■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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