■サマーヴィルの等面四面体(その475)
負号の間違いはないだろうか?
2tanθtan3θ=1
tan3θ=(3tanθ−tan^3θ)/(1−3tan^2θ)
2tanθtan3θ=(6tan^2θ−2tan^4θ)/(1−3tan^2θ)=1
6tan^2θ−2tan^4θ=1−3tan^2θ
2tan^4θ−9tan^2θ+1=0
tan^2θ=(9±√73)/4・・・あわない
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
2tanθtan4θ=1
も計算してみたい.
tan4θ=(4tanθ−4tan^3θ)/(1−6tan^2θ+tan^4θ)
(8tan^2θ−8tan^4θ)/(1−6tan^2θ+tan^4θ)=1
(8tan^2θ−8tan^4θ)=(1−6tan^2θ+tan^4θ)
9tan^4θ−14tan^2θ+1=0
tan^2θ=(7±√40)/9・・・あわない
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