加法结合律与交换律的图解（向量与几何构造）

GeoGebra 命令及参数

1. Ray(O, I) → f
2. Point(f) → A
3. Point(f) → C
4. Point(f) → B
5. Line(C, g) → h
6. Line(B, g) → i
7. Line(A, g) → j
8. Intersect(i, q) → D
9. Intersect(h, p) → E
10. Mirror(h, p) → h'
11. Mirror(i, q) → i'
12. Intersect(i', f) → F
13. Intersect(g, p) → J
14. Intersect(g, q) → K
15. PolyLine(O, J, C) → l
16. Translate(B, C - B) → C'_{1}
17. Translate(D, C - B) → D'_{1}
18. Translate(F, C - B) → BpC
19. Ray(BpC, D'_{1}) → r
20. Intersect(r, g) → L
21. PolyLine(Translate[O, (0, (1.2 * eps))], Translate[L, (0, (1.2 * eps))], Translate[BpC, (0, (1.2 * eps))]) → s
22. PolyLine(O, K, B) → k
23. Translate(O, (0, (-eps))) → O'
24. Translate(K, (0, (-eps))) → K'
25. Translate(B, (0, (-eps))) → C'_{2}
26. PolyLine(O', K', C'_{2}) → k'
27. Translate(O, B) → O'_{1}
28. Translate(J, B) → J'
29. Translate(C, B) → B'
30. PolyLine(O'_{1}, J', B') → l'
31. Translate(O', C) → O''
32. Translate(K', C) → K''
33. Translate(C'_{2}, C) → M
34. PolyLine(O'', K'', M) → k''
35. Translate(O', A) → O''_{1}
36. Translate(K', A) → K''_{1}
37. Translate(C'_{2}, A) → G
38. PolyLine(O''_{1}, K''_{1}, G) → k''_{1}
39. Translate(O, H) → O'_{2}
40. Translate(J, H) → J'_{1}
41. Translate(C, H) → C'
42. PolyLine(O'_{2}, J'_{1}, C') → l'_{1}
43. Translate(s, A) → s'