分数乘法的可视化演示：用多边形与网格展示分数相乘

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, a_1, b_1, f_2, g_2, C, D
2. Polygon(E, F, 4) → poly2, e_1, f_1, h, i, G, H
3. Sequence(A + i * (D - A), i, 0, 1, 1 / b) → L1
4. Sequence(B + i * (C - B), i, 0, 1, 1 / b) → L2
5. Sequence(Segment[Element[L1, k], Element[L2, k]], k, 2, b) → L3
6. Polygon(D, C, S, R) → poly3, d_1, c_1, s, r
7. Sequence(E + i * (F - E), i, 0, 1, 1 / d) → L4
8. Sequence(H + i * (G - H), i, 0, 1, 1 / d) → L5
9. Sequence(Segment[Element[L4, j], Element[L5, j]], j, 2, d) → L6
10. Intersect(g_2, a_1) → I
11. Intersect(b_1, a_1) → J
12. Segment(I, J) → j
13. Intersect(i, e_1) → K
14. Intersect(i, h) → L
15. Polygon(K, T, U, L) → poly4, k, t, u, l
16. Intersect(g_2, a_1) → M
17. Intersect(b_1, a_1) → N
18. Segment(M, N) → m
19. Intersect(f_2, b_1) → O
20. Intersect(g_2, f_2) → P
21. Segment(O, P) → n
22. Segment(P, M) → p
23. Segment(N, O) → q
24. Segment(O, P) → g_1
25. Vector(Q, V) → v
26. Translate(poly1, Vector[20 * e * v]) → poly1'
27. Translate(L3, Vector[20 * e * v]) → L3'
28. Translate(D, Vector[20 * e * v]) → D'
29. Translate(C, Vector[20 * e * v]) → C'
30. Translate(S, Vector[20 * e * v]) → S'
31. Translate(R, Vector[20 * e * v]) → R'
32. Polygon(D', C', S', R') → poly3', d', c', s', r'
33. Translate(poly2, Vector[10 * e * v]) → poly2'
34. Translate(K, Vector[10 * e * v]) → K'
35. Translate(T, Vector[10 * e * v]) → T'
36. Translate(U, Vector[10 * e * v]) → U'
37. Translate(L, Vector[10 * e * v]) → L'
38. Polygon(K', T', U', L') → poly4', k', t', u', l'
39. Translate(L6, Vector[10 * e * v]) → L6'
40. GCD(f, g) → o
41. Point(yAxis) → W
42. Segment(W, Z) → h_1
43. Segment(A_1, B_1) → i_1