■等面単体の体積(その388)
n=5の場合,
P0(1/2,(√5)/2,0,(√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)
を
P0(m/2,m√5/2,0,m√10/2,h)
P1(0,0,0,0,0)
P2(0,0,0,0,5h)
P3(2m,0,0,0,4h)
P4(3m/2,m√5/2,m√10/2,0,3h)
P5(m,m√5,0,0,2h)
としてみる.
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P0P1^2=4m^2+h^2
P0P2^2=4m^2+16h^2
P0P3^2=6m^2+9h^2
P0P4^2=6m^2+4h^2
P0P5^2=4m^2+h^2
P1P2^2=25h^2
P1P3^2=4m^2+16h^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=6m^2+4h^2
P4P5^2=4m^2+h^2
4m^2+h^2(5)<4m^2+16h^2(2)
6m^2+4h^2(4)<6m^2+9h^2(3)
25h^2(1)
P0P1=P1P2=P2P3=P3P4=P4P5=√5
P0P2=P1P3=P2P4=P3P5=√8
P0P3=P1P4=P2P5=3
P0P4=P1P5=√8
P0P5=√5
4m^2+h^2=25h^2=5,h^2=1/5,m^2=6/5
6m^2+4h^2=8
6m^2+9h^2=9
4m^2+16h^2=8
h^2=1/5,m^2=6/5はこれらを満たす.
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