■葉序らせん(その28)

  A(0,0,1/2)

  B(0,0,−1/2)

  C(0,√3/2,0)

  D(√(2/3),√3/6,0)

  E(−√(2/3),√3/6,0)

  A(0,0,1/2)

  C(0,√3/2,0)

  D(√(2/3),√3/6,0)

  F(α,β,γ)

  G(ξ,η,ζ)

 y軸の回りに回転させると

  A(−s/2,0,c/2)

  B(s/2,0,c/2)

  C(0,√3/2,0)

  D(c√(2/3),√3/6,s√(2/3))

  E(−c√(2/3),√3/6,s√(2/3))

  A(−s/2,0,c/2)

  C(0,√3/2,0)

  D(c√(2/3),√3/6,s√(2/3))

  F(αc−γs,β,αs+γc)

  G(ξc−ζs,η,ξs+ζc)

  O(0,y,0)

 △ADFの重心Hは

  H((α+√(2/3))/3,(β+√3/6)/3,(γ+1/2)/3)

G(ξ,η,ζ)はC+2CHで与えられる.

CH=((α+√(2/3))/3,(β+√3/6)/3−√3/2,(γ+1/2)/3)

2CH=(2(α+√(2/3))/3,2(β+√3/6)/3−√3,2(γ+1/2)/3)

C+2CH=(2(α+√(2/3))/3,2(β+√3/6)/3−√3/2,2(γ+1/2)/3)

AF^2=1

CF^2=1

DF^2=1

α=2√6/9=2√2/3√3

β=2√12/9=4/3√3

γ=√6α−1/2=12/9−1/2=5/6

ξ=2(5/3・√(2/3))/3=10/9・√(2/3)

η=2(4/3√3+1/2√3)/3−√3/2=11/9√3−3/2√3=−5/18√3

ζ=2(γ+1/2)/3=8/9

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