■葉序らせん(その64)

  H(√6/9,2√3/9,1/6)

  I(0,√3/6,0)

  J(5√6/27,11√3/54,4/9)

に間違いは見つからない.中心軸をHに映しても同じだろうか?

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 H(0,0,0)

 I(-3√6/27,-3√3/54,-3/18)

 J(2√6/27,-√3/54,5/18)

 H(0,0,0)

 I(-3c√6/27+3s/18,-3√3/54,-3s√6/27--3c/18)

 J(2c√6/27-5s/18,-√3/54,2s√6/2+5c/18)

 O(0,y,0)

y^2=(-3c√6/27+3s/18)^2+(y+3√3/54)^2

=(2c√6/27-5s/18)^2+(y+√3/54)^2

2916y^2

(-6c√6/54+9s/54)^2+(y+3√3/54)^2

=(4c√6/54-15s/54)^2+(y+√3/54)^2

2916y^2=(-6c√6+9s)^2+(54y+3√3)^2

=(4c√6-15s)^2+(54y+√3)^2

0=216c^2-108sc√6+81s^2+324√3y+27

=96c^2-120sc√6+225s^2+108√3y+3

=288c^2-360sc√6+675s^2+324√3y+9

72c^2-252sc√6+594s^2-18=0

4c^2-14sc√6+33s^2-1=0

4(1-s^2)-14sc√6+33s^2-1=0

3-14sc√6+29s^2=0

3+29s^2=14sc√6

9+174s^2+841s^4=1176s^2(1-s^2)

9-1002s^2+2017s^4=0

s^2=501±(251001-18153)^1/2/2017 (無理数)

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