■等面単体の体積(その158)
5次元正単体(辺の長さ1)
(−1/2,−√3/6,−√6/12,−√10/20,−√15/30)
(+1/2,−√3/6,−√6/12,−√10/20,−√15/30)
(0,√3/3,−√6/12,−√10/20,−√15/30)
(0,0,√6/4,−√10/20,−√15/30)
(0,0,0,0,√10/5,−√15/30)
(0,0,0,0,0,√15/6)
を平行移動させる
A(0,0,0,0,0,0)
B(1,0,0,0,0,a)
C(1/2,√3/2,0,0,0,2a)
D(1/2,√3/6,√6/3,0,0,3a)
E(1/2,√3/6,√6/3,√10/4,0,4a)
F(1/2,√3/6,√6/3,√10/4,√15/5,5a)
G(0,0,0,0,0,6a)
b^2=1+a^2
c^2=1+4a^2
d^2=1+9a^2
e^2=1+16a^2
f^2=1+25a^2
6a=fとおくと,
36a^2=1+25a^2,a^2=1/11
b^2=12/11,c^2=15/11,d^2=20/11,e^2=27/11,f^2=36/11
6a=eとおくと,
36a^2=1+16a^2,a^2=1/20
b^2=21/20,c^2=24/20,d^2=29/20,e^2=36/20,f^2=45/20
6a=dとおくと,
36a^2=1+9a^2,a^2=1/27
b^2=28/27,c^2=31/27,d^2=36/27,e^2=43/27,f^2=52/27
6a=cとおくと,
36a^2=1+4a^2,a^2=1/32
b^2=33/32,c^2=36/32,d^2=41/32,e^2=48/32,f^2=57/32
6a=bとおくと,
36a^2=1+a^2,a^2=1/35
b^2=36/35,c^2=39/35,d^2=44/35,e^2=51/35,f^2=60/35
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