■等面単体の体積(その154)
(その149)では
A(0,0,0,0)
B(1,0,0,a)
C(1/2,√3/2,0,2a)
D(1/2,√3/6,√6/3,3a)
E(0,0,0,4a)
としたが,
A(0,0,0,0)
B(1,1,0,a)
C(1,0,1,2a)
D(0,1,1,3a)
E(0,0,0,4a)
としてみる.
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b^2=2+a^2
c^2=2+4a^2
d^2=2+9a^2
4a=dとおくと,
16a^2=2+9a^2,a^2=2/7
b^2=16/7,c^2=22/7,d^2=32/7
4a=cとおくと,
16a^2=2+4a^2,a^2=1/6
b^2=13/6,c^2=16/6,d^2=21/6
4a=bとおくと,
16a^2=2+a^2,a^2=2/15
b^2=32/15,c^2=38/15,d^2=48/15
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[まとめ]いずれもNG.
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