α=[a0:a1,a2,・・・]

λ=[an+1:an+2,an+3,・・・]+[0:an,an-1,・・・,a1]

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α=Φのとき

λ＞[1:1,1,1,・・・]+[0:1,1,1,・・・,1]→φ+φ-1＝√5

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α=1+√2のとき

λ＞[2:2,2,2,・・・]+[0:2,2,2,・・・,2]→1+√2+√2-1＝√8

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α=(3+√13)/2のとき

λ＞[3:3,3,3,・・・]+[0:3,3,3,・・・,3]→(3+√13)/2+(-3+√13)/2＝√13

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α=(9+√221)/10=[2:2,1,1,2,2,1,1,・・・]のとき

λ＞[2:2,1,1,2,2,1,1,・・・]+[0:1,1,2,2,1,1,2,2,・・・,2]→(9+√221)/10+(-9+√221)/10＝√221/5

x=[2:2,1,1,2,2,1,1,・・・]

y=[0:1,1,2,2,1,1,2,2,・・・]=1/(1+1/(1+1/x))=1/(1+1/(x+1)/x)=1/(1+x/(x+1))=(x+1)/(2x+1)=(-9+√221)/10

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α=(√3)=[1:1,2,1,2,1,2,・・・]のとき

λ＞[2:1,2,1,2,・・・]+[0:1,2,1,2,・・・,1]→1+(√3)-1+√3＝√12

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α=(9√3+65)/22

(9√3+65)/22-3=(9√3-1)/22

22/(9√3-1)=(9√3+1)/11

(9√3+1)/11-1=(9√3-10)/11

11/(9√3-10)=(9√3+10)/13

(9√3+10)/13-1=(9√3-3)/13

13/(9√3-3)=(9√3+3)/18

(9√3+3)/18-1=(9√3-15)/18

18/(9√3-15)=(9√3+15)

(9√3+15)-30=(9√3-15)

1/(9√3-15)=(9√3+15)/18

(9√3+15)/18-1=(9√3-3)/18

18/(9√3-3)=(9√3+3)/13

(9√3+3)/13-1=(9√3-10)/13***

13/(9√3-10)=(9√3+10)/11

(9√3+10)/11-2=(9√3-12)/11

11/(9√3-12)=(9√3+12)/9

(9√3+12)/9-3=(9√3-15)/9

9/(9√3-15)=(9√3+15)/2

(9√3+15)/2-15=(9√3-15)/2

2/(9√3-15)=(9√3+15)/9

(9√3+15)/9-3=(9√3-12)/9

9/(9√3-12)=(9√3+12)/11

(9√3+12)/11-2=(9√3-10)/11

11/(9√3-10)=(9√3-10)/13***

α=(9√3+65)/22=[3:1,1,1,30,1,1,2,3,15,3,2,3,15,3,2,3,15,3,・・・]

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λ＞[2:3,15,3,・・・]+[0:3,15,3,2,・・・]

あるいは[3:15,3,2,・・・]+[0:2,3,15,3,・・・]かもしれない

x=[3:15,3,2,・・・]= 3+1/(15+1/(3+1/(2+1/x))

= 3+1/(15+1/(3+x/(2x+1))

= 3+1/(15+(2x+1)/(7x+3))

= 3+(7x+3)/(107x+46)

=(328x+141)/(107x+43)

x(107x+43)=(328x+141)

107x^2-285-141=0

x={285+(285^2+4・107・141)^1/2}/214=3.09

y=1/(2+1/(3+1/(15+1/x))

y=1/(2+1/(3+x/(15x+1))

y=1/(2+(15x+1)/(46x+3))

y=(46x+3)/(107x+7)=0.44

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