45度旋转矩阵的根式表示

GeoGebra 命令及参数

1. Circle(A, C) → c
2. Point(c) → B
3. Angle(C, A, B) → α
4. Line(B, A) → f
5. OrthogonalLine(A, f) → g
6. Intersect(c, g, 1) → D
7. Polygon(D, A, B) → poly1, b, d, a
8. Midpoint(D, B) → E
9. Segment(A, E) → h
10. Midpoint(A, E) → F
11. Midpoint(F, E) → G
12. Intersect(p, n) → H
13. Intersect(m, p) → I
14. Intersect(m, q) → J
15. Intersect(n, q) → K
16. If(y(B) < 0, "-", "") → a_3
17. If(x(B) < 0, "-", " ") → a_1
18. If(y(D) < 0, "-", "") → a_4
19. If(t, If[85° < α < 95°, false, If[175° < α < 185°, false, If[265° < α < 275°, false, If[α < 5°, false, If[355° < α, false, If[Mod[α, 45°] < °, true, If[Mod[α, 45°] > 44°, true, false]]]]]]], false) → e
20. Midpoint(B, E) → L
21. Midpoint(D, E) → N
22. Segment(E, B) → r
23. Segment(D, E) → s
24. If(x(D) < 0, "-", "") → a_2
25. If(e, false, If[t, true, false]) → o