■等面単体の体積(その398)

 (その387)は,さらに

  3m^2+h^2=16h^2=4

  3m^2+9h^2=4m^2+4h^2=6

も満たさなければならない.

  h^2=1/4,m^2=5/4

はそれらを満たす.

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 (その384)(その395)は,正三角形の場合であり,

  P0(0,0,0,0)

  P1(0,0,0,3h)

  P2(m,m√3,0,h)

  P3(2m,0,0,2h)

とおくと

  P0P1^2=9h^2

  P0P2^2=4m^2+h^2

  P0P3^2=4m^2+4h^2

  P1P2^2=4m^2+4h^2

  P1P3^2=4m^2+h^2

  P2P3^2=4m^2+h^2

  4m^2+h^2=4

  4m^2+4h^2=9h^2=6

も満たさなければならない.

  h^2=4/6,m^2=5/6

はそれらを満たす.

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