■葉序らせん(その114)

 z軸回りには,回転させないので,cc=1,sc=0

[ca・cb,−sa,ca・sb]

[sa・cb,+ca,sa・sb]

[−sb,0,cb]

A(ca・sb/2,sa・sb/2,cb/2)

B(−ca・sb/2,−sa・sb/2,−cb/2)

F(ca・cb)2√6/9+(−sa)4√3/9+(ca・sb)5/6,

(sa・cb)2√6/9+(+ca)4√3/9+(sa・sb)5/6,

(−sb)2√6/9+(cb)5/6)

AB^2=(ca・sb)^2+(sa・sb)^2=(sb)^2

AF^2={(ca・cb)2√6/9+(−sa)4√3/9+(ca・sb)2/6}^2

+{(sa・cb)2√6/9+(+ca)4√3/9+(sa・sb)2

/6}^2

=(cb)^224/81+48/81+(sb)^2/9+2(ca・cb)2√6/9(ca・sb)2/6+2(sa・cb)2√6/9(sa・sb)2/6}^2

=(cb)^224/81+48/81+(sb)^2/9+2(cb・sb)2√6/9・2/6

sb=s,cb=cとおくと,

s^2=24(1−s^2)/81+48/81+s^2/9+sc4√6/27

s^2(1+24/81−1/9)−72/81=sc4√6/27

s^296/81−8/9=sc4√6/27

96s^2−72=sc12√6

12s^2−6=sc√6

36(2s^2−1)^2=6s^2(1−s^2)

6(2s^2−1)^2=s^2(1−s^2)

25s^4−25s^2+6=0

s^2={25±(625−600)^1/2}/50

s^2=3/5,2/5

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[まとめ]これではA,B,Fの座標がわからない.

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