椭圆与比例变换的几何探索

GeoGebra 命令及参数

1. Ellipse((1, 0), (2.5, 0), 1.5) → e
2. Point(e) → F
3. If(yellow + blue ≟ 0, 1, If[ratio ≤ 1, 0, (0.79 * ratio2^(2)) - (1.72 * ratio2) + 0.99]) → a
4. If(yellow + blue ≟ 0, 1, If[ratio ≥ 1, 1, (-0.85 * ratio^(2)) + (1.78 * ratio)]) → b
5. If(yellow + blue ≟ 0, 1, If[ratio ≥ 1, 0, (0.79 * ratio^(2)) - (1.72 * ratio) + 0.99]) → c
6. Point(e) → E
7. Segment(F, (x(F), ht)) → f
8. Vector(F, G) → u
9. Translate(e, u) → e'
10. Polygon(G, F, E, H) → poly2, g, f_1, e_1, h
11. Segment(I, F) → i
12. Segment(E, J) → j
13. Vector(F, I) → v
14. Ellipse((1, ht), (2.5, ht), 1.5) → p
15. Ellipse((1, 0), (2.5, 0), 1.5) → q
16. Segment(H, E) → l
17. Ellipse((1, top), (2.5, top), 1.5) → k
18. Segment(C, A) → m
19. Segment(B, D) → n
20. Vector(A, C) → w
21. Vector(A, K) → r
22. Translate(B, r) → B'
23. Polygon(K, A, B, B') → poly1, k_1, a_1, b_1, b'
24. If(yellow2 + blue2 ≟ 0, 1, If[ratiox ≤ 1, 0, (0.79 * (1 / ratiox)^(2)) - (1.72 * 1 / ratiox) + 0.99]) → a2
25. If(yellow2 + blue2 ≟ 0, 1, If[ratiox ≥ 1, 1, (-0.85 * ratiox^(2)) + (1.78 * ratiox)]) → b2
26. If(yellow2 + blue2 ≟ 0, 1, If[ratiox ≥ 1, 0, (0.79 * ratiox^(2)) - (1.72 * ratiox) + 0.99]) → c2
27. Vector(F, A) → d
28. Translate(q, d) → q'
29. Translate(q, d) → q'_1
30. Translate(q'_1, r) → s
31. Translate(q'_1, r) → t
32. Segment(B', B) → g_1
33. Segment(K, A) → h_1
34. Sequence(Ellipse[(1, k), (2.5, k), 1.5], k, 10, 90, 10) → list1
35. Translate(list1, d) → list1'
36. Ray((8.5, 0), (8.5, 1)) → i_1
37. Sequence((8.5, n), n, 0, 100, 10) → list2
38. Point(i_1) → L
39. Sequence(Text[m + "ml", (8.65, m - 1.5)], m, 0, 100, 10) → list3
40. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1