■葉序らせん(その82)

  b=.443818の計算について再考.

  A(0,0,b)

  B(0,0,−b)

  C(0,h,0)

  D(x,y,0)

  E(−x,y,0)

  F(α,β,γ)

  G(ξ,η,ζ)

h^2+b^2=1

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=h^2

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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 y軸の回りに回転させると

  A(−bs,0,bc)

  B(bs,0,bc)

  C(0,h,0)

  D(xc,y,xs)

  E(−xc,y,−xs)

  F(αc−γs,β,αs+γc)

  G(ξc−ζs,η,ξs+ζc)

  O(0,Y,0)

AO^2=BO^2=Y^2+b^2s^2

CO^2=(Y−h)^2

DO^2=EO^2=(Y−y)^2+x^2c^2

では,xy平面への投影を考えている.

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