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分数除法 by Steve Phelps

分数除法 by Steve Phelps
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2021-11-02 04:05
多边形向量几何作图
①本范例演示分数除法的几何直观与计算过程；②涉及核心数学概念包括分数运算、除法原理、几何图形的构造；③作图要点：使用 GeoGebra 命令 Point, Polygon, Textfield, Sequence, If, Segment, Vector, Mod 构造分数除法模型，涉及对象 n, I, E, A, B, poly1, f, g, h, i, C, D, F, poly2, j, k, l, m, G, H, d11, d1, d22, d2, n11, n1, n22, n2, l1, l2, l3, l4, l5, l6, l7, J, l8, K, I5, l9；④适合初中及以上数学教学，用于分数除法的可视化教学与理解。

GeoGebra 命令及参数

  1. Point(xAxis) → I
  2. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  3. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  4. Textfield(d11) → d1
  5. Textfield(d22) → d2
  6. Textfield(n11) → n1
  7. Textfield(n22) → n2
  8. Sequence(H + (a / d11 * (G - H)), a, 0, d11) → l1, {(-0.875, 1.75), (-0.7678571428571429, 1.75), (-0.6607142857142857, 1.75), (-0.5535714285714286, 1.75), (-0.44642857142857145, 1.75), (-0.3392857142857143, 1.75), (-0.2321428571428572, 1.75), (-0.125, 1.75)}
  9. Sequence(A + (a / d22 * (D - A)), a, 0, d22) → l2, {(0.875, 1), (0.875, 1.1875), (0.875, 1.375), (0.875, 1.5625), (0.875, 1.75)}
  10. Sequence(E + (a / d11 * (F - E)), a, 0, d11) → l3, {(-0.875, 1), (-0.7678571428571429, 1), (-0.6607142857142857, 1), (-0.5535714285714286, 1), (-0.44642857142857145, 1), (-0.3392857142857143, 1), (-0.2321428571428572, 1), (-0.125, 1)}
  11. Sequence(B + (a / d22 * (C - B)), a, 0, d22) → l4, {(1.625, 1), (1.625, 1.1875), (1.625, 1.375), (1.625, 1.5625), (1.625, 1.75)}
  12. Sequence(Polygon[l1(a), l1(a + 1), l3(a + 1), l3(a)], a, 1, d11) → l5, {0.0803571428571429, 0.0803571428571428, 0.0803571428571429, 0.08035714285714285, 0.08035714285714285, 0.0803571428571428, 0.0803571428571429}
  13. Sequence(Polygon[l2(a), l2(a + 1), l4(a + 1), l4(a)], a, 1, d22) → l6, {0.140625, 0.140625, 0.140625, 0.140625}
  14. Sequence(Polygon[l1(a), l1(a + 1), l3(a + 1), l3(a)], a, 1, n11) → l7, {0.0803571428571429, 0.0803571428571428, 0.0803571428571429}
  15. If(0 ≤ n ≤ 1, Dilate[E, 1 - n, I], I) → J
  16. Sequence(Polygon[l2(a), l2(a + 1), l4(a + 1), l4(a)], a, 1, n22) → l8, {0.140625}
  17. Point(xAxis) → K
  18. If(0 ≤ n ≤ 1, Translate[l7, J - E], Translate[l7, I - E]) → l9
  19. If(0 ≤ n ≤ 1, Translate[l5, J - E], Translate[l5, I - E]) → l10
  20. If(0 ≤ n ≤ 1, Translate[l6, Dilate[A, 1 - n, I] - A], Translate[l6, I - A]) → l11
  21. If(2 ≤ n ≤ 3, Dilate[E, 3 - n, K], K) → L
  22. If(2 ≤ n ≤ 3, Dilate[A, 3 - n, K], K) → M
  23. If(2 ≤ n ≤ 3, Translate[l6, M - A], Translate[l6, K - A]) → l13
  24. If(2 ≤ n ≤ 3, Translate[l5, L - E], Translate[l5, K - E]) → l14
  25. If(2 ≤ n ≤ 3, Translate[l8, M - A], Translate[l8, K - A]) → l12
  26. Segment(N, O) → p
  27. Segment(P, Q) → q
  28. Vector(R, S) → u
  29. Mod((n11 * d22), (n22 * d11)) → W1

AI 绘图提示语参考

绘制一个用于演示分数除法几何意义的动态图形。在坐标轴上放置两个点作为参考。构造两个正方形，一个位于左侧，另一个位于右侧，每个正方形内部按分母数值划分成等宽的竖直或水平条带，并用不同颜色填充部分条带以表示分子。添加多个文本输入框用于调整分子和分母的数值。通过滑块控制动画，展示当分子或分母变化时，条带如何平移或缩放，直观体现除法结果。最后用线段和向量标注关键比例关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。