算术几何平均不等式2.0：几何与函数的交汇

GeoGebra 命令及参数

1. Circle((0, 0), (a + b) / 2) → c
2. Segment(((-((a + b) / 2)), 0), ((-((a + b) / 2)) + a, 0)) → d
3. Segment(((a + b) / 2 - b, 0), ((a + b) / 2, 0)) → e
4. Segment(((-((a + b) / 2)) + a, 0), ((-((a + b) / 2)) + a, sqrt((a * b)))) → GM
5. Intersect(c, d, 1) → A
6. Intersect(c, GM, 1) → B
7. Segment(A, B) → f
8. Intersect(c, e, 1) → C
9. Segment(B, C) → g
10. Point(d) → D
11. Polygon(A, B, D) → poly1, d_1, a_1, b_1
12. Polygon(B, D, C) → poly2, c_1, b_2, d_2
13. Segment((0, 0), (0, (a + b) / 2)) → AM
14. Intersect(c, GM, 1) → E
15. Point(d) → F
16. Polygon((0, -5), (0, -5 + GM), 4) → GMsquared
17. Polygon((0, -5), (0, -5 + a), (0 - b, -5 + a), (0 - b, -5)) → AtimesB, i, j, k, l