用几何变换直观验证对数性质

GeoGebra 命令及参数

1. Segment(A, B) → g
2. Segment(C, D) → h
3. Segment(E, F) → i
4. Vector(C, ((a * b), ln(a))) → v
5. Vector(A, ((a * b), ln(b))) → w
6. Length(v) → L_{v}
7. Length(w) → L_{w}
8. Vector((c, 0)) → u
9. Translate(A, u) → A'
10. Translate(B, u) → B'
11. Segment(A', B') → g'
12. Translate(C, Vector[(v * c / ((a * b) - a))]) → C'
13. Translate(D, Vector[(v * c / ((a * b) - a))]) → D'
14. Segment(C', D') → h'
15. Midpoint(i) → G
16. RotateText(text6, pi / 2) → text7
17. RotateText(text4, ((3 * pi)) / 2) → text8
18. Midpoint(Segment[G, F]) → H
19. Segment(I, J) → k
20. Vector((j, 0)) → m
21. Segment(M, N) → l
22. Vector((j^(2) - j, 0)) → p
23. Translate(I, Vector[(n, 0)]) → I'
24. Translate(J, Vector[(n, 0)]) → J'
25. Segment(I', J') → k'
26. Semicircle(M, N) → q
27. Point(q, 1 - α) → O
28. Segment(O, (j^(2), ln(j))) → r
29. RotateText(text10, ((3 * pi)) / 2) → text11
30. RotateText(text12, pi / 2) → text13
31. Textfield(t) → InputBox1
32. Textfield(a_1) → InputBox2