■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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