自然数求和的四种方法

GeoGebra 命令及参数

1. Vector((1, 0)) → u
2. Vector((0, 1)) → v
3. Polygon((-1, -1), (0, -1), 4) → poly1
4. Centroid(poly1) → M
5. Sequence(Sequence[Translate[poly1, Vector[(c * u) + ((r + 1) * v)]], c, 1, r], r, 0, s) → L_8
6. Sequence(Sequence[Translate[poly1, Vector[(c * u) + ((r + 1) * v)]], c, 1, r], r, 1, s) → L_6
7. Sequence(Sequence[Translate[M, Vector[(c * u) + ((r + 1) * v)]], c, 1, r], r, 1, s) → L_7
8. Sequence(Sequence[Translate[poly1, Vector[(c * u) + (r * v)]], r, 1, c], c, 1, s) → L_1
9. Sequence(Sequence[Translate[M, Vector[(c * u) + (r * v)]], r, 1, c], c, 1, s) → L_2
10. Sequence(m, m, 1, s) → L_3
11. Reverse(L_3) → L_4
12. Segment(A, B) → f
13. Sequence(Translate[M, Vector[(c * u)]], c, 1, s) → L_5
14. Reverse(L_5) → L_{10}
15. Sequence(Semicircle[L_{10}(c), L_5(c)], c, 1, s / 2) → L_{13}
16. Mod(s, 2) → e
17. Div(s, 2) → d
18. Sequence(Translate[M, Vector[((c + 20) * u)]], c, 1, s) → L_9
19. Reverse(L_9) → L_{11}
20. Sequence(Semicircle[L_{11}(c), L_9(c)], c, 1, s / 2) → L_{12}
21. Segment(H, J) → k
22. Sequence(Translate[M, Vector[((s + 1) / 2 * u) + (r * v)]], r, 1, s / 2 + 1) → L_{15}
23. Midpoint(A, B) → D
24. Textfield(q) → InputBox1
25. Sequence((z_1 * (z_1 + 1) / 2), z_1, 1, s) → L_{14}