■葉序らせん(その63)

  H(√6/9,2√3/9,1/6)

  I(0,√3/6,0)

  J(5√6/27,11√3/54,4/9)

 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))

  F(αc−γs,β,αs+γc)

  G(ξc−ζs,η,ξs+ζc)

  O(0,y,0)

  H(c√(2/3)/3−s/6,2√3/9,s√(2/3)/3+c/6)

  H(c√6/9−s/6,2√3/9,s√6/9+c/6)

  I(0,√3/6,0)

  J(5c√6/27−4s/9,11√3/27,5s√6/27+4c/9)

HO^2=IO^2=JO^2

{c√6/9−s/6}^2+(y−2√3/9)^2

=(y−√3/6)^2

={5c√6/27−4s/9}^2+(y−11√3/27)^2

{2c√6/18−3s/18}^2+(18y/18−4√3/18)^2

=(6y/6−√3/6)^2

={5c√6/27−12s/27}^2+(27y/27−11√3/27)^2

1/18^2{{2c√6−3s}^2+(18y−4√3)^2}

=1/6^2(6y−√3)^2

=1/27^2{{5c√6−12s}^2+(27y−11√3)^2}

{{2c√6−3s}^2+(18y−4√3)^2}

=9(6y−√3)^2

24c^2−12sc√6+9s^2+324y^2−144√3y+48

=324y^2−108√3y+27

24c^2−12sc√6+9s^2=36√3y−21

8c^2−4sc√6+3s^2=12√3y−7

81(6y−√3)^2

=4{{5c√6−12s}^2+(27y−11√3)^2}

2916y^2−972√3y+243

=600c^2−480sc√3+576s^2+2916y^2−2376√3y+1452

1404√3y−1209=600c^2−480sc√3+576s^2

468√3y−403=200c^2−160sc√3+192s^2

312c^2−156sc√6+117s^2=468√3y−273

200c^2−160sc√3+192s^2=468√3y−403

112c^2+4sc√3−75s^2=130

112c^2+4sc√3−75(1−c^2)=130

187c^2+4sc√3=205

187c^2−205=4sc√3

34969c^4−76670c^2+42025=48s^2c^2

34969c^4−76670c^2+42025=48(1−c^2)c^2

35017c^4−76718c^2+42025=0

 これよりc^2,s^2,yが求められるはずであるが,D<0となって解をもたない.

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