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Article #13577

Re: Please teach me this question.

#13577
From: Kouichi Kumon
Date: Sun, 21 Jul 1996 00:00
65 lines
2859 bytes
In article <960721084908.2014@pcvan.or.jp> CXM64862@pcvan.or.jp writes:
>   $B2<5-$N#2Bj$N;d$NEz0F$N8m$j$r;XE&$7$F$/$@$5$$!#LdBj=8$H2rEz$,0[$J$j!"(B
> $B<+J,$G:NE@$G$-$J$$$N$G$9!#(B

$B9TNs$OK:5Q$NH`J}$K$"$k$N$G!"LdBj(B2$B$O%Q%9!#LdBj(B1$B$NJ}$@$1!"!"(B

$B<c43$N%?%$%W%_%9$H!"M>J,$J<j4V$r3]$1$F$$$^$9$,!"K\<AE*$J4V0c$$$O(B
$B$J$$$h$&$K;W$$$^$9!#(B


> $B!ZLdBj#1![!JEl5~=PHG?7?t3X%9%?%s%@!<%I1i=,$h$jH4?h!K(B
> $B!!(Ba,b,c,d$B$O(Bc$B!b(B0, d$B!b(B0$B$NM-M}?t$G!"(B
>	     SQR(2)a+b
>	   --------------
>	     SQR(2)c+d
> $B$bM-M}?t$G$"$k$H$-!"(Bad-bc$B$NCM$r5a$a$h!#(B
> ----------------------------------------------------------------------
> $B!ZLdBj#1$N;d$NEz0F![(B

>	     SQR(2)a+b      m
>	   -------------- = ---    (m,n$B$O8_$$$KAG$J@0?t(B, m,n$B!b(B0)$B$H$*$/!#(B
>	     SQR(2)c+d      n
>
>     <=>  n(SQR(2)a+b)=m(SQR(2)c+d)
>     <=>  SQR(2)(an-bm)+bn-dm=0
		     $B",(Bcm$B$N%?%$%W%_%9$M!#(B
>
>    a,b,c,d$B$OM-M}?t$h$j!"(Ban-cm=0, bn-dm=0
>	 $B$h$C$F(Ban=cm , dm=bn
>	 $B$h$C$F(Badmn=bcmn
>	       (ad-bc)mn=0
>	 m,n$B!b(B0$B$h$j(B ad-bc=0$B!JEz!K(B
>
>    m=0$B$N$H$-L@$i$+$K(Ba=0,b=0 $B$G$3$N>l9g$b@.$jN)$D!#(B

$B2sEz$,0[$J$k$H8@$&$N$O!">e$N(B($BEz(B)$B$,0c$&$N$+!">ZL@2aDx$,0c$&$N$+(B
$B$N$I$A$i$G$7$g$&$+!"(B($BEz(B)$B$O$"$C$F$$$k$H;W$&$N$@$1$l$I!)(B

$B$A$J$_$KM>J,$J<j4V$H8@$C$?$N$O!"(B
m/n $B$H$*$$$?;~$K(Bm != 0$B$N2>Dj$r$*$$$?$3$H!#(B
n != 0$B$@$1$G!"?J$a$?J}$,C1=c$K$J$j$^$9!#(B

$B$D$^$j!"(Ban = cm, dm = bn$B$+$i!"(B
	a = cm/n, b = dm/n
$B$K$J$j!"$3$l$r(Bad-bc$B$KBeF~$9$k$H!"(B
	ad-bc = cdm/n - cdm/n = 0
$B$H$J$j!"(Bm != 0$B$N2>Dj$OITMW$K$J$j$^$9!#(B

$BJL$N>ZL@J}K!$H$7$F$O!"85$N<0$NJ,Jl$rM-M}2=$7$F!"(B
$B!tM-M}2=$9$k:]$KJ,JlJ,;R$K3]$1$kCM$,(B0$B$K$J$i$J$$$3$H$O<($9$H$7$F$b!"(B

(2ac - bd) + (bc - ad)sqrt(2)
-----------------------------
	2 c^2  - d ^ 2

$B$K$7$F!"(Bsqrt(2)$B$N78?t(B(bc - ad)/(2 c^2 - d^2) $B$,(B0$B$G$J$1$l$P$J$i$J$$$H$7(B
$B$F!">ZL@$9$kJ}K!$b$"$k$G$7$g$&$,!"Ez0F$H$7$F<($5$l$?J}K!$G==J,$K@5$7$$(B
$B$H;W$$$^$9$h!#(B

$B!t$H$s$G$b$J$$Mn$77j$,$"$k$N$+$J!)(B
--
			$B5WLg9L0l!w(BP$B%W%m%8%'%/%HIt(B.$BIY;NDL8&5f=j(B
			kumon@flab.fujitsu.co.jp
			$BBeI=(B 044-777-1111
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Message-ID: <KUMON.96Jul21164836@asami.flab.fujitsu.co.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <960721084908.2014@pcvan.or.jp>

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X-Google-Language: Japanese,JIS
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From: kumon@proc.flab.fujitsu.co.jp (Kouichi Kumon)
Subject: Re: Please teach me this question.
Date: 1996/07/21
Message-ID: <KUMON.96Jul21164836@asami.flab.fujitsu.co.jp>
X-Deja-AN: 169171844
distribution: fj
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sender: news@proc.flab.fujitsu.co.jp
references: <960721084908.2014@pcvan.or.jp>
organization: Fujitsu Laboratories Ltd., ...
reply-to: kumon@flab.fujitsu.co.jp
newsgroups: fj.sci.math