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橡皮筋拉伸器 - 放大 by Laura Morey

橡皮筋拉伸器 - 放大 by Laura Morey
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2016-12-22 00:42
变换几何作图
这个范例演示了橡皮筋拉伸器如何放大图形。核心数学概念包括放大变换。通过使用GeoGebra命令如Segment, Circle, Intersect, Midpoint等，可以构造出放大效果。适合初中及以上学生学习放大变换。

GeoGebra 命令及参数

  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