■拡張ワイソフ記号(その7)

 {4}(11)と{4}(12)で比較してみたい.ak=1

 y0=1,y2=0

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【1】{4}(11)

 y0−y1=λ

 y1/√2−y2/√2=λ→y1=√2λ

 1−√2λ=λ→λ=√2−1

 y1=2−√2,y2=0

 x1=2−√2,x2=0

 1−y1=√2−1,1−y2=1

  h0=Σ(1,n)aj^2(1−yj)/{Σ(1,n)aj^2}^1/2

=(√2−1+1)/√2=1

  h1=Σ(2,n)aj^2(1−yj)/{Σ(2,n)aj^2}^1/2

=1/1=1

  S=(4s0h0+s1h1)/2

しかし,s0,s1がわからないので

  S1=4−2x1^2=4−4(3−2√2)=8√2−4

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【2】{4}(12)

 y0−y1=λ

 y1/√2−y2/√2=2λ→y1=2√2λ

 1−2√2λ=λ→λ=(2√2−1)/7

 y1=(8−2√2)/7,y2=0

 x1=(8−2√2)/7,x2=0

 1−y1=(2√2−1)/7,1−y2=1

  h0=Σ(1,n)aj^2(1−yj)/{Σ(1,n)aj^2}^1/2

=((8−2√2)/7+1)/√2=15/√2−2/7

  h1=Σ(2,n)aj^2(1−yj)/{Σ(2,n)aj^2}^1/2

=1/1=1

  S=(4s0h0+s1h1)/2

しかし,s0,s1がわからないので

  S2=4−2x1^2=4−2(72−32√2)/49=(52+64√2)/49

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【3】体積比

 体積比S2/S1は

  (52+64√2)/49/(8√2−4)

=(52+64√2)(8√2−4)/49・112

=(816+160√2)/49・112

 この体積比を,Π(1−yk)を使って表せるか?

  (2√2−1)/7/(√2−1)

=(2√2−1)(√2−1)/7

=(5−3√2)/7  (NG)

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