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小数、四舍五入与截断

小数、四舍五入与截断
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2020-06-09 04:12
函数数列解析几何
本范例演示小数、四舍五入与截断的概念。通过使用GeoGebra命令，如Random、Sequence、Element等，可以直观地展示这些数学概念。适合初中及以上学生学习。

GeoGebra 命令及参数

  1. Random(1, 9) → h
  2. Random(1, 9) → g
  3. Random(1, 9) → f
  4. Random(1, 9) → e
  5. Random(1, 9) → d
  6. Random(0, 9) → c
  7. Random(0, 9) → b
  8. Circle(A, 0.5) → c_1
  9. Line(A, xAxis) → i
  10. Point(i) → B
  11. Sequence(Dilate[B, n / 18, A], n, 1, 17) → liste3
  12. Element(liste3, 5) → K
  13. Element(liste3, 3) → J
  14. Segment(J, K) → m
  15. Midpoint(P, B) → D_1
  16. OrthogonalLine(D_1, xAxis) → g_1
  17. Midpoint(A, P) → Z
  18. Segment(A, Z) → t
  19. OrthogonalLine(A, t) → n
  20. Intersect(c_1, n) → U, V
  21. OrthogonalLine(V, n) → b_1
  22. Intersect(b_1, g_1) → L_1
  23. Element(liste3, 15) → Q
  24. Segment(A, B) → j
  25. Sequence(Dilate[B, n / 9, A], n, 1, 8) → liste2
  26. Element(liste2, 1) → C
  27. Element(liste2, 2) → D
  28. Element(liste2, 3) → E
  29. Element(liste2, 4) → F
  30. Element(liste2, 5) → G
  31. Element(liste2, 6) → H
  32. Element(liste2, 7) → I
  33. Element(liste3, 7) → L
  34. Element(liste3, 9) → M
  35. Element(liste3, 11) → N
  36. Element(liste3, 13) → O
  37. Segment(J, Q) → k
  38. Element(liste2, 8) → R
  39. Distance(P, Q) → a
  40. If(l ≟ 0, b, If[l ≟ 1, (10 * b) + c, If[l ≟ 2, (100 * b) + (10 * c) + d, If[l ≟ 3, (1000 * b) + (100 * c) + (10 * d) + e, If[l ≟ 4, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f, If[l ≟ 5, (100000 * b) + (10000 * c) + (1000 * d) + (100 * e) + (10 * f) + g, If[l ≟ 6, (1000000 * b) + (100000 * c) + (10000 * d) + (1000 * e) + (100 * f) + (10 * g) + h]]]]]]) → o
  41. OrthogonalLine(P, t) → p
  42. Circle(A, 1) → q
  43. Intersect(q, n) → S, T
  44. OrthogonalLine(U, n) → f_1
  45. Circle(P, 0.5) → d_1
  46. Circle(B, 0.5) → e_1
  47. Intersect(d_1, p) → W, A_1
  48. Intersect(e_1, b_1) → B_1, C_1
  49. Intersect(e_1, f_1) → E_1, F_1
  50. Polygon(V, A_1, W, U) → poly1, v, a_1, w, u
  51. Polygon(A_1, C_1, F_1, W) → poly2, a_2, c_2, f_2, w_1
  52. OrthogonalLine(Z, xAxis) → r
  53. Circle(Z, 2) → s
  54. Intersect(s, r) → G_1, H_1
  55. Intersect(f_1, r) → I_1
  56. Vector(I_1, G_1) → z
  57. If(l ≟ 0, (100000 * c) + (10000 * d) + (1000 * e) + (100 * f) + (10 * g) + h, If[l ≟ 1, (10000 * d) + (1000 * e) + (100 * f) + (10 * g) + h, If[l ≟ 2, (1000 * e) + (100 * f) + (10 * g) + h, If[l ≟ 3, (100 * f) + (10 * g) + h, If[l ≟ 4, (10 * g) + h, If[l ≟ 5, h, If[l ≟ 6, 0]]]]]]) → h_1
  58. Circle(D_1, 2) → k_1
  59. Vector(L_1, K_1) → u_1
  60. If(l_1, b + (c + 1) / 10, If[m_1, b + c / 10, If[o_1, (10 * b) + c + (d + 1) / 10, If[n_1, (10 * b) + c + d / 10, If[q_1, (100 * b) + (10 * c) + d + (e + 1) / 10, If[p_1, (100 * b) + (10 * c) + d + e / 10, If[s_1, (1000 * b) + (100 * c) + (10 * d) + e + (f + 1) / 10, If[r_1, (1000 * b) + (100 * c) + (10 * d) + e + f / 10, If[v_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + (g + 1) / 10, If[t_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + g / 10]]]]]]]]]) → z_1
  61. Line(M_1, xAxis) → b_2
  62. Point(b_2) → N_1
  63. OrthogonalLine(M_1, b_2) → i_2
  64. OrthogonalLine(N_1, b_2) → j_2
  65. Point(i_2) → O_1
  66. OrthogonalLine(O_1, i_2) → l_2
  67. Intersect(j_2, l_2) → P_1
  68. Polygon(M_1, O_1, P_1, N_1) → poly3, m_2, o_2, p_2, n_2
  69. If(q_2, a_3, If[r_2, b_3, If[s_2, c_3, If[t_2, d_3, If[u_2, e_3, If[v_2, f_3, If[w_2, g_3, If[z_2, h_3]]]]]]]) → i_3
  70. Line(Q_1, xAxis) → j_3
  71. Point(j_3) → R_1
  72. OrthogonalLine(Q_1, j_3) → l_3
  73. OrthogonalLine(R_1, j_3) → m_3
  74. Point(l_3) → S_1
  75. OrthogonalLine(S_1, l_3) → n_3
  76. Intersect(n_3, m_3) → T_1
  77. Polygon(Q_1, S_1, T_1, R_1) → poly4, q_4, s_3, t_3, r_4
  78. If(u_3, i_4, If[v_3, b, If[w_3, j_4, If[z_3, k_4, If[a_4, l_4, If[b_4, m_4, If[c_4, n_4, If[d_4, o_4, If[e_4, p_4, If[f_4, s_4, If[g_4, t_4, If[h_4, u_4]]]]]]]]]]]) → v_4
  79. Line(U_1, xAxis) → a_5
  80. Point(a_5) → V_1
  81. OrthogonalLine(U_1, a_5) → b_5
  82. OrthogonalLine(V_1, a_5) → c_5
  83. Point(b_5) → W_1
  84. OrthogonalLine(W_1, b_5) → d_5
  85. Intersect(d_5, c_5) → Z_1
  86. Polygon(U_1, W_1, Z_1, V_1) → poly5, u_5, w_4, z_4, v_5
  87. If(j_5, r_5, If[l_5, s_5, If[m_5, t_5, If[n_5, w_5, If[o_5, z_5, If[q_5, a_6]]]]]) → b_6
  88. Line(A_2, xAxis) → c_6
  89. Point(c_6) → B_2
  90. OrthogonalLine(A_2, c_6) → d_6
  91. OrthogonalLine(B_2, c_6) → e_6
  92. Point(d_6) → C_2
  93. OrthogonalLine(C_2, d_6) → f_6
  94. Intersect(e_6, f_6) → D_2
  95. Polygon(C_2, D_2, B_2, A_2) → poly6, c_7, d_7, b_7, a_7
  96. Polygon(V, C_1, F_1, U) → poly7, v_6, c_8, f_7, u_6
  97. Circle(H + (0.075, 0.075), 0.3) → k_6
  98. Circle(G + (0.075, 0.075), 0.3) → q_3
  99. Circle(F + (0.075, 0.075), 0.3) → g_2
  100. Circle(D + (0.075, 0.075), 0.3) → d_2
  101. Circle(E + (0.075, 0.075), 0.3) → e_2
  102. Circle(C + (0.075, 0.075), 0.3) → e_5
  103. Circle(D + (0.075, 0.075), 0.3) → f_5
  104. Circle(E + (0.075, 0.075), 0.3) → g_5
  105. Circle(F + (0.075, 0.075), 0.3) → g_6
  106. Circle(G + (0.075, 0.075), 0.3) → h_2
  107. Circle(F + (0.075, 0.075), 0.3) → h_5
  108. Circle(G + (0.075, 0.075), 0.3) → h_6
  109. Circle(H + (0.075, 0.075), 0.3) → k_2
  110. Circle(E + (0.075, 0.075), 0.3) → k_3
  111. Circle(G + (0.075, 0.075), 0.3) → k_5
  112. Circle(F + (0.075, 0.075), 0.3) → p_3
  113. Circle(H + (0.075, 0.075), 0.3) → p_5
  114. Circle(H + (0.075, 0.075), 0.3) → r_3
  115. Polygon(J_1, Q_2, V_1, U_1) → poly8, j_6, q_6, v_7, u_7
  116. Polygon(R_2, S_2, R_1, Q_1) → poly9, r_6, s_6, r_7, q_7
  117. Polygon(T_2, U_2, N_1, M_1) → poly10, t_6, u_8, n_6, m_6
  118. If(j_5, r6, If[l_5, s_5, If[m_5, t_5, If[n_5, w_5, If[o_5, z_5, If[q_5, a_6]]]]]) → bb
  119. Polygon(V_2, W_2, B_2, A_2) → poly11, v_8, w_6, b_8, a_8
  120. Point(u_6) → Z_2
  121. Vector(Z_2, A_3) → z_6
  122. Translate(P, z_6) → P'
  123. Translate(J, z_6) → J'
  124. LaTeX(Element[text, l_6]) → texte23
  125. If(l_1, b + c / 10, If[m_1, b + c / 10, If[o_1, (10 * b) + c + (d + 1) / 10, If[n_1, (10 * b) + c + d / 10, If[q_1, (100 * b) + (10 * c) + d + (e + 1) / 10, If[p_1, (100 * b) + (10 * c) + d + e / 10, If[s_1, (1000 * b) + (100 * c) + (10 * d) + e + (f + 1) / 10, If[r_1, (1000 * b) + (100 * c) + (10 * d) + e + f / 10, If[v_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + g / 10, If[t_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + g / 10]]]]]]]]]) → zz
  126. Polygon(B_3, C_3, D_3, E_3) → poly12, b_9, c_9, d_8, e_7
  127. Point(c_9) → F_3
  128. Point(e_7) → G_3
  129. Polygon(G_3, F_3, D_3, E_3) → poly13, g_7, f_8, d_9, e_8
  130. Ray(H_3, I_3) → p_6
  131. Point(p_6) → J_3
  132. OrthogonalLine(J_3, p_6) → h_7

AI 绘图提示语参考

画一个圆形，中心在坐标原点，半径为0.5。从圆心向x轴引一条直线，并在直线上取一个点。以圆心为中心，将这个点沿x轴向右平移18等分，生成17个点。选取第5、3、7、9、11、13、15个点，分别与圆心连线。以第3个点和第5个点为端点画一条线段。找到这条线段的中点，并画出垂直于x轴的直线。以圆心为中心，画一个半径为1的圆，与垂直线相交于两点。以第7个点为中心，画一个半径为0.5的圆。以第5个点为中心，画一个半径为0.5的圆。分别找到这两个小圆与垂直线的交点，并画出它们与第3个点和第5个点连线的垂线。
以上提示语为根据原始绘图命令整理而来，仅供参考。