■葉序らせん(その130)

  A(0,0,b)

  B(0,0,−b)

  C(0,h,0)

  D(x,y,0)

  E(−x,y,0)

  F(α,β,γ)

AC^2=h^2+b^2=1

AD^2=x^2+y^2+b^2=1

CD^2=x^2+(y−h)^2=1

x^2+y^2−2yh+h^2=1

1−b^2−2yh+h^2=1

b^2=−2hy+h^2

y=(h^2−b^2)/2h=(2h^2−1)/2h

y^2=(2h^2−1)^2/4h^2

x^2=h^2−y^2

−b^2=x^2+y^2−1

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 F(α,β,γ)の計算は以下の通りである.

 △ACDの重心Gは

  A(0,0,b)

  C(0,h,0)

  D(x,y,0)

  G(x/3,(h+y)/3,b/3)

F(α,β,γ)はB+2BGで与えられる.

BG=(x/3,(h+y)/3,b/3+b)

2BG=(2x/3,2(h+y)/3,8b/3)

B+2BH=(2x/3,2(h+y)/3,5b/3)=F(α,β,γ)

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