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分数与带分数的转换

分数与带分数的转换
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2014-01-05 09:13
解析几何几何作图
①这个范例通过可视化方式演示了如何将假分数转换为带分数；②涉及的核心数学概念包括分数的基本性质、等值分数、带分数与假分数的互化；③作图要点——从下方『构造摘要』提炼用到了Circle（圆）、Line（线）、Intersect（交点）、OrthogonalLine（垂线）、Segment（线段）、Polygon（多边形）等GeoGebra命令/对象；④适合初中数学学生学习和理解分数的基本运算与转换，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Circle(A, length) → c
  2. Line(A, xAxis) → a
  3. Intersect(c, a, 2) → B_1
  4. Circle(A, height) → d
  5. OrthogonalLine(A, a) → b
  6. Intersect(d, b, 2) → C_1
  7. OrthogonalLine(B_1, a) → e
  8. OrthogonalLine(C_1, e) → f
  9. Intersect(e, f) → D_1
  10. Segment(A, B_1) → g
  11. Segment(C_1, D_1) → h
  12. Segment(A, C_1) → i
  13. Segment(B_1, D_1) → j
  14. Circle(A, unit) → k
  15. Circle(A, 2 * unit) → p
  16. Circle(A, 3 * unit) → q
  17. Circle(A, 4 * unit) → r
  18. Circle(A, 5 * unit) → s
  19. Circle(A, 6 * unit) → t
  20. Circle(A, 7 * unit) → c1
  21. Circle(A, 8 * unit) → d1
  22. Circle(A, 9 * unit) → e1
  23. Circle(A, 10 * unit) → f1
  24. Circle(A, 11 * unit) → g1
  25. Circle(A, 12 * unit) → h1
  26. Circle(A, 13 * unit) → k1
  27. Circle(A, 14 * unit) → p1
  28. Circle(A, 15 * unit) → q1
  29. Circle(A, 16 * unit) → r1
  30. Circle(A, 17 * unit) → s1
  31. Circle(A, 18 * unit) → t1
  32. Circle(A, 19 * unit) → c2
  33. Circle(A, 20 * unit) → d2
  34. Circle(A, 21 * unit) → e2
  35. Circle(A, 22 * unit) → f2
  36. Circle(A, 23 * unit) → g2
  37. Circle(A, 24 * unit) → h2
  38. Intersect(k, g, 1) → E_1
  39. Intersect(p, g, 1) → F_1
  40. Intersect(q, g, 1) → G_1
  41. Intersect(r, g, 1) → H_1
  42. Intersect(s, g, 1) → I_1
  43. Intersect(t, g, 1) → J_1
  44. Intersect(c1, g, 1) → K_1
  45. Intersect(d1, g, 1) → L_1
  46. Intersect(e1, g, 1) → M_1
  47. Intersect(f1, g, 1) → N_1
  48. Intersect(g1, g, 1) → O
  49. Intersect(h1, g, 1) → P
  50. Intersect(k1, g, 1) → Q
  51. Intersect(p1, g, 1) → R
  52. Intersect(q1, g, 1) → S
  53. Intersect(r1, g, 1) → T
  54. Intersect(s1, g, 1) → U
  55. Intersect(t1, g, 1) → V
  56. Intersect(c2, g, 1) → W
  57. Intersect(d2, g, 1) → Z
  58. Intersect(e2, g, 1) → A1
  59. Intersect(f2, g, 1) → B1
  60. Intersect(g2, h2, 1) → C1
  61. Intersect(g2, g) → D1,
  62. Intersect(h2, g) → E1,
  63. Circle(A, denominator * unit) → k2
  64. Circle(A, 2 * denominator * unit) → p2
  65. Circle(A, 3 * denominator * unit) → q2
  66. Circle(A, 4 * denominator * unit) → r2
  67. Circle(A, 5 * denominator * unit) → s2
  68. Circle(A, 6 * denominator * unit) → t2
  69. Circle(A, 7 * denominator * unit) → c3
  70. Circle(A, 8 * denominator * unit) → d3
  71. Circle(A, 9 * denominator * unit) → e3
  72. Circle(A, 10 * denominator * unit) → f3
  73. OrthogonalLine(E_1, g) → l
  74. OrthogonalLine(F_1, g) → m
  75. OrthogonalLine(G_1, g) → n
  76. OrthogonalLine(H_1, g) → a1
  77. OrthogonalLine(I_1, g) → b1
  78. OrthogonalLine(J_1, g) → i1
  79. OrthogonalLine(K_1, g) → j1
  80. OrthogonalLine(L_1, g) → l1
  81. OrthogonalLine(M_1, g) → m1
  82. OrthogonalLine(N_1, g) → n1
  83. OrthogonalLine(O, g) → a2
  84. OrthogonalLine(P, g) → b2
  85. OrthogonalLine(Q, g) → i2
  86. OrthogonalLine(R, g) → j2
  87. OrthogonalLine(S, g) → l2
  88. OrthogonalLine(T, g) → m2
  89. OrthogonalLine(U, g) → n2
  90. OrthogonalLine(V, g) → a3
  91. OrthogonalLine(W, g) → b3
  92. OrthogonalLine(Z, g) → g3
  93. OrthogonalLine(A1, g) → h3
  94. OrthogonalLine(B1, g) → i3
  95. OrthogonalLine(D1, g) → j3
  96. OrthogonalLine(E1, g) → k3
  97. Intersect(k3, h) → K1
  98. Intersect(j3, h) → L1
  99. Intersect(h, i3) → M1
  100. Intersect(h, h3) → N1
  101. Intersect(h, g3) → O1
  102. Intersect(h, b3) → P1
  103. Intersect(h, a3) → Q1
  104. Intersect(h, n2) → R1
  105. Intersect(h, m2) → S1
  106. Intersect(h, l2) → T1
  107. Intersect(h, j2) → U1
  108. Intersect(h, i2) → V1
  109. Intersect(h, b2) → W1
  110. Intersect(h, a2) → Z1
  111. Intersect(h, n1) → A2
  112. Intersect(h, m1) → B2
  113. Intersect(h, l1) → C2
  114. Intersect(j1, h) → D2
  115. Intersect(i1, h) → E2
  116. Intersect(h, b1) → F2
  117. Intersect(h, a1) → G2
  118. Intersect(h, n) → H2
  119. Intersect(h, m) → I2
  120. Intersect(h, l) → J2
  121. Intersect(h, i) → K2
  122. Segment(L1, D1) → l3
  123. Segment(M1, B1) → m3
  124. Segment(N1, A1) → n3
  125. Segment(O1, Z) → p3
  126. Segment(P1, W) → q3
  127. Segment(Q1, V) → r3
  128. Segment(R1, U) → s3
  129. Segment(S1, T) → t3
  130. Segment(T1, S) → a4
  131. Segment(U1, R) → b4
  132. Segment(V1, Q) → c4
  133. Segment(W1, P) → d4
  134. Segment(Z1, O) → e4
  135. Segment(A2, N_1) → f4
  136. Segment(B2, M_1) → g4
  137. Segment(C2, L_1) → h4
  138. Segment(D2, K_1) → i4
  139. Segment(E2, J_1) → j4
  140. Segment(F2, I_1) → k4
  141. Segment(G2, H_1) → l4
  142. Segment(H2, G_1) → m4
  143. Segment(I2, F_1) → n4
  144. Segment(J2, E_1) → p4
  145. Intersect(k2, g) → B,
  146. Intersect(p2, g) → C,
  147. Intersect(q2, g) → D,
  148. Intersect(r2, g) → E,
  149. Intersect(s2, g) → F,
  150. Intersect(t2, g) → G,
  151. Intersect(c3, g) → H,
  152. Intersect(d3, g) → I,
  153. Intersect(e3, g) → J,
  154. Intersect(f3, g) → K,
  155. Circle(A, 11 * denominator * unit) → q4
  156. Circle(A, 12 * denominator * unit) → r4
  157. Intersect(q4, g) → L,
  158. Intersect(r4, g) → M,
  159. Intersect(i, h) → N
  160. Circle(N, numerator * unit) → s4
  161. Intersect(s4, h) → F1,
  162. Circle(A, numerator * unit) → t4
  163. Intersect(t4, g) → G1,
  164. Polygon(A, G1, F1, N) → poly1, a_1, g1_1, f1_1, n_1
  165. Segment(H1, I1) → a5
  166. Polygon(J1, L2, 4) → poly2, b5, c5, d5, e5, M2, N2
  167. Polygon(O2, P2, 4) → poly3, o2, g5, h5, i5, Q2, R2

AI 绘图提示语参考

画一个坐标系，显示一个圆和x轴的交点，再画一个与x轴垂直的线，找到该线与圆的交点。接着，以原点为中心，分别画半径为1到10个单位的同心圆，并找到这些圆与x轴的交点。最后，连接这些交点，形成由多个线段组成的图形，展示分数转换的过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。