate(pic1, w) → pic1'_1
  98. Translate(pic1'_1, w) → pic4
  99. Translate(pic1''_1, w) → pic5
  100. Translate(pic2', w) → pic2''
  101. Translate(pic3, w) → pic3'
  102. Translate(pic4, w) → pic4'
  103. Translate(pic4', w) → pic4''
  104. Translate(pic4', u) → pic4''_1
  105. Translate(pic5, u) → pic5'
  106. Translate(pic4'', u) → pic4'''
  107. Translate(pic2'', w) → pic2'''
  108. Translate(pic2''', w) → pic6
  109. Translate(pic3', w) → pic3''
  110. Translate(pic3'', w) → pic3'''
  111. Translate(pic5', w) → pic5''
  112. Translate(pic5'', w) → pic5'''
  113. Midpoint(H_1, G_1) → B_2
  114. Midpoint(G_1, E_1) → C_2
  115. Midpoint(E_1, F_1) → D_2
  116. Midpoint(F_1, U_1) → E_2
  117. Midpoint(V_1, L_1) → G_2
  118. Midpoint(L_1, K_1) → H_2
  119. Midpoint(K_1, J_1) → I_2
  120. Midpoint(J_1, I_1) → J_2
  121. Midpoint(S, T) → K_2
  122. Midpoint(T, U) → N_2
  123. Midpoint(U, O) → O_2
  124. Midpoint(F, N) → P_2
  125. Midpoint(N, L) → Q_2
  126. Midpoint(L, M) → R_2
  127. Midpoint(P_1, O_1) → S_2
  128. Midpoint(O_1, N_1) → T_2
  129. Midpoint(N_1, M_1) → U_2
  130. Midpoint(M_1, W_1) → V_2
  131. Midpoint(V, C_1) → W_2
  132. Midpoint(C_1, Z) → Z_2
  133. Midpoint(Z, D_1) → A_3
  134. Midpoint(Q_1, R_1) → B_3
  135. Midpoint(R_1, S_1) → C_3
  136. Midpoint(S_1, T_1) → E_3
  137. Midpoint(T_1, Z_1) → F_3
  138. Mirror(A_3, D_1) → D_3

AI Drawing Prompt Reference

Draw a composite figure consisting of a parallelogram and a cylinder. The figure includes multiple points, line segments, and intersection points. The construction order is: first draw the parallelogram, then add the cylinder, then determine key positions using perpendicular lines and intersections, and finally connect these points with midpoints to form a grid. The figure should reflect the geometric representation of vector addition and subtraction, as well as translation transformations.
The prompt above was compiled from the original drawing commands and is for reference only.