ΥڡϤƤʥ֥åޡɲΥڡޤϤƤʥ֥åޡ Υڡlivedoor åפɲΥڡޤlivedoor å

ܼ

Ϥ

桼åɤθ߽ˡˤꡢa,bФƼΩġ

  • a=bq_1~+~r_1͡\frac{a}{b}=q_1~+~\frac{r_1}{b}=q_1~+~\frac{1}{\frac{b}{r1}}
  • b=r_1~q_2~+~r_2͡\frac{b}{r_1}=q_2~+~\frac{r_2}{r_1}=q_2~+~\frac{1}{\frac{r_1}{r_2}}
  • r_1=r_2~q_3~+~r_3͡\frac{r_1}{r_2}=q_3~+~\frac{r_3}{r_2}=q_3~+~\frac{1}{\frac{r_2}{r_3}}
  • r_{n-2}=q_n~r_{n-1}~+~r_n͡\frac{r_{n-2}}{r_{n-1}}=q_n~+~\frac{r_n}{r_{n-1}}=q_n~+~\frac{1}{\frac{r_{n-1}}{r_n}}
  • rn-1=rnqn+1͡rn-1/rn=qn+1

ơμǹԤäƤΤϡʬʬri-1ʬridz껻ơʬqi+11꾮ͭʬri+1/riʬͭʬ0ǤʤФεտȤǤ롣
r-1=ar0=bȤ롣

äơͭa/bϼΤ褦ѷǤ롣

\frac{a}{b}=q_1+\frac{1}{\frac{b}{r_1}}=q_1+\frac{1}{q_2+\frac{1}{\frac{r_1}{r_2}}}~=\cdots=q_1+\frac{1}{q_2+\frac{1}{q_3~+~\cdots~\frac{1}{q_n~+~\frac{1}{q_{n+1}}}}}

Ϣʬ

[]ͭa/bημɽȤa/bϢʬŸȤ
ημϢʬȤ
ϢʬϼΤ褦ˤɽǤʻ󡢴άΤˡ

a/b=[q1 ; q2,q3,,qn,qn+1]

ͭϢʬ̵Ϣʬ

ͭϢʬŸ

[]ϢʬŸȤͭ¤ιǻߤޤΤͭϢʬȸƤ֡ǤϤʤΤ̵ϢʬȤ

[]ͭͭϢʬδط
(1)ͭϢʬͭϢʬǤ롣
(2)ͭϢʬͭǤ롣

[]

(1)桼åɤθ߽ˡͭ²Υƥåפǽλ뤿ᡣ

(2)ͭϢʬ̾ʬηѷǤΤǡ餫ͭǤ롣

̵ϢʬŸ

[]̵̵Ϣʬδط
(1)̵Ϣʬ̵ϢʬǤ롣
(2)̵Ϣʬ̵Ǥ롣

[]̵ͭϢʬδطФơжä

¿ϢʬŸ

۴ĤϢʬ

㡧2=[1;2,2,2,]

㡧3=[1;1,2,1,2,]

\phi~=~\frac{1+~\sqrt{5}}{2}Ȥ:1ϲȸƤФˡ

=[1;1,1,1,]

[]ĤιबޤȤޤäƷ֤ϢʬΤȤ۴ϢʬȤ֤Ǿʬ۴ηȤ

[]ǽιफ۴ĤΤ۴ϢʬȤǤϤʤ۴Ϣʬ۴ϢʬȤ
ϰ̣ʤΤǡ1ʬ۴ĤΤ۴ϢʬȤ

[]饰󥸥
¿xФơx۴ϢʬŸ뤳Ȥȡx2̵Ǥ뤳ȤƱͤǤ롣

[]axοȤ롣ΤȤx=[a;a,a,]x衣

۴ĤʤϢʬ

㡧=[3;7,15,1,292,1,1,1,2,1,3,]

ʾΤ褦ˡ§ĤʤϢʬǤ롣

㡧e=[1;1,2,1,1,4,1,1,6,]

eϵ§ϢʬǤ롣

[]ʬҤ1ǤϤʤϢʬñϢʬȤޤǤϤʤϢʬñǤʤϢʬȤ

ʸ

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