包含三角形PQR的最小正方形

GeoGebra 命令及参数

1. Polygon(P, Q, R) → triangle, r, p, q
2. Sort({Length[p], Length[q], Length[r]}) → sides
3. Element(sides, 3) → a
4. Element(sides, 2) → b
5. Element(sides, 1) → c
6. CircumcircleSector((a, 0), ((a * sqrt(2) / 2), (a * sqrt(2) / 2)), (0, a)) → d
7. Point(d) → rotate
8. Vector(rotate) → u
9. Vector(endpoint) → v
10. Polygon((0, 0), rotate, endpoint) → copy, b_1, e, a_1
11. Function((a * cos(x)), 0, 1.5707963267948966) → Δx_1
12. Function((a * cos(x)) - (b * cos(x + θ)), 0, 1.5707963267948966) → Δx_2
13. Function((a * sin(x)), 0, 1.5707963267948966) → Δy_1
14. Function((b * sin(x + θ)), 0, 1.5707963267948966) → Δy_2
15. Intersect(Δx_1, Δx_2, 0, 1.5707963267948966) → A
16. Intersect(Δx_1, Δy_2, 0, 1.5707963267948966) → C
17. Intersect(Δx_2, Δy_1, 0, 1.5707963267948966) → D
18. Intersect(Δx_2, Δy_2, 0, 1.5707963267948966) → E, G
19. Intersect(Δy_1, Δy_2, 0, 1.5707963267948966) → F
20. RemoveUndefined({x(A), x(B), x(C), x(D), x(E), x(F)}) → ts
21. Sequence(Max[{Δx_1(Element[ts, i]), Δx_2(Element[ts, i]), Δy_1(Element[ts, i]), Δy_2(Element[ts, i])}], i, 1, Length[ts]) → squares
22. IndexOf(Min[squares], squares) → indeks
23. Element(ts, indeks) → t_{optimal}
24. Polygon((0, 0), ((a * cos(t_{optimal})), (a * sin(t_{optimal}))), ((b * cos(t_{optimal} + θ)), (b * sin(t_{optimal} + θ)))) → polygon1, g, h, i
25. Element(squares, indeks) → optimalside
26. Polygon(O, O + ((-optimalside), 0), O + ((-optimalside), optimalside), O + (0, optimalside)) → optimalsquare, o, j, k, l
27. Max({Δx_1(t), Δx_2(t), Δy_1(t), Δy_2(t)}) → currentside
28. Polygon(M, M + ((-currentside), 0), M + ((-currentside), currentside), M + (0, currentside)) → currentsquare, m, f, n, s