■等面単体の体積(その265)

 (その262)に誤り発見.

P1(0,0,0)

P2((√6)/2,(√10)/2,0)

P3(√6,0,0)

  P1P2=P2P3=P3P4=2

  P1P3=P2P4=√6

  P1P4=√6

を満たすようにP4(x,y,z)をおく.

  x^2+y^2+z^2=6

  (x−√6)^2+y^2+z^2=4

  (x−√6/2)^2+(y−√10/2)^2+z^2=6

  (x−√6)^2+6−x^2=4

  −2√6x=−8,x=4/√6=2√6/3

  y^2+z^2=6−8/3=10/3

  (y−√10/2)^2+z^2=6−1/6=35/6

  −√10y+10/4+10/3=35/6

  −√10y=(70−30−40)/12=0

  y=0

  z^2=10/3

P1(0,0,0)

P2((√6)/2,(√10)/2,0)

P3(√6,0,0)

P4(2√6/3,0,√30/3)

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