■葉序らせん(その45)
A(−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)
DE,CGは
(y−√3/6)^2+2c^2/3
=(y−√3/2)^2
=(y−η)^2+(ξc−ηs)^2
y^2−y√3/3+1/12+2c^2/3
=y^2−y√3+3/4
=y^2−2ηy+η^2+ξ^2c^2−2ξηcs+η^2s^2
√3y−1+c^2=0
(2η−√3)y+3/4−η^2−ξ^2c^2+2ξηcs−η^2s^2
√3y=s^2
このあとが続かない.
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A,C,Fは
y^2+s^2/4=(y−√3/2)^2=(y−β)^2+(αc−γs)^2
=y^2−√3y+3/4
=y^2−2βy+β^2+(αc−γs)^2
4√3y+s^2−3=0
このあとが続かない.
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4√3y=4s^2
4√3y=3−s^2
s^2=3/5,c^2=2/5,y=√3/5
cos(∠AOC)=−9/50/{3/25+s^2/4)^1/2・3√3/10
=−9/50/{3/25+3/20)^1/2・3√3/10
=−9/50/(27/100)^1/2・3√3/10
=−9/50/27/100=−18/27=−2/3 (OK)
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