矩形倒水动态模型：线性方程与导数可视化

GeoGebra 命令及参数

1. Line(J, xAxis) → j
2. OrthogonalLine(C, yAxis) → b
3. OrthogonalLine(C, xAxis) → a
4. OrthogonalLine(A, yAxis) → d
5. Intersect(a, d) → D
6. OrthogonalLine(A, xAxis) → c
7. Intersect(b, c) → B
8. Polygon(A, D, C, B) → tgtRectangle, tgt_w, d_1, c_1, tgt_h
9. Circle(J, tgtPerim / 2) → k
10. Intersect(k, j, 2) → K
11. RandomUniform(x(J) + 1, x(K) - 1) → RandRect
12. Intersect(xAxis, yAxis) → E
13. Point(Circle[E, tgt_w]) → F
14. Segment(E, F) → e
15. Point(Circle[F, tgt_h]) → G
16. Segment(F, G) → f
17. Point(Circle[G, c_1]) → H
18. Segment(G, H) → g
19. Point(Circle[H, d_1]) → I
20. Segment(H, I) → h
21. Segment(J, K) → l
22. Point(l) → L
23. Circle(L, K) → p
24. OrthogonalLine(L, l) → m
25. Intersect(p, m, 2) → M
26. OrthogonalLine(M, yAxis) → n
27. OrthogonalLine(J, l) → q
28. Intersect(n, q) → N
29. Polygon(J, L, M, N) → PouringRectangle, j_1, l_1, m_1, n_1
30. Circle(D, newAreaHeight) → r
31. Intersect(r, a) → P, Q
32. OrthogonalLine(Q, a) → s
33. Intersect(c, s) → R
34. Segment(R, Q) → t_1
35. Polygon(A, D, Q, R) → pouredAreaRectangle, a_2, d_2, q_1, r_1
36. Vector(D, Q) → u
37. Vector(J, N) → v
38. Line(waterS, m_1) → f_1
39. Intersect(f_1, l_1) → T
40. Line(waterT, tgt_w) → g_1
41. Intersect(g_1, r_1) → O
42. Polygon(A, D, waterT, O) → poly1, a_1, d_3, watert, o
43. Polygon(J, L, T, waterS) → poly2, j_2, l_2, t_2, waters
44. Midpoint(l) → S