■等面単体の体積(その389)
n=6の場合,
P0(√(1/2),0,√(1/2),1,√3)
P1(0,0,0,0,0)
P2(√2,√3,0,0,0)
P3(√8,0,0,0,0)
P4(√(9/2),0,√(9/2),0,0)
P5(√2,0,√2,2,0)
を
P0(m√(1/2),0,m√(1/2),m,m√3,h)
P1(0,0,0,0,0,0)
P2(0,0,0,0,0,6h)
P3(m√2,m√3,0,0,0,5h)
P4(m√8,0,0,0,0,4h)
P5(m√(9/2),0,m√(9/2),0,0,3h)
P6(m√2,0,m√2,2m,0,2h)
としてみる.
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P0P1^2=5m^2+h^2
P0P2^2=5m^2+25h^2
P0P3^2=8m^2+16h^2
P0P4^2=9m^2+9h^2
P0P5^2=8m^2+4h^2
P0P6^2=5m^2+h^2
P1P2^2=36h^2
P1P3^2=5m^2+25h^2
P1P4^2=8m^2+16h^2
P1P5^2=9m^2+9h^2
P1P6^2=8m^2+4h^2
P2P3^2=5m^2+h^2
P2P4^2=8m^2+4h^2
P2P5^2=9m^2+9h^2
P2P6^2=8m^2+16h^2
P3P4^2=5m^2+h^2
P3P5^2=8m^2+4h^2
P3P6^2=9m^2+9h^2
P4P5^2=5m^2+h^2
P4P6^2=8m^2+4h^2
P5P6^2=5m^2+h^2
5m^2+h^2(6)<5m^2+25h^2(2)
8m^2+4h^2(5)<8m^2+16h^2(3)
9m^2+9h^2(4)
25h^2(1)
P0P1=P1P2=P2P3=P3P4=P4P5=P5P6=√6
P0P2=P1P3=P2P4=P3P5=P4P6=√10
P0P3=P1P4=P2P5=P3P6=√12
P0P4=P1P5=P2P6=√12
P0P5=P1P6=√10
P0P6=√6
5m^2+h^2=36h^2=6,h^2=1/6,m^2=7/6
8m^2+4h^2=10
9m^2+9h^2=12
8m^2+16h^2=12
5m^2+4h^2=10
h^2=1/6,m^2=7/6はこれらを満たす.
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