HDTenEightyP/NetNews huggingface dataset:
From: suzuki@qwerty.creo-rd.co.jp (Toshitaka Suzuki)
Subject: Re: Quiz
Reply-To: suzuki@creo-rd.co.jp.UUCP (Toshitaka Suzuki)
Organization: CREO R&D Co., Ltd. Tokyo Japan
Distribution: fj
Date: Fri, 21 Aug 1992 10:29:51 GMT

$BNkLZ!w%/%l%*#R!u#D$G$9!#(J

In article <matznaga.714119387@amadeus> matznaga@mozart.pu-toyama.ac.jp (Matznaga martin Hitoshi) writes:
>>>{ a^2 + b^2 | a, b $B$O@0?t(J }
>
>>$B$3$l$O;d$K$O$h$/$o$+$j$^$;$s$,!"$?$V$s9g$C$F$$$k$N$G$7$g$&!#(J
>
>$B$=$l$O!"$=$&$G$9$h!#(J
>$B3J;RE@$rD:E@$K;}$D@5J}7A$H$$$&$N$O(J (0,0) $B$H(J (a,b) $B$r7k$VD>@~$r#1JU$H(J
>$B$9$k@5J}7A$H8+$F$$$$$s$@$+$i!"$=$NLL@Q$O(J $B%T%?%4%i%9$NDjM}$+$i(J 
>a^2+b^2 $B$G$9!#(J

$B4V$K$"$C$?J8$r>J$+$J$$$G2<$5$$$h!#(J
$B;d$@$C$F!"!V(J{ a^2 + b^2 | a, b $B$O@0?t(J }$B!W$0$i$$$O$o$+$j$^$9$h!#$=$l$,(J
$B$o$+$i$J$-$c!"?tNs$r=P$9$N$5$(BgJQ$G$7$g$&!)(J
$B;d$,!V$h$/$o$+$i$J$$!W$N$O!"(J

In article <NAGAE.92Aug14000534@ipc4.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:
>$B%,%&%9$N@0?t$N%N%k%`$N=89g$G$9$M!%(J
>$B%,%&%9$N@0?t$NC19`%$%G%"%k$N%N%k%`$N=89g$+$J!$(J0$B$,$J$$$+$i!%(J

$B$3$l$G$9$h!#=,$C$?3P$($b$J$$$7!#(J


$BNkLZ!!=S9'!J(Jsuzuki@creo-rd.co.jp$B!K(J
$B3t<02q<R%/%l%*%"!<%k%"%s%I%G%#!!El5~ET9A6h<G(J5-1-13$B!!F|=;6b;0ED%S%k#93,(J
TEL 03-3454-9302$B!J3+H/ItD>DL!K!?(J03-3454-1330$B!JBeI=!K(J  FAX 03-3454-1372
From: asdf@tansei.cc.u-tokyo.ac.jp (Asdf)
Newsgroups: fj.sci.math
Subject: Re: Quiz
Date: 14 Aug 92 12:48:23 GMT
Distribution: fj
Organization: Computer Centre, University of Tokyo
In-reply-to: suzuki@creo-rd.co.jp's message of 6 Aug 92 03:31:58 GMT

In article <1992Aug6.033158.26509@creo-rd.co.jp> suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:

>$BLdBj(J
>  $B2<5-$N?tNs$G!"8e$KB3$/?t$O(J$B!)(J  $B$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
>
>    1  2  4  5  8  9  10  13  16  17  18  20  $B!&!&!&(J
>    $B!JL5(J$B8B$KB3$-$^$9!K(J

$B3J;RE@$rD:E@$K;}$D@5J}7A$KFb@\$9$k(J
$B3J;RE@$rD:E@$K;}$D@5J}7A$NLL@Q(J

$B$J$s$F$I$&$+$J(J?
--
                  -------------------------------------------------------
                  $B1J0f!!?5(J$B0l!!!!!!!!!!El5~Bg3X!!Lt3XIt!!LtIJ@=B$9)3X65<<(J
                  Nagai Shin-ich    E-mail:asdf@tansei.cc.u-tokyo.ac.jp
                  -------------------------------------------------------
From: r2230@L8221C.rtri.or.jp (Shingo Matsumoto)
Newsgroups: fj.sci.math
Subject: Re: Quiz
Date: 19 Aug 92 00:00:39 GMT
Reply-To: r2230@L8221C.rtri.OR.JP (Shingo Matsumoto)
Distribution: fj
Organization: Railway Technical Research Institute, Tokyo, Japan

$@>>K\!w#J#RAm8&(J

In article <TSHINGO.92Aug13161339@sysipi.sys.titech.ac.jp> tshingo@sys.titech.ac.jp (Shingo Takahashi) writes:
>   >$@LdBj(J
>   >  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
>   >
>   >    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
>   >    $@!JL58B$KB3$-$^$9!K(J
>
>$@!VBh#19`$+$iBh(Jr$@9`$^$G$,(J a1,a2,...,ar $@$G$"$k?tNs!W$OL58B$K$"$j$^$9!#Nc(J
>$@$($P!"(J
$@!JCfN,!K(J
>$@!V=c?h$K!W?t3X$NLdBj$H$$$&$3$H$G$9$,!"$b$7$=$&$J$i$P>r7o$r$D$1$?J}$,$h(J
>$@$$$H;W$$$^$9!#(J

$@5.J}$N8@$$J,$O$b$C$H$b$G$9$,!"$=$l$G$OG$0U$NM-8B8D$NMWAG$r<($7$F(J
$@$=$N?tNs$r$"$i$o$9$3$H$,!"$G$-$J$/$J$C$F$7$^$$$^$9!#(J
$@!J$b$7!"@53N$K5-=R$9$k$H$9$l$P!"$=$N?tNs$r@8@.$9$k%"%k%4%j%:%`$r(J
$@5-=R$;$M$P$J$k$^$$!#!K(J
$@$3$3$O!V>o<1E*$K!W9M$($F$[$7$$$b$N$G$9!#(J

$@>>K\??8c!!E4F;Am9g5;=Q8&5f=j(J
From: tah@coins.is.tsukuba.ac.jp (Takahiko HORIUCHI)
Newsgroups: fj.sci.math
Subject: Re: smartness of sequence (was Re: Quiz)
Date: 20 Aug 92 13:30:22 GMT
Reply-To: tah@wslab.is.tsukuba.ac.jp (Takahiko HORIUCHI,[WISDOM],5052)
Distribution: fj
Organization: Wisdom Systems Lab., U. of Tsukuba, Tsukuba-City, Ibaraki, Japan

$@KYFb!w?t3XAG?M$G$9!%(J
$@$I$&$b$3$N<j$NLdBj$O!$$d$i$:$K$$$i$l$J$$!%!%!%(J

On 08/20/92(19:44) tacchan@flab.fujitsu.co.jp (Tatsuo KONDO) wrote
in <TACCHAN.92Aug20194452@topor.soft.flab.fujitsu.co.jp> (fj.sci.math:1525/coins):
 |$@$&$C$7$^$C$?!<(J(^.^;;;)
 |$@#2HVL\$N""$OITMW$G$9(J(_ _;)

$@$@$C$?$s$G$9$+!%$H$$$&$3$H$O!$(J
0,1,2,4,5,8,<a>,14,17,26,40,41,44,53,80,<b>,122 $@$NB3$-$O(J



<a>=13
<b>=121
125,134,161,242,364,365,368,377,404,485,728,... $@$G$9$+!)(J

$@$&!A$s!%2?$N?tNs$@$m$&!%(J
$@A02sF1MM!$;d$K$O%(%l%,%s%H$JEz$($,J,$+$i$J$$!%(J

$@!!!!!!!!!!!!!!!!!!!!!!!!(J     tah@wslab.is.tsukuba.ac.jp
Newsgroups: fj.sci.math
From: suzuki@qwerty.creo-rd.co.jp (Toshitaka Suzuki)
Subject: Re: Quiz
Reply-To: suzuki@creo-rd.co.jp.UUCP (Toshitaka Suzuki)
Organization: CREO R&D Co., Ltd. Tokyo Japan
Distribution: fj
Date: Fri, 14 Aug 1992 08:27:41 GMT

In article <TSHINGO.92Aug13161339@sysipi.sys.titech.ac.jp> tshingo@sys.titech.ac.jp (Shingo Takahashi) writes:
>$B!V=c?h$K!W?t3X$NLdBj$H$$$&$3$H$G$9$,!"$b$7$=$&$J$i$P>r7o$r$D$1$?J}$,$h(J
>$B$$$H;W$$$^$9!#(J

$B;d$,!V=c?h$K!W?t3X$NLdBj$H8@$C$?$N$O!"JL$K!V?t3XE*$J7W;;$K$h$C$F=P$k$@$1(J
$B$GFC$K0UL#$,$J$$?tNs$G$"$k!W$H$$$&$3$H$G$O$J$/!"!V?t3XE*$K7W;;$9$k$3$H$,(J
$B=PMh$k!W$H$$$&$3$H$G$9!#$3$NLdBj$O!"0l1~!V%/%$%:!W$G$9$+$i!"?tNs$K$O$A$c(J
$B$s$H0UL#$,$"$j$^$9$N$G!"$=$N0UL#$rEz$($FM_$7$$$N$G$9!#(J
$B$J$*!"@52r$OJ#?t$"$k$+$bCN$l$^$;$s$,!";d$,9M$($F$$$kEz$O$b$A$m$s@52r$H(J
$B$7$F!"$b$7$=$l$h$j$b%(%l%,%s%H$J2rEz$,$"$l$P$=$l$b@52r$H$9$k$3$H$K$7$^(J
$B$7$g$&!#(J


In article <gYaEF.tah@coins.is.tsukuba.ac.jp> tah@wslab.is.tsukuba.ac.jp (Takahiko HORIUCHI,[WISDOM],5052) writes:
>$B?t3XITF@0U$J$s$G!$%Q%:%kE*$J5-=R$G$4$a$s$J$5$$!%(J
>
>$B$^$:!$<+A3?t$r#2>h$7$^$9!%#a!'!P(J1,4,9,16,25,...$B!Q(J
>$B$3$N=89g#a$NG$0U$N#2$D$N?t$r2C;;$7$^$9!%!J<+J,<+?H$G$b$h$$!K(J
>$BB>?M$H2C;;#b!'!P(J5,10,13,17,20,25,26,...$B!Q(J
>$B<+J,$H2C;;#c!'!P(J2,8,18,32,...$B!Q(J
>
>$B#a(JU$B#b(JU$B#c$N=89g$r!$>:=g$KJB$Y$??tNs$G$O!)(J

$B7k2LE*$K?tNs$O$=$&$$$&?tNs$K$J$j$^$9$N$G!"!V8e$KB3$/?t$O!)!W$KBP$7$F(J
$B@52r$r:9$7>e$2$^$9!#(J
$B$7$+$7!"!V$I$s$J5,B'$N?tNs$G$7$g$&!)!W$NEz$H$7$F$O!"$$$^0l$D$-$l$$$J(J
$BEz$G$O$"$j$^$;$s$h$M!#$3$l$,@52r$@$C$?$iLdBj$H$7$FLLGr$/$J$$$G$9$M!#(J
$B<B$O$b$&>/$7$-$l$$$JEz$,$"$C$F!"$=$N7k2L?tNs$O>e5-$N$h$&$K$J$k$o$1$G!"(J
$B$=$3$,LdBj$G$9!#(J

$BNkLZ!!=S9'!J(Jsuzuki@creo-rd.co.jp$B!K(J
$B3t<02q<R%/%l%*%"!<%k%"%s%I%G%#!!El5~ET9A6h<G(J5-1-13$B!!F|=;6b;0ED%S%k#93,(J
TEL 03-3454-9302$B!J3+H/ItD>DL!K!?(J03-3454-1330$B!JBeI=!K(J  FAX 03-3454-1372
From: koshi@okds1.osaka-kyoiku.ac.jp (Kunio Koshigiri)
Newsgroups: fj.sci.math
Subject: Re: smartness of sequence (was Re: Quiz)
Date: 21 Aug 92 09:35:00 GMT
Distribution: fj
Organization: Osaka Kyoiku University

In article <TACCHAN.92Aug19135640@topor.soft.flab.fujitsu.co.jp> tacchan@flab.fujitsu.co.jp (Tatsuo KONDO) writes:
>
> $BJV2N$J$i$LJVLd!'<!$N""$K$O!"$I$s$J?t$,F~$k$G$7$g$&!)(J
>                 $B$^$?!"?tNs$N5,B'$O!)(J
> 0, 1, 2, 4, 5, 8, $B""(J, 14, 17, 26, 40, 41, $B""(J, 44, 53, 80, $B""(J, 122, ...

$B1[6M!wBg:e650iBg(J

$B$3$l$^$G$N3'$5$s$NEz$r8+$F$N46A[$G$9!#(J

     0                            0
	1  2                        1    2
   4  5  8                  11    12    22
  13 14 17 26             111   112   122   222
 40 41 44 53 80        1111  1112  1122  1222  2222
121 122 ...         11111 11112 ...

$B;0?JK!$KD>$7$F;03Q7A$K$J$i$Y$k$HH~$7$$!#(J

K. Koshigiri
koshi@cc.osaka-kyoiku.ac.jp
From: tah@coins.is.tsukuba.ac.jp (Takahiko HORIUCHI)
Newsgroups: fj.sci.math
Subject: Re: Quiz
Date: 13 Aug 92 11:20:22 GMT
Reply-To: tah@wslab.is.tsukuba.ac.jp (Takahiko HORIUCHI,[WISDOM],5052)
Distribution: fj
Organization: Wisdom Systems Lab., U. of Tsukuba, Tsukuba-City, Ibaraki, Japan

$@KYFb!wC^GHBg$G$9!%(J

On 08/06/92(12:31) suzuki@creo-rd.co.jp (Toshitaka Suzuki) wrote
in <1992Aug6.033158.26509@creo-rd.co.jp> (fj.sci.math:1506/coins):

 |$@LdBj(J
 |  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
 |
 |    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
 |    $@!JL58B$KB3$-$^$9!K(J
 |
$@?t3XITF@0U$J$s$G!$%Q%:%kE*$J5-=R$G$4$a$s$J$5$$!%(J

$@$^$:!$<+A3?t$r#2>h$7$^$9!%#a!'!P(J1,4,9,16,25,...$@!Q(J
$@$3$N=89g#a$NG$0U$N#2$D$N?t$r2C;;$7$^$9!%!J<+J,<+?H$G$b$h$$!K(J
$@B>?M$H2C;;#b!'!P(J5,10,13,17,20,25,26,...$@!Q(J
$@<+J,$H2C;;#c!'!P(J2,8,18,32,...$@!Q(J

$@#a(JU$@#b(JU$@#c$N=89g$r!$>:=g$KJB$Y$??tNs$G$O!)(J

                                     $@KYFb!w$D$/$P(J
$@!!!!!!!!!!!!!!!!!!!!!!(J tah@wslab.is.tsukuba.ac.jp
Newsgroups: fj.sci.math
From: tshingo@sys.titech.ac.jp (Shingo Takahashi)
Subject: Re: Quiz
Organization: Tokyo Institute of Technology, Yokohama, Japan.
Distribution: fj
Date: Thu, 13 Aug 1992 07:13:39 GMT

$@9b66!w(J$@El9)Bg$G$9!#(J

In article <1992Aug13.014435.16718@creo-rd.co.jp> suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:

   >$@LdBj(J
   >  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
   >
   >    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
   >    $@!JL58B$KB3$-$^$9!K(J

$@!VBh#19`$+$iBh(Jr$@9`$^$G$,(J a1,a2,...,ar $@$G$"$k?tNs!W$OL58B$K$"$j$^$9!#Nc(J
$@$($P!"(J

  $@0lHL9`(J an=\sum_{k=1}^{r}Sk,

                    ak(n-1)(n-2)$@!D(J(n-k+1)(n-k-1)$@!D(J(n-r+1)(n-r)  
         $@$?$@$7(J Sk=--------------------------------------------
                       (k-1)(k-2)$@!D!&(J1$@!&(J(-1)$@!D(J(k-r)

$@$J$I$G$9!#!J$3$l$rMxMQ$9$l$PBh(Jr+1$@9`(J$@$K9%$-$J?t$r$b$C$F$3$i$l$k!#!K(J

$@!V=c?h$K!W?t3X$NLdBj$H$$$&$3$H$G$9$,!"$b$7$=$&$J$i$P>r7o$r$D$1$?J}$,$h(J
$@$$$H;W$$$^$9!#(J
--
            $@El5~9)6HBg3XBg3X1!Am9gM}9)3X8&5f2J%7%9%F%`2J3X@l96(J
                        $@9b66(J $@??8c(J  
Newsgroups: fj.sci.math
From: matznaga@mozart.pu-toyama.ac.jp (Matznaga martin Hitoshi)
Subject: Re: Quiz
Organization: TOYAMA Prefecutural University
Distribution: fj
Date: 18 Aug 1992 06:29:47 GMT

$@IY;38)N)Bg3X$N>>1J$G$9!#(J

suzuki@qwerty.creo-rd.co.jp (Toshitaka Suzuki) writes:
>In article <ASDF.92Aug14230128@tansei2.tansei.cc.u-tokyo.ac.jp> asdf@tansei.cc.u-tokyo.ac.jp (Asdf) writes:

>>$@3J;RE@$rD:E@$K;}$D@5J}7A$NLL@Q(J

$@$*$*!"$J$k$[$I!#(J

>In article <NAGAE.92Aug14000534@ipc4.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:

>>{ a^2 + b^2 | a, b $@$O@0?t(J }

>$@$3$l$O;d$K$O$h$/$o$+$j$^$;$s$,!"$?$V$s9g$C$F$$$k$N$G$7$g$&!#(J

$@$=$l$O!"$=$&$G$9$h!#(J
$@3J;RE@$rD:E@$K;}$D@5J}7A$H$$$&$N$O(J (0,0) $@$H(J (a,b) $@$r7k$VD>@~$r#1JU$H(J
$@$9$k@5J}7A$H8+$F$$$$$s$@$+$i!"$=$NLL@Q$O(J $@%T%?%4%i%9$NDjM}$+$i(J 
a^2+b^2 $@$G$9!#(J

>$@$7$+$7!"#0$N07$$$HC1=cL@2r$5$H$$$&E@$G$OA0<T$NJ}$,>/$7$$$$$G$9$M!#(J

$@E@$K=LB`$7$?@5J}7A$NLL@Q(J 0 $@$r?tNs$KF~$l$l$P!"$$$C$7$g$G$9$M!#(J
-- 
		$@>>1J(J $@6Q!wAm9g8&5f=j(J.$@IY;38)N)Bg3X(J
		matznaga@pu-toyama.ac.jp
From: nagae@an.isl.titech.ac.jp (Takanori Nagae)
Newsgroups: fj.sci.math
Subject: Re: Quiz
Date: 13 Aug 92 15:05:34 GMT
Reply-To: nagae@an.isl.titech.ac.jp
Distribution: fj
Organization: Imaging Science and Engineering Lab., Tokyo Inst. of Tech., Japan
In-reply-to: suzuki@creo-rd.co.jp's message of 13 Aug 92 01:44:35 GMT

In article <1992Aug13.014435.16718@creo-rd.co.jp> suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:

|>$@LdBj(J
|>  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N(J$@?tNs$G$7$g$&!)(J
|>
|>    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J
|>    $@!JL58B$KB3$-$^$9!K(J
|
|$@$3$l$K$D$$$F!"$[$H$s$IH?1~$,$"$j$^$;$s$N$G!"%R%s%H$r=P$9$3$H$K$7$^$9!#(J
|
|$@0J2<$K%R%s%H$,=q$$$F$"$j$^$9(J$@!#(J

|(2) $@?tNs$O!"A08e4X78$,$"$k$o$1$G$O$J$/!"$"$k=89g$r>:=g$KJB$Y$?$b$N$G$9!#(J
                                         ^^^^^^^^^^^^^^^^^^^^^^^^^^
$@$"$C(J!

{ a^2 + b^2 | a, b $@$O@0?t(J }

$@$G$7$g$&!%$U$U$U!%(J
$@%,(J$@%&%9$N@0?t$N%N%k%`$N=89g$G$9$M!%(J
$@%,%&%9$N@0?t$NC19`%$%G%"%k$N%N%k%`$N=89g$+$J!$(J0$@$,$J$$$+$i!%(J

# $@$*$\$s(J$@$/$i$$$O%]%9%H$7$J$$$G$*$3$&$H;W$C$?$N$K$#!%!%(J
_  __  __
 ][  ][  ]$@1J9>(J $@9'5,(J nagae@an.isl.titech.ac.jp
[__][__][_ $@El9)Bg(J $@A|>pJs9)3X8&5f;\@_(J $@0B5o1!8&(J
From: matsuno@ainec1.lab.toyodenki.co.jp (MATSUNO Yoshiaki)
Newsgroups: fj.sci.math
Subject: drawing a N-dimensional cube (In Japanese/Kanji)
Date: 20 Aug 92 09:57:02 GMT
Followup-To: fj.sci.math
Distribution: fj
Organization: TOYO Denki Seizo K.K., Kanagawa, Japan


  $@$A$O$d$V$k(J $@$G$9!#(JN $@<!85D6N)J}BN$r?^$KI=$9OC$G$9!#(J
$@!t(J $@$3$3$O=i$a$F$G$9$M!#?t3X6l<j$@$C$?$7(J...

  $@D9$5$,(J N $@%S%C%H$N%S%C%HNsA4BN$N=89g$r(J B(N) $@$H$7$^$9!#EvA3!$(JN > 0 $@$G(J
$@$9!#Nc$($P!$(J
	B(3) = { 000, 001, 010, 011, 100, 101, 110, 111 }
$@$H$J$j$^$9!#<B:]$K07$C$F$$$k$N$O(J N $@$,?tI4$+$i?t@i$/$i$$$N>l9g$G$9!#(J
  x $@$,%S%C%HNs$G$"$k$H$-!$#1$NN)$C$F$$$k%S%C%H$N?t$r(J
	ones(x)
$@$GI=$9$3$H$K$7$^$9!#(JB(N) $@$NItJ,=89g(J B(M,N) $@$r(J
	B(M,N) = { x | x \in B(N), ones(x) = M }
$@$GDj5A$7$^$9!#$?$@$7!$(J0 <= M <= N $@$G$"$k$H$7$^$9!#(J

  B(N) $@$O(J N $@<!85D6N)J}BN$ND:E@A4BN$HF10l;k$G$-$^$9!#(JB(M,N) $@$NMWAG(J x $@$N(J
$@<~0O$r8+EO$9$H!$NY$j9g$&D:E@$K$O(J B(M-1,N) $@$H(J B(M+1,N) $@$NMWAG$,JB$s$G$$(J
$@$^$9!#$$$A$P$s6a$$(J B(M,N) $@$NMWAG$XJU$r$?$I$C$F9T$/$K$O!$$$$C$?$s(J 
B(M-1,N) $@$+(J B(M+1,N) $@$NMWAG$r7PM3$9$k$3$H$K$J$j$^$9!#MW$9$k$K%O%_%s%0(J
$@5wN%$,#2$N$H$3$m$K$"$k$o$1$G$9$+$i!#(JB(M,N) $@$OD6N)J}BN>e!$BS>e$KJB$s$G(J
$@$$$k$H9M$($F$$$$$s$G$7$g$&!$$?$V$s!#(J(?_?)

  $@$G!$$3$&$$$&!$$"$k(J B(M,N) $@$NMWAG$N<~JU$NMM;R$r?^$K$7$h$&$H;W$&$N$G$9(J
$@$,!$$I$&$9$l$PM}2r$7$d$9$$?^$K$J$k$N$+$o$+$j$^$;$s!#%"%$%G%"$,$"$C$?$i!$(J
$@65$($F$/$@$5$$!#$h$m$7$/$*4j$$$7$^$9!#(J
--
$@$A$O$d$V$k(J
From: ytanaka@icot.or.jp (Yuichi TANAKA)
Newsgroups: fj.sci.math
Subject: Re: Quiz
Date: 22 Aug 92 13:30:17 GMT
	<NAGAE.92Aug14000534@ipc4.an.isl.titech.ac.jp>
	<ASDF.92Aug14230128@tansei2.tansei.cc.u-tokyo.ac.jp>
	<1992Aug17.034250.14853@creo-rd.co.jp>
Distribution: fj
Organization: Institute for New Generation Computer Technology (ICOT)

In article <1992Aug17.034250.14853@creo-rd.co.jp>
suzuki@qwerty.creo-rd.co.jp (Toshitaka Suzuki) writes:

 > # $B!V3J;RE@$rD:E@$K;}$D@5#n3Q7A!J#n!b#4!K!W$OB8:_$7$J$$$N$+$J!)(B
 > 
 > $BNkLZ!!=S9'!J(Bsuzuki@creo-rd.co.jp$B!K(B
 > $B3t<02q<R%/%l%*%"!<%k%"%s%I%G%#!!El5~ET9A6h<G(B5-1-13$B!!F|=;6b;0(B$BED%S%k#93,(B
 > TEL 03-3454-9302$B!J3+H/ItD>DL!K!?(B03-3454-1330$B!JBeI=!K(B  FAX 03-3454-1372

$BL@$i$+$K!"<!85$r(B$B>e$2$l$P!J(B3$B<!85$G==J,!K#n!a(B3$B$H(B6$B$N(B
$B>l9g$b(BOK$B$G$"$k$3$H$,$o$+$j$^$9!#(B

$B$5$i$K!"$3$l0J30$N#n!J!f(B3$B!K$N>l9g(B$B$O!"2?<!85$KKd$a(B
$B9~$s$G$b3J;RE@>e$K>h$i$J$$$3$H$,4JC1$K>ZL@$G$-$^$9!#(B

$B$G$O0lHL$K!"#m<!85$N3J;RE@$r9M(B$B$($?$H$-!";03Q7A$N(B
$BD:E@$,3J;RE@>e$K>h$k$?$a$N!J;03Q7A$N7A>u$N!KI,MW(B
$B==J,>r7o$O2?$G$7$g$&$+!)(B $B$3$l$O7k(B$B9=0U30$J7A$N>r7o$K(B
$B$J$k$N$G6C$+$5$l$^$9!#Ez$($OK?2J3X;o$N(B11$B7n9f$K:\$j(B
$B$^$9$N$G$*3Z$7$_$K!#(B

--
$BEDCf(B $BM5(B$B0l(B     ( ytanaka@icot.or.jp )
$B!J:b!K?7@$Be%3%s%T%e!<%?5;=Q3+H/5!9=(B $BBh#68&5f<<(B       TEL: 03-3456-3194
 $B")(B108  $BEl5~ET9A6h;0ED(B 1-4-28  $B;0ED9q:]%S%k(B 21F       FAX: 03-3456-1618
From: mizusaki@otsl.oki.co.jp
Newsgroups: fj.sci.math
Subject: Re: Quiz
Date: 19 Aug 92 03:07:01 GMT
Reply-To: mizusaki@otsl.oki.co.jp
Distribution: fj
Organization: Oki Technosystems Laboratory Inc., Nagoya, Japan.
In-reply-to: suzuki@qwerty.creo-rd.co.jp's message of 17 Aug 92 03:42:50 GMT

$B?e:j!w#O#T#S#L$G$9!#(B

In article Message-ID: <1992Aug17.034250.14853@creo-rd.co.jp>
 suzuki@qwerty.creo-rd.co.jp (Toshitaka Suzuki) writes:

> >{ a^2 + b^2 | a, b $B$O@0?t(B }
> >
> >$B$G$7$g$&!%$U$U$U!%(B
> >$B%,%&%9$N@0?t$N%N%k%`$N=89g$G$9$M!%(B
> >$B%,%&%9$N@0?t$NC19`%$%G%"%k$N%N%k%`$N=89g$+$J!$(B0$B$,$J$$$+$i!%(B
> 
> $B$3$l$O;d$K$O$h$/$o$+$j$^$;$s$,!"$?$V$s9g$C$F$$$k$N$G$7$g$&!#(B
> $B$7$+$7!"#0$N07$$$HC1=cL@2r$5$H$$$&E@$G$OA0<T$NJ}$,>/$7$$$$$G$9$M!#(B

$B$"$l!"A4$/F1$8$@$H;W$$$^$9$,!#(B
  
  
  
                                     $B?e:j(B  $BBs(B
                                     mizusaki@otsl.oki.co.jp
                                     $B2-%F%/%N%7%9%F%`%:%i%\%i%H%j(B
                                     $B8&5fItBhFs8&5f<<(B
From: tacchan@flab.fujitsu.co.jp (Tatsuo KONDO)
Newsgroups: fj.sci.math
Subject: Re: smartness of sequence (was Re: Quiz)
Date: 20 Aug 92 10:44:52 GMT
	<FURUTA.92Aug20182054@srarc2.sra.CO.JP>
Distribution: fj
Organization: Fujitsu Laboratories Ltd., Kawasaki, Japan.
In-reply-to: furuta@srarc2.sra.CO.JP's message of 20 Aug 92 09:20:52 GMT

$@6aF#!wIY;NDL8&(J$@$G$9!#(J

In article <FURUTA.92Aug20182054@srarc2.sra.CO.JP>
furuta@srarc2.sra.CO.JP (Atsushi Furuta) writes:

:>    $@$&$&!"$o$+$j$^$;$s!#(J(;_;) ^^ $@$N(J $@""(J $@$,$J$$$H$9$k$H!"$=$l$i$7$-2rEz$O(J
:>  $@8+$D$1$i$l$?$N$G(J$@$9$,!D(J

$@$&$C$7$^$C$?!<(J(^.^;;;)
$@#2HVL\$N""$OITMW$G$9(J(_ _;)


:>    $@$A$J$_$K!";d$N9M$($?$H$3$m$G$O:G=i(J$@$N(J $@""(J $@$O(J 13, $@:G8e$N(J $@""(J $@$O(J 121 $@$@$C(J
:>  $@$?$s$G$9$,!"$"$C$F$^$9$+!)(J

$@0J2<(J rot13/47 :-)
$@SQSrSuS/ShPRd[qV(J$@S3odSfSSSz_4SSSQS;S/SjSDPR(J

$@!t(J  $@@52r$OMh=5F,$/$i$$$K%]%9%H$7$^$9!#(J
-----
	$@6aF#!wIY;NDL8&(J
From: mohta@necom830.cc.titech.ac.jp (Masataka Ohta)
Newsgroups: fj.sci.math
Subject: Delauny interpolation
Date: 19 Aug 92 08:42:54 GMT
Distribution: fj
Organization: Tokyo Institute of Technology

$@!!0JA0!"#3<!85$N%5%s%W%kE@$N4V$NJd4V$NOC$7$,$3$3$G$G$F$^$7$?$,!"4XO"Ej9F(J
$@$,$"$j$^$7$?$N$G!"E>:\$7$F$*$-$^$9!#(J

					$@B@ED!!>;9'(J
					mohta@cc.titech.ac.jp
>From: watson@maths.uwa.oz.au (David Watson)
Newsgroups: comp.graphics,sci.math
Subject: Re: Delaunay Interpolation
Keywords: surface interpolation, Delaunay triangulation, CAGD
Date: 19 Aug 92 00:28:55 GMT
Organization: University of Western Australia


pjt@newton.cs.jhu.edu (Paul Tanenbaum) writes:

>     Suppose I have a bunch of sample points from the boundary of a closed
>volume in $R^3$.  Suppose in particular that I have been given the Delaunay
>triangulation of these boundary points.  I'd like to interpolate a $C^3$
>surface through these vertices.  The related surface-interpolation algorithms
>I've found seem not to be applicable:  they either assume that the
>triangulation is regular (usually of degree six) or that the surface is
>monotonic with respect to some plane.
>     Does there exist an algorithm to solve this problem?  References to
>the literature would be greatly appreciated.

There are many ways to interpolate from a Delaunay tesselation.  The quickest
is with barycentric coordinates but is only $C^0$.  If you require higher
smoothness then it is a question of data set size - for 100 data or so just
fit a radial basis spline.  If you must deal with subsets, splines will
give discontinuities at subset boundaries.  Sibson's natural neighbour
interpolation -
Sibson, R., 1981, A brief description of natural neighbour interpolation, _in_ 
Barnett, V., ed., Interpreting multivariate data: John Wiley, p.21--36.
Alfield, P., 1989, Scattered data interpolation in three or more 
variables, _in_ Mathematical methods in computer aided geometric 
design, Lyche, T., and Schumaker, L.L., ed., Academic Press, San Diego,
p. 12-13.
Watson, D.F., and Philip, G.M., 1987, Neighborhood-based interpolation: Geobyte, 2(2),
p. 12--16.
will provide continuous slopes everywhere but at the data points themselves.
Incorporating estimated gradients will give total continuity.

For a summary of interpolation techniques that can be extended to higher
dimensions, see
	ftp marlin.nosc.mil /pub/contour.file
for an ASCII, TeX, or PostScript, file.

Email questions are welcome.
--
Dave Watson                          Internet: watson@maths.uwa.edu.au
Department of Mathematics            
The University of Western Australia               Tel: (61 9) 380 3359
Nedlands, WA 6009  Australia.                     FAX: (61 9) 380 1028


Newsgroups: fj.sci.math
From: matznaga@mozart.pu-toyama.ac.jp (Matznaga martin Hitoshi)
Subject: Re: Quiz
Organization: TOYAMA Prefecutural University
Distribution: fj
Date: 17 Aug 1992 06:47:40 GMT

$@IY;38)N)Bg3X$N>>1J$G$9!#(J

suzuki@creo-rd.co.jp (Toshitaka Suzuki) writes:
>$@NkLZ!w%/%l%*#R!u#D$G$9!#(J
>$@#1=54VA0$K;d$,=P$7$?LdBj(J

>>  $@2<5-$N?tNs$G!"8e$KB3$/?t$O!)(J  $@$^$?!"$I$s$J5,B'$N?tNs$G$7$g$&!)(J
>>
>>    1  2  4  5  8  9  10  13  16  17  18  20  $@!&!&!&(J

$@%+%s%K%s%0$r$7$^$7$?!#(J
A Handbook of Integer Sequence (Academic Press) $@$K$h$l$P!"(J

1 2 4 5 8 19 10 13 16 17 18 20 

$@$O(J The sum of 2 squares $@$@$=$&$G$9!#(J
$@<!$N?t$O(J 25 $@$@$=$&$G!";29MJ88%$,#2$D$"$,$C$F$$$^$7$?!#(J

Euler $@$N(J "Opera Omnia" 1911  Vol 1 pp 417  $@5Z$S(J
Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen,
	Series A. Vol 53 pp 872

$@$G$9!#(J

$@!t2?$,=q$$$F$"$k$N$+C/$+D4$Y$F$/$l$k$H$&$l$7$$$J(J

$@$A$J$_$K!"$3$NK\$K(J 1 2 4 5 $@$G$O$8$^$k?tNs!JM-8B$N$b$N$r4^$`!K$O(J
14$@8D:\$C$F$$$^$7$?!#(J
-- 
		$@>>1J(J $@6Q!wAm9g8&5f=j(J.$@IY;38)N)Bg3X(J
		matznaga@pu-toyama.ac.jp
Newsgroups: fj.sci.math
From: suzuki@qwerty.creo-rd.co.jp (Toshitaka Suzuki)
Subject: Re: Quiz
Reply-To: suzuki@creo-rd.co.jp.UUCP (Toshitaka Suzuki)
Organization: CREO R&D Co., Ltd. Tokyo Japan
Distribution: fj
Date: Mon, 17 Aug 1992 03:42:50 GMT

In article <ASDF.92Aug14230128@tansei2.tansei.cc.u-tokyo.ac.jp> asdf@tansei.cc.u-tokyo.ac.jp (Asdf) writes:
>$B$"$l!)$=$&$9$k$H!"(J
>
>$B3J;RE@$rD:E@$K;}$D@5J}7A$NLL@Q(J
>
>$B$@$1$G$$$$$N$+$J!)!J<+?.$O$J$$!#!K(J

$B@52r$G$9!#$3$l$,!";d$N9M$($F$$$?2rEz$=$N$b$N$G$9!#(J

# $B<B$O!"%H%$%l$G:B$C$F$$$k;~$K>2$N%^%9L\$r8+$F$$$F;W$$$D$$$?$N$G$7$?(J(^_^;)


In article <NAGAE.92Aug14000534@ipc4.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:
>$B$"$C(J!
>
>{ a^2 + b^2 | a, b $B$O@0?t(J }
>
>$B$G$7$g$&!%$U$U$U!%(J
>$B%,%&%9$N@0?t$N%N%k%`$N=89g$G$9$M!%(J
>$B%,%&%9$N@0?t$NC19`%$%G%"%k$N%N%k%`$N=89g$+$J!$(J0$B$,$J$$$+$i!%(J

$B$3$l$O;d$K$O$h$/$o$+$j$^$;$s$,!"$?$V$s9g$C$F$$$k$N$G$7$g$&!#(J
$B$7$+$7!"#0$N07$$$HC1=cL@2r$5$H$$$&E@$G$OA0<T$NJ}$,>/$7$$$$$G$9$M!#(J


# $B!V3J;RE@$rD:E@$K;}$D@5#n3Q7A!J#n!b#4!K!W$OB8:_$7$J$$$N$+$J!)(J

$BNkLZ!!=S9'!J(Jsuzuki@creo-rd.co.jp$B!K(J
$B3t<02q<R%/%l%*%"!<%k%"%s%I%G%#!!El5~ET9A6h<G(J5-1-13$B!!F|=;6b;0ED%S%k#93,(J
TEL 03-3454-9302$B!J3+H/ItD>DL!K!?(J03-3454-1330$B!JBeI=!K(J  FAX 03-3454-1372
Newsgroups: fj.sci.math