■ABCからDEへ(その52)

D6,ρについて

P0(0,0,0,0,0,0)

P1(1,0,0,0,0,0)

P2(1,1/√3,0,0,0,0)

P3(1,1/√3,1/√6,0,0,0)

P4(1,1/√3,1/√6,1/√10,0,0)

P5(1,1/√3,1/√6,1/√10,1/√15,0)

P6(1,1/√3,1/√6,1/√10,1/√15,2/√3)

  cosθ=10/{6+10}^1/2{10+15}^1/2=1/2***

  cosθ=15/{10+15}^1/2{15+3/4}^1/2=6/√63

  cosθ=√3/2/{15+3/4}^1/2=√3/63=1/√21

 

σについて

P0(0,0,0,0,0,0)

P1(1,0,0,0,0,0)

P2(1,1/√3,0,0,0,0)

P3(1,1/√3,1/√6,0,0,0)

P4(1,1/√3,1/√6,1/√10,0,0)

P5(1,1/√3,1/√6,1/√10,3/√10,0)

P6(1,1/√3,1/√6,1/√10,3/√10,1/√2)

  cosθ=10/{6+10}^1/2{10+15}^1/2=1/2***

  cosθ=10/{6+10}^1/2{10+10/9}^1/2=5/2・3/10=3/4

  cosθ=10/9/{10+10/9}^1/2{10/9+2}^1/2=10/9・3/10/√28/3=1/√28

  cosθ=√2/{10/9+2}^1/2=√2/√28/9)=3/√14

 

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(その41)(その42)に一致

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