notice that there are two points in the tan (namely (0,1), (1,0) ) such that the distance between the two points is \sqrt2, so the diagonal of the square must be at least \sqrt2, and the side length must be at least 1.
P89 · 等腰直角三角形装入正方形 · 讨论
best value at n=1
in fact this proof also works for n=2