Pensieve header: February 9: The 1206 Riddle.

GraphicsRow[{
Graphics[{Orange,Disk /@ Tuples[{1,-1},2],Blue, Disk[{0,0},(Sqrt[2])-1]}, Frame->True],
Graphics3D[{Orange,Ball /@ Tuples[{1,-1},3],Blue, Ball[{0,0,0},(Sqrt[3])-1]}]
}, ImageSize -> 720]

r[n_]=N[(((2 (π^(n/2)) ((((Sqrt[n])-1))^n))/(n (Gamma[(n/2)]))))/(4^n)]

Table[r[n], {n,1,100}]

ListPlot[Table[Log[r[n]], {n,1,2000}]]