几何构造求平方根值

GeoGebra 命令及参数

1. Point(xAxis) → C
2. Segment(A, B) → f
3. Segment(B, C) → g
4. Midpoint(A, C) → D
5. Semicircle(A, C) → c
6. OrthogonalLine(B, g) → h
7. Intersect(c, h) → E,
8. Segment(E, B) → i
9. Midpoint(i) → F
10. Midpoint(H, I) → J
11. Segment(H, G) → j
12. Translate(G, Vector[(If[a < 2, a / 2, 1] * Vector[G, I])]) → G'
13. Segment(G, G') → k
14. Rotate(I, If[2 < a < π + 2, (a - 2) / (π - 2), π], J) → I'
15. Segment(J, I') → l
16. CircleArc(J, I, I') → d
17. OrthogonalLine(G, k) → m
18. Intersect(d, m) → K,
19. Translate(G, Vector[(If[6.5 < a < 8, (a - 6.5) / 1.5, 1] * Vector[G, K])]) → G'_1
20. Segment(G, G'_1) → n
21. Midpoint(j) → L
22. Angle(G'_1, G, H) → α