>>808 の計算

正n角形Sの頂点を　S_k（cos(2kπ/n), sin(2kπ/n)）
正(n+2)角形Tの頂点を　T_k（cos(2kπ/(n+2)), sin(2kπ/(n+2))）
とおく。
　辺S_{k-1}S_k と 辺T_{k-1}T_k の交点をU
　辺S_{k-1}S_k と 辺T_k T_{k+1} の交点をV
とおく。

Uは辺T_{k-1}T_k 上にある。　↑u = (1-L)↑t_k + L ↑t_{k-1},
Vは辺T_k T_{k+1}上にある。　↑v = (1-m)↑t_k + m ↑t_{k+1},
U,Vは辺S_{k-1}S_k にある：
　↑u・↑s_{k-1/2} = ↑v・↑s_{k-1/2} = cos(π/n),
ここに　↑s_{k-1/2} = (↑s_{k-1} + ↑s_k)/(2cos(π/n)),
これを解いて
　L = {cos(π/n) - cos(2kπ/(n+2)-(2k-1)π/n)}
　　/ {cos(2(k-1)π/(n+2)-(2k-1)π/n) - cos(2kπ/(n+2)-(2k-1)π/n)},
　m = {cos(π/n) - cos(2kπ/(n+2)-(2k-1)π/n)}
　　/ {cos(2(k+1)π/(n+2)-(2k-1)π/n) - cos(2kπ/(n+2)-(2k-1)π/n)},

△(U T_k V) = (1/2)UT_k・VT_k sin(∠UT_kV)
　= L m * (1/2)T_{k-1}T_k・T_kT_{k+1} sin(∠T_{k-1} T_k T_{k+1})
　= L m *△(T_{k-1} T_k T_{k+1}),
ここで
　T_{k-1}T_k = T_k T_{k+1} = 2sin(π/(n+2)),
　∠(T_{k-1} T_k T_{k+1}) = π - 2π/(n+2),
より
　△(T_{k-1} T_k T_{k+1}) = 2{sin(π/(n+2))}^2 sin(2π/(n+2)),