■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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