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Article #13710

Re: [Q] Fractional approximation of a solution 'a' of a^4-a^2-1=0

#13710
From: H'Osamu
Date: Wed, 26 Jun 1996 00:00
38 lines
1974 bytes
$@$H$"$kK\$GFI$s$@$N$G$9$,!JCf;35A(J$@:nCx!X?t$N@$3&!Y3$LD<R4)!K!"(J

>	 a = $@"e(J(($@"e(J5 $@!^(J 1) / 2)
>	   = 1.272019649... , 0.786151377...
>$@$@$+$i(J$@!"(J
>	 127/100,1272/1000....

$@$3$N>l9g!"6a;wCM$N8m:9$N8B3&$O(J 1/($@J,Jl(J) $@DxEY!#(J
$@$7$+$7!"!VO"J,?tE83+!W$J$k(J$@$b$N$r1~MQ$9$k$H!"8m:9$N8B3&$,(J
$@$5$i$K>.$5$/$J$k$=$&$G$9!#(J
$@Nc$H$7$F!"(Jsqrt(2) $@$rJ,?t6a;w$9$k>l9g!#(J

sqrt(2)-1 = 1/(sqrt(2)+1)
	   = 1/(2+(sqrt(2)-1))
	   = 1/(2+1/(sqrt(2)+1))
	   = 1/(2+1/(2+(sqrt(2)-1)))
	   = 1/(2+1/(2+1/(sqrt(2)+1)))
	   = 1/(2+1/(2+1/(2+(sqrt(2)-1))))
	   = 1/(2+1/(2+1/(2+1/(sqrt(2)+1))))
	   = 1/(2+1/(2+1/(2+1/(2+(sqrt(2)-1))))),

$@0J2<!"F1MM$K$7$F!"<!<0$rF@$^$9!#(J

sqrt(2)   = 1 + 1/(2+1/(2+1/(2+1/(2+1/(2+1/(2+...))))))

$@$3$NL58BO"J,?t$rE,Ev$J9`$GBG$A@Z$C$FF@$i$l$kJ,?t$r!"(Jsqrt(2) $@$N(J
$@6a;wCM$H$9$k>l9g!"8m:9$N8B3&$O(J 1/($@J,Jl(J)**2 $@DxEY$J$s$@$=$&$G$9!#(J

$@>e=R$N!X?t$N@$3&!Y$O!"2J3X7<LX;(;o(J$@!J2J3XD+F|!)(J $@?t3X%;%_%J!<!)!K$N(J
$@O":\J8$r$^$H$a$?K\$@$=$&$G$9!#O"J,?tE83+$N8m:9$K4X$9$k>ZL@$^$G$O(J
$@:\$C(J$@$F$$$^$;$s$G$7$?!#(J

a = $@"e(J(($@"e(J5 $@!^(J 1) / 2) $@$N>l9g$O!VFs=E:,9f!W$K$J$C$F$$$^$9$M!#(J
$@$I$&$d$C$FO"J,?tE83+(J$@$9$l$PNI$$$G$9$+$M(J (^^;)
--
HOSHINO.OSAMU@EIC.ERI.TODAY
[TEL] +81-3-3812-2111 Ex.5774
[E-Mail] o3m@eri.u-tokyo.ac.jp
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From: o3m@eri.u-tokyo.ac.jp (H'Osamu)
Subject: Re: [Q] Fractional approximation of a solution 'a' of a^4-a^2-1=0
Date: 1996/06/26
Message-ID: <O3M.96Jun26150246@igamo.eri.u-tokyo.ac.jp>
X-Deja-AN: 162423710
references: <4qoijp$gj@inetgw.gb.sankyoseiki.co.jp>
supersedes: <O3M.96Jun26144205@igamo.eri.u-tokyo.ac.jp>
organization: Earthquake Research Institute, University of Tokyo, Tokyo, Japan.
reply-to: o3m@eri.u-tokyo.ac.jp
newsgroups: fj.sci.math