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Rubber Band Stretcher - Dilations by Laura Morey

Rubber Band Stretcher - Dilations by Laura Morey
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2016-12-22 00:42
TransformationGeometric Construction
This example demonstrates how a rubber band stretcher enlarges shapes. The key mathematical concept is dilation. Using GeoGebra commands such as Segment, Circle, Intersect, and Midpoint, the enlargement effect is constructed. Suitable for middle school and above students to learn about dilation.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Circle(A, a / 2) → c
  3. Intersect(c, a, 1) → C
  4. Midpoint(A, C) → D
  5. Midpoint(C, B) → E
  6. Point(a) → F
  7. Circle(C, F) → d
  8. Intersect(d, a, 2) → G
  9. Circle(D, F) → e
  10. Circle(E, G) → f
  11. Intersect(e, a, 2) → H
  12. Circle(A, H) → g
  13. Intersect(f, a, 2) → I
  14. Circle(B, I) → h
  15. Ellipse(H, F, C) → k
  16. Ellipse(G, I, B) → p
  17. Point(a) → J
  18. Circle(D, J) → q
  19. Midpoint(A, D) → K
  20. Midpoint(D, C) → L
  21. Midpoint(C, E) → M
  22. Midpoint(E, B) → N
  23. Circle(K, J) → r
  24. Intersect(r, a, 2) → O
  25. Circle(A, O) → s
  26. Intersect(q, a, 2) → P
  27. Circle(L, P) → t
  28. Intersect(t, a, 2) → Q
  29. Circle(C, Q) → c_1
  30. Intersect(c_1, a, 2) → R
  31. Circle(M, R) → d_1
  32. Intersect(d_1, a, 2) → S
  33. Circle(E, S) → e_1
  34. Intersect(e_1, a, 2) → T
  35. Circle(N, T) → f_1
  36. Intersect(f_1, a, 2) → U
  37. Circle(B, U) → g_1
  38. Ellipse(O, J, D) → h_1
  39. Ellipse(P, Q, C) → k_1
  40. Ellipse(R, S, E) → p_1
  41. Ellipse(T, U, B) → q_1
  42. Circle(A, a / 3) → r_1
  43. Circle(A, (2 * a / 3)) → s_1
  44. Intersect(r_1, a, 1) → V
  45. Intersect(s_1, a, 1) → W
  46. Midpoint(A, V) → Z
  47. Midpoint(V, W) → A_1
  48. Midpoint(W, B) → B_1
  49. Point(a) → C_1
  50. Circle(V, C_1) → t_1
  51. Circle(Z, C_1) → c_2
  52. Intersect(c_2, a, 2) → D_1
  53. Circle(A, D_1) → d_2
  54. Intersect(t_1, a, 2) → E_1
  55. Circle(A_1, E_1) → e_2
  56. Intersect(e_2, a, 2) → F_1
  57. Circle(W, F_1) → f_2
  58. Intersect(f_2, a, 2) → G_1
  59. Circle(B_1, G_1) → g_2
  60. Intersect(g_2, a, 2) → H_1
  61. Circle(B, H_1) → h_2
  62. Ellipse(D_1, C_1, V) → k_2
  63. Ellipse(E_1, F_1, W) → p_2
  64. Ellipse(G_1, H_1, B) → q_2
  65. Circle(A, a / 5) → r_2
  66. Circle(A, (2 * a / 5)) → s_2
  67. Circle(A, (3 * a / 5)) → t_2
  68. Circle(A, (4 * a / 5)) → c_3
  69. Intersect(r_2, a, 1) → I_1
  70. Intersect(s_2, a, 1) → J_1
  71. Intersect(t_2, a, 1) → K_1
  72. Intersect(c_3, a, 1) → L_1
  73. Midpoint(A, I_1) → M_1
  74. Midpoint(J_1, I_1) → N_1
  75. Midpoint(J_1, K_1) → O_1
  76. Midpoint(K_1, L_1) → P_1
  77. Midpoint(L_1, B) → Q_1
  78. Point(a) → R_1
  79. Circle(I_1, R_1) → d_3
  80. Circle(M_1, R_1) → e_3
  81. Intersect(e_3, a, 2) → S_1
  82. Circle(A, S_1) → f_3
  83. Intersect(d_3, a, 2) → T_1
  84. Circle(N_1, T_1) → g_3
  85. Intersect(g_3, a, 2) → U_1
  86. Circle(J_1, U_1) → h_3
  87. Intersect(h_3, a, 2) → V_1
  88. Circle(O_1, V_1) → k_3
  89. Intersect(k_3, a, 2) → W_1
  90. Circle(K_1, W_1) → p_3
  91. Intersect(p_3, a, 2) → Z_1
  92. Circle(P_1, Z_1) → q_3
  93. Intersect(q_3, a, 2) → A_2
  94. Circle(L_1, A_2) → r_3
  95. Intersect(r_3, a, 2) → B_2
  96. Circle(Q_1, B_2) → s_3
  97. Intersect(s_3, a, 2) → C_2
  98. Circle(B, C_2) → t_3
  99. Ellipse(S_1, R_1, I_1) → c_4
  100. Ellipse(T_1, U_1, J_1) → d_4
  101. Ellipse(V_1, W_1, K_1) → e_4
  102. Ellipse(Z_1, A_2, L_1) → f_4
  103. Ellipse(B_2, C_2, B) → g_4