■等面単体の体積(その400)
(その399)の続き.Q4=Q5
P1(0,0,0,0)
P2(2m,0,0,h)
P3(3m/2,m√5/2,m√10/2,2h)
P4(m,m√5,0,3h)
P5(m,m√5,0,−2h)
としてみると,
P1P2^2=4m^2+h^2
P1P3^2=6m^2+4h^2
P1P4^2=6m^2+9h^2
P1P5^2=6m^2+4h^2
P2P3^2=4m^2+h^2
P2P4^2=6m^2+4h^2
P2P5^2=6m^2+9h^2
P3P4^2=4m^2+h^2
P3P5^2=4m^2+16h^2
P4P5^2=25h^2
4m^2+h^2(3)<4m^2+16h^2(1)
6m^2+4h^2(3)<6m^2+9h^2(2)
25h^2(1)
P1P2=P2P3=P3P4=P4P5=√5
P1P3=P2P4=P3P5=√8
P1P4=P2P5=3
P1P5=√8
より,
4m^2+h^2=25h^2=5→h^2=1/5,m^2=6/5
6m^2+4h^2=4m^2+16h^2=8
6m^2+9h^2=9
h^2=1/5,m^2=6/5はこれらを満たす.
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