■等面単体の体積(その383)
P0(1,0,√2)
P1(0,0,0)
P2(1,√2,0)
P3(2,0,0)
P0P1=P1P2=P2P3=√3
P0P2=P1P3=2
P0P3=√3
試しに
P0(m,0,m√2,h)
P1(0,0,0,0)
Px(0,0,0,4h)
P2(m,m√2,0,3h)
P3(2m,0,0,2h)
とおくと,
P0P1^2=3m^2+h^2
P0Px^2=3m^2+9h^2
P0P2^2=4m^2+4h^2
P0P3^2=3m^2+h^2
P1Px^2=16h^2
P1P2^2=3m^2+9h^2
P1P3^2=4m^2+4h^2
PxP2^2=3m^2+h^2
PxP3^2=4m^2+4h^2
P2P3^2=3m^2+h^2
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[まとめ]組み合わせが複雑になりそうだ.絞り込みが必要と思われる.
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