■等面単体の体積(その246)
P1P2=P2P3=P3P4=2
P1P3=P2P4=√6
P1P4=√6
P1(0,0,0,0)
P2(2,0,0,0)
P4(1,√5,0,0)
はこれを満たす.
P3(x,y,z,0)
とおくと,
x^2+y^2+z^2=6
(x−2)^2+y^2+z^2=4
(x−1)^2+(y−√5)^2+z^2=4
(x−2)^2+6−x^2=4
−4x+4+6=4,x=3/2
1/4+y^2+z^2=4
1/4+(y−√5)^2+z^2=4,y=(√5)/2,z=(√10)/2
P1(0,0,0,0)
P2(2,0,0,0)
P3(3/2,(√5)/2,(√10)/2,0)
P4(1,√5,0,0)
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