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印度方法求根号二

印度方法求根号二
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2017-02-02 02:38
测试改名0向量几何作图
这个范例展示了印度古代求根号二的方法。它涉及几何作图和等腰三角形的性质。通过构造等腰三角形和利用几何变换，可以直观地理解根号二的近似值。主要使用了Polygon, Dilate, OrthogonalLine, Intersect, Segment, Midpoint, Circle, Ray, Vector, Translate等命令。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Dilate(C, 2 / 3, D) → C'
  3. Dilate(C, 2 / 3, B) → C'_1
  4. OrthogonalLine(C', h) → j
  5. OrthogonalLine(C'_1, g) → k
  6. Intersect(j, k) → E
  7. Intersect(k, i) → F
  8. Segment(A, B) → l
  9. Intersect(l, j) → G
  10. Segment(C', E) → m
  11. Segment(E, C'_1) → n
  12. Segment(A, F) → p
  13. Segment(F, D) → q
  14. Segment(D, C') → r
  15. Segment(C'_1, B) → s
  16. Midpoint(r) → K
  17. OrthogonalLine(K, r) → g_1
  18. Intersect(g_1, l) → L
  19. Dilate(B, 1 / 18, A) → B'
  20. Dilate(D, 1 / 18, A) → D'
  21. Circle(F, D) → c
  22. Intersect(c, p, 1) → H
  23. OrthogonalLine(H, p) → t
  24. OrthogonalLine(F, q) → a
  25. OrthogonalLine(B', l) → b
  26. OrthogonalLine(D', p) → d
  27. OrthogonalLine(G, l) → e
  28. Intersect(d, e) → I
  29. Intersect(g_1, d) → J
  30. Intersect(b, d) → M
  31. Intersect(t, b) → N
  32. Intersect(a, b) → O
  33. Intersect(r, b) → P
  34. OrthogonalLine(D', p) → f_1
  35. Intersect(f_1, s) → Q
  36. Segment(D', Q) → h_1
  37. Segment(F, O) → i_1
  38. Segment(H, N) → j_1
  39. Segment(M, Q) → k_1
  40. Segment(P, M) → l_1
  41. Segment(B', M) → m_1
  42. Segment(L, G) → n_1
  43. Segment(I, G) → p_1
  44. Segment(J, L) → q_1
  45. Ray(B, C'_1) → r_1
  46. Ray(D, C') → s_1
  47. Intersect(r_1, s_1) → R
  48. Vector(J, L) → u
  49. Vector(N, H) → v
  50. Translate(R, u) → R'
  51. Translate(R, v) → R'_1
  52. Translate(R'_1, Vector[(0, 0)]) → S
  53. Translate(R'_1, Vector[(0, 0)]) → T
  54. Translate(R'_1, Vector[(0, 0)]) → U
  55. OrthogonalLine(R'_1, r) → t_1
  56. OrthogonalLine(R', m) → a_1
  57. Intersect(t_1, a_1) → V
  58. Segment(C', R'_1) → b_1
  59. Segment(C'_1, R') → c_1
  60. Segment(R'_1, V) → d_1
  61. Segment(V, R') → e_1
  62. Dilate(R', 1 / 6, C'_1) → R''
  63. OrthogonalLine(R'', c_1) → f_2
  64. Intersect(f_2, m) → W
  65. Intersect(f_2, c_1) → Z
  66. Vector(C'_1, R'') → w
  67. Polygon(E, W, R'', C'_1) → poly2, e_2, w_1, r'', c'_1
  68. Translate(E, w) → E'
  69. Translate(W, w) → W'
  70. Translate(R'', w) → R'''
  71. Translate(C'_1, w) → A_1
  72. Polygon(E', W', R''', A_1) → poly2', e', w', r''', a_2
  73. Translate(E', w) → E''
  74. Translate(W', w) → W''
  75. Translate(R''', w) → B_1
  76. Translate(A_1, w) → C_1
  77. Polygon(E'', W'', B_1, C_1) → poly2'', e'', w'', b_2, c_2
  78. Translate(E'', w) → E'''
  79. Translate(W'', w) → W'''
  80. Translate(B_1, w) → D_1
  81. Translate(C_1, w) → E_1
  82. Polygon(E''', W''', D_1, E_1) → poly2''', e''', w''', d_2, e_3
  83. Translate(E''', w) → F_1
  84. Translate(W''', w) → G_1
  85. Translate(D_1, w) → H_1
  86. Translate(E_1, w) → I_1
  87. Polygon(F_1, G_1, H_1, I_1) → poly3, f_3, g_2, h_2, i_2
  88. Translate(F_1, u_1) → J_1
  89. Translate(G_1, u_1) → K_1
  90. Translate(H_1, u_1) → L_1
  91. Translate(I_1, u_1) → M_1
  92. Polygon(J_1, K_1, L_1, M_1) → poly3', j_2, k_2, l_2, m_2
  93. Translate(J_1, w) → N_1
  94. Translate(K_1, w) → O_1
  95. Translate(L_1, w) → P_1
  96. Translate(M_1, w) → Q_1
  97. Polygon(N_1, O_1, P_1, Q_1) → poly3'', n_2, o_1, p_2, q_2
  98. Intersect(b_1, d_1) → R_1
  99. Polygon(O_1, V, R_1, C') → poly4, o_2, v_1, r_2, c'
  100. Polygon(D, P, O, F) → poly5, d_3, p_3, o, f_4
  101. Polygon(F, O, N, H) → poly6, f_5, o_3, n_3, h_3
  102. Polygon(H, N, B', A) → poly7, h_4, n_4, b', a_3
  103. Polygon(M, J, L, B') → poly8, m_3, j_3, l_3, b'_1
  104. Polygon(J, I, G, L) → poly9, j_4, i_3, g_3, l_4
  105. Polygon(I, Q, B, G) → poly10, i_4, q_3, b_3, g_4
  106. Segment(O, E) → t_2
  107. Segment(I, E) → k_3
  108. Polygon(M, O, E, I) → poly11, m_4, o_4, e_4, i_5
  109. Polygon(I, E, C'_1, Q) → poly12, i_6, e_5, c'_2, q_4
  110. Polygon(O, P, C', E) → poly13, o_5, p_4, c'_3, e_6