■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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