■等面単体の体積(その385)
(その383)において,試しに
P0(m,0,m√2,h)
P1(0,0,0,0)
Px(0,0,0,4h)
P2(m,m√2,0,2h)
P3(2m,0,0,3h)
とおくと,
P0P1^2=3m^2+h^2
P0Px^2=3m^2+9h^2
P0P2^2=4m^2+h^2
P0P3^2=3m^2+4h^2
P1Px^2=16h^2
P1P2^2=3m^2+4h^2
P1P3^2=4m^2+9h^2
PxP2^2=3m^2+4h^2
PxP3^2=4m^2+h^2
P2P3^2=3m^2+h^2
3m^2+h^2(2)<3m^2+4h^2(3)<3m^2+9h^2(1)
4m^2+h^2(2)<4m^2+9h^2(1)
16h^2(1)
これは辺の長さが3種類以上であるからNG.
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