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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