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Tangram v2

Tangram v2
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2018-11-18 09:30
TrianglePolygonTransformation
In collections Virtual Manipulatives
This example demonstrates the geometric construction of a tangram. It involves key mathematical concepts such as triangles, polygons, and geometric transformations. Using GeoGebra commands like Circle, OrthogonalLine, Intersect, and Rotate, it dynamically shows how the various pieces of a tangram can be combined through rotations, translations, and circle constructions to form different shapes. Suitable for middle school and above students to learn geometric constructions and transformations.

GeoGebra Commands & Parameters

  1. Circle(A, (1 / 4 * Size)) → c
  2. OrthogonalLine(A, xAxis) → f
  3. Intersect(c, f, 2) → B
  4. Rotate(B, BigT1Rotate°, A) → B'
  5. Line(B', A) → g
  6. OrthogonalLine(A, g) → h
  7. Intersect(c, h, 2) → C
  8. Vector(A, B') → u
  9. Vector(A, C) → v
  10. Translate(C, u) → C'
  11. Translate(C', u) → C''
  12. Translate(C, Vector[(-2 * u)]) → C'_1
  13. Intersect(c, h, 1) → D
  14. Polygon(D, C'_1, C'') → t1, c'', d, c'_1
  15. Circle(E, (1 / 4 * Size)) → e
  16. OrthogonalLine(E, xAxis) → i
  17. Intersect(e, i, 2) → F
  18. Rotate(F, BigT2Rotate°, E) → F'
  19. Vector(E, F') → w
  20. OrthogonalLine(E, w) → j
  21. Intersect(e, j, 1) → G
  22. Intersect(e, j, 2) → H
  23. Vector(E, G) → a
  24. Translate(G, Vector[(2 * w)]) → G'
  25. Translate(G, Vector[(2 * (-w))]) → G'_1
  26. Polygon(H, G'_1, G') → t2, g', h_1, g'_1
  27. Circle(I, (1 / 4 * Size)) → k
  28. OrthogonalLine(I, xAxis) → l
  29. Intersect(k, l, 2) → J
  30. Rotate(J, SquareRotate°, I) → J'
  31. Vector(I, J') → b
  32. OrthogonalLine(I, b) → m
  33. Intersect(k, m, 1) → K
  34. Intersect(k, m, 2) → L
  35. OrthogonalLine(I, m) → n
  36. Intersect(k, n, 2) → M
  37. Polygon(J', L, M, K) → q1, j', l_1, m_1, k_1
  38. Circle(N, (1 / 8 * Size)) → p
  39. OrthogonalLine(N, xAxis) → q
  40. Intersect(p, q, 2) → O
  41. Rotate(O, SmallT1Rotate°, N) → O'
  42. Vector(N, O') → r
  43. OrthogonalLine(N, r) → s
  44. Intersect(p, s, 1) → P
  45. Vector(N, P) → t
  46. Line(N, O') → f_1
  47. Intersect(p, f_1, 1) → Q
  48. Translate(Q, Vector[(2 * t)]) → Q'
  49. Translate(Q, Vector[(2 * (-t))]) → Q'_1
  50. Polygon(O', Q'_1, Q') → t3, q', o', q'_1
  51. Circle(R, (1 / 8 * Size)) → c_1
  52. OrthogonalLine(R, xAxis) → g_1
  53. Intersect(c_1, g_1, 2) → S
  54. Rotate(S, SmallT2Rotate°, R) → S'
  55. Line(S', R) → i_1
  56. OrthogonalLine(R, i_1) → j_1
  57. Intersect(c_1, i_1, 2) → T
  58. Intersect(c_1, j_1, 2) → U
  59. Vector(R, S') → u_1
  60. Vector(R, U) → v_1
  61. Translate(T, v_1) → T'
  62. Translate(T', v_1) → T''
  63. Intersect(c_1, j_1, 1) → V
  64. Vector(R, V) → w_1
  65. Translate(T, w_1) → T'_1
  66. Translate(T'_1, w_1) → W
  67. Polygon(S', W, T'') → t4, t'', s', w_2
  68. Circle(Z, (sqrt(2) / 8 * Size)) → d_1
  69. OrthogonalLine(Z, xAxis) → n_1
  70. Intersect(d_1, n_1, 2) → A_1
  71. Rotate(A_1, MediumTRotate°, Z) → B_1
  72. Line(Z, B_1) → p_1
  73. OrthogonalLine(Z, p_1) → q_1
  74. Intersect(d_1, q_1, 2) → D_1
  75. Intersect(d_1, p_1, 1) → E_1
  76. Intersect(d_1, q_1, 1) → F_1
  77. Vector(Z, B_1) → a_1
  78. Vector(Z, F_1) → b_1
  79. Vector(Z, D_1) → e_1
  80. Translate(E_1, b_1) → G_1
  81. Translate(G_1, b_1) → H_1
  82. Translate(E_1, e_1) → I_1
  83. Translate(I_1, e_1) → J_1
  84. Polygon(B_1, J_1, H_1) → t5, r_1, s_1, t_1
  85. Circle(K_1, (1 / 8 * Size)) → c_2
  86. OrthogonalLine(K_1, xAxis) → f_2
  87. Intersect(c_2, f_2, 2) → L_1
  88. Rotate(L_1, ParallelogramRotate°, K_1) → M_1
  89. Line(M_1, K_1) → g_2
  90. OrthogonalLine(K_1, g_2) → h_2
  91. Intersect(c_2, h_2, 1) → O_1
  92. Intersect(c_2, g_2, 2) → P_1
  93. Intersect(c_2, h_2, 2) → Q_1
  94. Vector(K_1, Q_1) → u_2
  95. Vector(K_1, M_1) → v_2
  96. Vector(K_1, O_1) → a_2
  97. Vector(K_1, P_1) → b_2
  98. Translate(P_1, u_2) → R_1
  99. Translate(R_1, u_2) → S_1
  100. Translate(S_1, u_2) → T_1
  101. Translate(P_1, a_2) → U_1
  102. Translate(M_1, a_2) → V_1
  103. Translate(V_1, a_2) → W_1
  104. Translate(W_1, a_2) → Z_1
  105. Translate(M_1, u_2) → A_2
  106. Polygon(Z_1, U_1, T_1, A_2) → q2, z_1, i_2, j_2, k_2