■葉序らせん(その77)

 (その76)の計算では

  A(x,0,-b)

  D(x,0,b)

  C(-x,1/2,0)

  B(-x,-1/2,0)

  A(x,bs,-bc)

  D(x,-bs,bc)

  C(-x,c/2,s/2)

  B(-x,-c/2,-s/2)

  O(ξ,0,0)

  A(x-ξ,bs,-bc)

  D(x-ξ,-bs,bc)

  C(-x-ξ,c/2,s/2)

  B(-x-ξ,-c/2,-s/2)

  E(α-ξ,-γs,γc)

  O(0,0,0)

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cos(∠COD)=(-x^2+ξ^2-bsc/2)/{((x-ξ)^2+b^2s^2)((x+ξ)^2+c^2/4)}^1/2

cos(∠BOC)=((x+ξ)^2-c^2/4)/((x+ξ)^2+c^2/4))

cos(∠AOB)=(-x^2+ξ^2-bsc/2)/{((x-ξ)^2+b^2s^2)((x+ξ)^2+c^2/4)}^1/2

cos(∠AOD)=((x-ξ)^2-b^2s^2)/((x-ξ)^2+s^2))

cos(∠AOC)=(-x^2+ξ^2+bsc/2)/{((x-ξ)^2+b^2s^2)((x+ξ)^2+c^2/4)}^1/2

cos(∠BOD)=(-x^2+ξ^2+bsc/2)/{((x-ξ)^2+b^2s^2)((x+ξ)^2+c^2/4)}^1/2

cos(∠DOE)=((x-ξ)(α-ξ)+bγs^2)/{(x-ξ)^2+b^2s^2)((α-ξ)^2+γ^2s^2)}^1/2

∠COD=∠AOB,∠AOC=∠BODとなる.

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