等差数列求和 by Idan Tal

GeoGebra 命令及参数

1. Point(Segment[(-1, -1), (-1, -10)]) → A
2. Segment((-1, 0), A) → n
3. Point(Segment[(0, 2), (4, 2)]) → B
4. Point(Segment[(x(B), 1), (x(B) + 5, 1)]) → C
5. Segment((x(B), 1), (x(C), 1)) → d
6. Segment((0, 2), B) → a_1
7. Polygon((0, 0), ((2 * a_1) + ((n - 1) * d), (-n)), (0, (-n))) → poly1, a, b, c
8. Vector((-1, 0), A) → k
9. Vector(A, (-1, 0)) → l
10. Sequence(Polygon[(0, (-k)), (0, (-k) - 1), (a_1, (-k) - 1), (a_1, (-k))], k, 0, n - 1) → list1
11. Vector((0, 2), (x(B), 2)) → w
12. Vector((x(B), 2), (0, 2)) → j
13. Vector((x(B), 1), (x(C), 1)) → w_1
14. Vector((x(C), 1), (x(B), 1)) → c_1
15. Vector((a_1, (-n) - 1), (0, (-n) - 1)) → p
16. Vector((0, (-n) - 1), (a_1, (-n) - 1)) → m
17. Vector((a_1, (-n) - 1), (a_1 + ((n - 1) * d), (-n) - 1)) → q
18. Vector((a_1 + ((n - 1) * d), (-n) - 1), (a_1, (-n) - 1)) → r
19. Vector((a_1 + ((n - 1) * d), (-n) - 1), ((2 * a_1) + ((n - 1) * d), (-n) - 1)) → s
20. Vector(((2 * a_1) + ((n - 1) * d), (-n) - 1), (a_1 + ((n - 1) * d), (-n) - 1)) → t
21. Vector((0, (-n) - 2), (a_1 + ((n - 1) * d), (-n) - 2)) → u
22. Vector((a_1 + ((n - 1) * d), (-n) - 2), ((2 * a_1) + ((n - 1) * d), (-n) - 2)) → u_1
23. Vector((a_1 + ((n - 1) * d), (-n) - 2), (0, (-n) - 2)) → v
24. Vector(((2 * a_1) + ((n - 1) * d), (-n) - 2), (a_1 + ((n - 1) * d), (-n) - 2)) → v_1
25. Polygon((0, 0), Intersect[x = Length[a_1], a], (a_1, 0)) → poly2, e_1, f_1, g_1
26. Rotate(poly2, (-α), (a_1 + ((0.5 * d) * (n - 1)), (-0.5 * n))) → poly2'
27. Rotate(list1, (-α), (a_1 + ((0.5 * d) * (n - 1)), (-0.5 * n))) → list1'
28. Zip(Sequence[Polygon[(a_1 + (d * (i - 1)), (-W)), (a_1 + (d * (i - 1)), (-W) - 1), (a_1 + (d * i), (-W) - 1), (a_1 + (d * i), (-W))], i, 1, W], W, Sequence[k, k, 0, Length[n] - 1]) → list2
29. Rotate(list2, (-α), (a_1 + ((0.5 * d) * (n - 1)), (-0.5 * n))) → list2'
30. Sequence(If[f(a_1 + ((k - 1) * d)) < (-k), Polygon[(a_1 + ((k - 1) * d), (-k)), (a_1 + (k * d), (-k)), (a_1 + (k * d), f(a_1 + (k * d))), (a_1 + ((k - 1) * d), f(a_1 + ((k - 1) * d)))], If[f(a_1 + (k * d)) < (-k), Polygon[Intersect[f, y = (-k)], (a_1 + (k * d), (-k)), (a_1 + (k * d), f(a_1 + (k * d)))]]], k, 1, n - 1) → list3
31. Sequence(a_1 + ((i - 1) * d), i, 1, n) → list4
32. Rotate(list3, (-α), (a_1 + ((0.5 * d) * (n - 1)), (-0.5 * n))) → list3'