分数相乘的几何可视化：用多边形与序列构造比例

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
3. Textfield(d11) → d1
4. Textfield(d22) → d2
5. Textfield(n11) → n1
6. Textfield(n22) → n2
7. Sequence(H + (a / d11 * (G - H)), a, 0, d11) → l1
8. Sequence(A + (a / d22 * (D - A)), a, 0, d22) → l2
9. Sequence(E + (a / d11 * (F - E)), a, 0, d11) → l3
10. Sequence(B + (a / d22 * (C - B)), a, 0, d22) → l4
11. Sequence(Polygon[l1(a), l1(a + 1), l3(a + 1), l3(a)], a, 1, d11) → l5
12. Sequence(Polygon[l2(a), l2(a + 1), l4(a + 1), l4(a)], a, 1, d22) → l6
13. Sequence(Polygon[l1(a), l1(a + 1), l3(a + 1), l3(a)], a, 1, n11) → l7
14. Sequence(Polygon[l2(a), l2(a + 1), l4(a + 1), l4(a)], a, 1, n22) → l8
15. Point(yAxis) → O
16. Segment(N, O) → p
17. Segment(P, Q) → q
18. Point(yAxis) → I
19. If(0 ≤ n ≤ 1, Translate[l5, I - Dilate[E, n, I]], Translate[l5, I - E]) → l9
20. If(0 ≤ n ≤ 1, Translate[l7, I - Dilate[E, n, I]], Translate[l7, I - E]) → l10
21. If(2 ≤ n ≤ 3, Translate[l6, I - Dilate[A, n - 2, I]], Translate[l6, I - A]) → l11
22. If(2 ≤ n ≤ 3, Translate[l8, I - Dilate[A, n - 2, I]], Translate[l8, I - A]) → l12
23. Polygon(I, J, L, K) → q1, i_1, j_1, l_1, k_1