■ABCからDEへ(その33)

 421の基本単体の頂点は,ρについて

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

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

P2(1,1/√3,0,0,0,0,0,0)

P3(1,1/√3,1/√6,0,0,0,0,0)

P4(1,1/√3,1/√6,1/√10,0,0,0,0)

P5(1,1/√3,1/√6,1/√10,1/√15,0,0,0)

P6(1,1/√3,1/√6,1/√10,1/√15,1/√21,0,0)

P7(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,0)

P7(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,√(9/4))

について,

  cosθ=−b1^2/{b1^2}^1/2{b1^2+b2^2}^1/2

  cosθ=−b2^2/{b1^2+b2^2}^1/2{b2^2+b3^2}^1/2

  cosθ=−b3^2/{b2^2+b3^2}^1/2{b3^2}^1/2

などを計算する.

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  cosθ=−1/{1}^1/2{1+3}^1/2=−1/2

  cosθ=−3/{1+3}^1/2{3+6}^1/2=−3/6

  cosθ=−6/{3+6}^1/2{6+10}^1/2=−6/12

  cosθ=−10/{6+10}^1/2{10+15}^1/2=−10/20

  cosθ=−15/{10+15}^1/2{15+21}^1/2=−15/30

  cosθ=−21/{15+21}^1/2{21+28}^1/2=−21/42・・・ここまでは60°

  cosθ=−28/{21+28}^1/2{28+4/9}^1/2=−28/7/(256/9)^1/2=−4・3/16=−3/4***

  cosθ=−4/9/{28+4/9}^1/2{4/9}^1/2=−2/3/(256/9)^1/2=−2/3・3/16=−1/8

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