ߥƥ
10פäƲġġ(ܤ)

1 á2 cm 12 cm^2
2 á3 cm 27 cm^2
3 á5 cm 75 cm^2
4 á8 cm 192 cm^2
5 á13 cm 507 cm^2
6 á21 cm 1,323 cm^2
7 á34 cm 3,468 cm^2
8 á55 cm 9,075 cm^2
9 á89 cm 23,763 cm^2
10 á144 cm 62,208 cm^2
­ơ101,032 cm^2.
ä礭ͤͽۤƤޤ
ǥե꡼ʤФä᤯ԤΤˡ||
623ڡ 0:05:54 25296
ޥ
ޤޤҤǤϥߥʤɤΤǤ...

ʤߤˤꡢExcelȤƺä...櫓ǤϤޤ󡣤ȡʡ˷׻ˡͤƤäϤΤǤīż֤ǻפǥʤΤǡ¤ϡ֤󤼤ñʷ׻ˡפäꤹΤΤޤ....

ʤߤ1442333äƤΤǸη׻ˤʤޤˡȡ
PowerBook G4 623ڡ 0:06:30 MAIL:masaru-y@sansu.org HomePage:25297
ߥƥ

­ơ100,656 cm^2.
㤦Ȥޤ­㤤ޤ(^^;;
623ڡ 0:06:52 25298
ޥ
ȤǤ̿ΤϵΤʤԤΤϲøǤ礦(^^;;
PowerBook G4 623ڡ 0:07:06 MAIL:masaru-y@sansu.org HomePage:25299
Taro
եܥʥåΰžʤȤ⤫ޤȤ˰ŻǤ󤸤㤢ʤʡ
ޤ˱߼Ψ˺Ƥorz
ľ塡 623ڡ 0:08:20 25300
taku
excelñ˷׻ߥäƤޤ1¿cm^2ͤƤޤ
623ڡ 0:08:38 MAIL:takuo@kcv.ne.jp 25301
ȥȥ
ExcelǤޤȤ⡣
ǤȾ¤¤10ĶȤƤޤ
ʼ˸лԡ 623ڡ 0:09:16 MAIL:h-sakai@zb3.so-net.ne.jp 25302
sugitakukun
Ҥä֤ơԣϣΫäƥǤϲǤm(_ _)m
׻ʤǤ

ǡޥ뤵β򸫤Ǽ
ʤۤɡΤ˾ꤤ׻ˡǤ
ñĤꤽǤ͡

ĤʤȹͤƤˤФǤʥ
623ڡ 0:10:55 MAIL:sugitakuunikun@msn.com 25303

øѤ3*F_(n+1)*F_nF_0=1F_1=1

Ȥ֤äƤȤäФäƤޤä
̤̪ 623ڡ 0:11:22 MAIL:ishizaki@qa.so-net.ne.jp 25304
ߥƥ
995 km^2
5.099510^8 km^2
5.099510^18 cm^2
ʤΤǡ٤׻Ͼʤޤ43øǤ礦
(Ǥ褦ˡȸĿͥǡϿ(^^)
623ڡ 0:11:24 HomePage:ߤ25305
DrK
󤼤Ǥ
nøΤäȤ礭Ⱦ¤AnȤ
פϦAnAn+1
An=(An-1)(An-2)
᤿ΤǤ
ϳڱफ?㤦ʡ 623ڡ 0:12:10 MAIL:satoka@star.odn.ne.jp 25306
ԡᲿ˿
ѤȤΤ˺ƺǽ24äƤޤޤ||
ʡ綥Ͼ졡 623ڡ 0:12:32 HomePage:ԤDzԤ25307

֤ꤹϣԣ
3*(2*1^2+2^2+3^2+5^2+8^2+13^2+21^2+34^2+55^2+89^2+144^2)=100656
Ǥ͡
ƽ 623ڡ 0:13:58 HomePage:θ줳ߤ󡪡25308
CRYING DOLPHIN
ؤΥߤͤΥ󥸡

̿ΤΥηȤȡʤϤΤգcmȤơ
գգαߤᣱꡢ
ѹפࣳᣳ.ĤĶУϣˡ
ʲ̿ΤߤͤĹǤѤ
ߣߣߣߣĤȿܤ
øΣߣϤƣĶ롣
ǯԥ奦ȡ 623ڡ 0:14:25 HomePage:θ³äƤɤΤ餤25309
ԡᲿ˿
#25299 #25305
ϵ峰̿Τǽ⤤ȸơ˹Τ
Ωä褷Ȥˤ
ǽŪˤϼνϤѤڤ줺ǡ
ȡʤäϤƤߤξ細ߤͤΤԲǽ
׻ΤѤǤ͡
긫ƤĤΡ֥ХХ׻פФޤ
ʡ綥Ͼ졡 623ڡ 0:20:39 HomePage:ԤDzԤ25310
ߤ
ξϥ뤸ʤǡø夰餤׻Ǥ
ʤΤ˹Ԥޤ

ˤƤⶲ٤ǽϡ
623ڡ 0:20:47 25311
ߥƥ
>>25310
ѷ׻ʤǤ͡
ޤäŤޤǤ(^^;;
623ڡ 0:21:36 HomePage:ߤ25312
sugitakukun
ǡʤ꤬Ф줿ΤǼ׻³ԡ
ϵɽѤ1.96608*10^19cm^2
ø 2971215053*4807526949*34.3*10^19cm^2
飴ø塩

եܥʥå׻ְäƤǽ硣
Ĥ⤦񤭹ޤƤʡ^^;
623ڡ 0:22:02 MAIL:sugitakuunikun@msn.com 25313
tomh
Fibonacciκǽn(n-2øκȾ¤)
F(n+2)-1ˤʤ뤳ȤȤäƤޤ

89=F(9+2) < 1+(1000000/12)=92.28 < F(10+2)=144

ʤΤǡ10øǤ
ԡ 623ڡ 0:24:21 MAIL:tomh@yahoo.co.jp HomePage:H to M25314
ݤ
#25309
ãĤ˰ɼ
Ǥ͡ݤϼȤäΡȤۤۡ
åŷ񡡡 623ڡ 0:24:27 MAIL:hopes@mba.ocn.ne.jp HomePage:HOPES褤Ȥ٤Ϥ25315
sugitakukun
#25313
äѤְ㤨ɽѽФΤľ»ȤäƤɤʬ
#25305ǤäƤʡ
623ڡ 0:24:51 MAIL:sugitakuunikun@msn.com 25316
ޤ륱
#25311
ʤˡ
623ڡ 0:25:35 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱25317
chitacu
ְä򣳲Ϣ³øˤƤۤλء(
623ڡ 0:31:50 MAIL:t_tomohiro@hotmail.com 25318
ߤ
#25317ʤޤ륱󤵤
줬ȷĤ뤿ˤޤäƤ뤫顢äƤǤġġ
623ڡ 0:36:03 25319
סϺ
׻Ƿ׻ޤ
ʤˤʤϤʤǤ礦
623ڡ 0:54:02 25320

ExcelǤޤȸΤǤPCˤOffice󥹥ȡ
ƤʤΤǡOpenOfficeѤޤ
623ڡ 0:54:48 25321
fumio
Ǥޤ
623ڡ 1:02:51 25322
Ҥܤ
եܥʥåα̣襤ޤ
623ڡ 2:27:18 25323
Ȥ
mupad light 2.5.3 Υޥ2ĤǺѤΰ̹बǤޤ
褺եܥʥå
(((1+sqrt(5))/2)^(i)-((1-sqrt(5))/2)^(i))/sqrt(5)
դǤϥեܥʥåȾ¤DZ߼Ψ3ȤƤѤ
((((1+sqrt(5))/2)^(i)-((1-sqrt(5))/2)^(i))/sqrt(5))^(2)*3
mupad 2.5.3
expand(((((1+sqrt(5))/2)^(i)-((1-sqrt(5))/2)^(i))/sqrt(5))^(2)*3);
ά
sum(%,i=1..n);
3*(3/2-sqrt(5)/2)^(n)/10-3*(-1)^(n)/5
+3*(sqrt(5)/2+3/2)^(n)/10-3*sqrt(5)*(3/2-sqrt(5)/2)^(n)/10
+3*sqrt(5)*(sqrt(5)/2+3/2)^(n)/10
nn+2Ȥ
3*(3/2-sqrt(5)/2)^(n+2)/10-3*(-1)^(n+2)/5
+3*(sqrt(5)/2+3/2)^(n+2)/10-3*sqrt(5)*(3/2-sqrt(5)/2)^(n+2)/10
+3*sqrt(5)*(sqrt(5)/2+3/2)^(n+2)/10
Ѥΰ̹

expand(3*(3/2-sqrt(5)/2)^(9+2)/10-3*(-1)^(9+2)/5
+3*(sqrt(5)/2+3/2)^(9+2)/10-3*sqrt(5)*(3/2-sqrt(5)/2)^(9+2)/10
+3*sqrt(5)*(sqrt(5)/2+3/2)^(9+2)/10);38448
10ܡ()
expand(3*(3/2-sqrt(5)/2)^(10+2)/10-3*(-1)^(10+2)/5
+3*(sqrt(5)/2+3/2)^(10+2)/10-3*sqrt(5)*(3/2-sqrt(5)/2)^(10+2)/10
+3*sqrt(5)*(sqrt(5)/2+3/2)^(10+2)/10);100656
äѤλȤfreeΤΤФǤǶ
Ѥmaplefreexcas(ե)ǾѤREDUCE
freeJACAL()θǤƤޤmathmatica򿿻
Τ⤢褦ǤϤޤǤ
⤦330ʬǤ͡ڤäǤǤϡ
˭ԡ 623ڡ 3:37:47 MAIL:fttnm528@ybb.ne.jp 25324
Ȥ
ޤ
#25324 Ǥΰ̹
>3*(3/2-sqrt(5)/2)^(n+2)/10-3*(-1)^(n+2)/5
>+3*(sqrt(5)/2+3/2)^(n+2)/10-3*sqrt(5)*(3/2-sqrt(5)/2)^(n+2)/10
>+3*sqrt(5)*(sqrt(5)/2+3/2)^(n+2)/10

ϵɽѤ
////////5099490000000000000cm^2Ȥ
42ܤ2388092983642150830cm^2
43ܤ6252108599470297530cm^2
43á()
¾οͤ45øѤ㤦ΤǤ԰¤Ǥ
⤦4ʤ̲ʤΤŰȻפޤ
ͥåȡեǤ⤷褦Ǥϡ
˭ԡ 623ڡ 4:13:55 MAIL:fttnm528@ybb.ne.jp 25326
Ҷ˥ޥ
֤˷׻Ƥä顢ñ衼Ǥ⡢ʤݤäǤ
ԡ 623ڡ 5:48:08 25327
奢˥ޥ
򤷤ޤ
ԡ 623ڡ 5:53:19 25328
Ҷ˥ޥ
ʤߤˡ奢˥ޥ뤵ȤϡǤʤǤ⤢ޤ󡣤ޤ郎᤯ʤäǤ
ԡ 623ڡ 6:01:10 25329
uchinyan
ϤϤ褦ޤ
եܥʥå¤ݥȤǤ͡
괺ŻǤ
ȡޤϡsqrt(100000/3) ϡۤܡ180餤äȡ
1ø˺礬2cm10øǺ礬144cmǡ11øˤ180ĶΤǡ
10øʤȤȤǡ
ࡢø (^^;
ͥνȡ 623ڡ 8:50:31 MAIL:uchi@sco.bekkoame.ne.jp 25330
kasama
Ϥ褦ޤ
ľ˹ͤХեܥʥåǤ礦(*^_^*)
եȤǥƥȡͤ򤢤ƤϤƷ׻ޤ(^_^;)
623ڡ 9:14:34 25331
DrK
#25330
褦ʹͤǤ
ҡ 623ڡ 9:15:57 MAIL:satoka@star.odn.ne.jp 25332
uchinyan
(äȽޤ)
ޤˤ⤤øʲˡ#25330ǽ񤤤Τǡޥ (^^;

(äݤˡ)
ǰʤ顢ޤꤦޤˡפĤƤޤ
#25330Τø򡢤ޤ˷׻ƳǧΤּʵޤ
󡢼οؤäݤˡ򻻿äݤΤϤǤ
ä񤷤

(ؤäݤˡ)
¿ʬɤʤ񤫤ƤȤϻפޤ
դꡢn ø̿ΤκȾ f(n+1) cm ϡΥեܥʥåˤʤäƤޤ
f(n+1) = f(n) + f(n-1), n >= 1
f(0) = f(1) = 1
(Ѥߤޤ󡣼餬ְäƤޤn ĤƤս꤬ޤޤ)
ǡn ø̿ΤѤι S(n) cm^2 ϡ = 3 Ȥơ
S(n) = 3 * ((f(0))~2 + (f(1))^2 + (k=1,n) {(f(k+1))^2}) = 3 * (k=0,n+1) {(f(k))^2} <-----
Ĥޤꡢñˡեܥʥå¤3ܤˤʤäƤޤ
ǡꡢ
f(n+1) * f(n) = (f(n) + f(n-1)) * f(n) = (f(n))^2 + f(n) * f(n-1)
(f(n))^2 = f(n+1) * f(n) - f(n) * f(n-1)
(k=1,n) {(f(k))^2} = f(n+1) * f(n) - f(1) * f(0) = f(n+1) * f(n) - f(0)
(k=0,n) {(f(k))^2} = (եܥʥånޤǤ) = f(n+1) * f(n)
ʤΤǡ
S(n) = 3 * (k=0,n+1) {(f(k))^2} = 3 * f(n+2) * f(n+1) <-----
ǡS(n) > 100000 n ФȤˤʤޤ
f(n) ϡf(0) Ϥơ1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... ꡢ<-----
3 * f(12) * f(11) = 3 * 233 * 144 = 100656 > 100000 > 38448 = 3 * 144 * 89 = 3 * f(11) * f(10) <-----
ʤΤǡ100000 ĶΤϡn + 1 = 11, n = 10Ĥޤꡢ10ø塢ʬޤ<-----
ʤϻȤޤǤϤ顢
f(n) = f(n+1) - f(n-1)
(k=1,n) {f(k)} = f(n+1) + f(n) - f(1) - f(0)
(k=0,n) {f(k)} = (եܥʥånޤǤ) = f(n+2) - 1
Ǥ͡
ñ˵ޤäơäȤӤäꡣޤʤΤǤ
ͥνȡ 623ڡ 12:29:04 MAIL:uchi@sco.bekkoame.ne.jp 25334
ϥ饮㡼ƥ
¾οͤ򤭤ޤ
̶彣 623ڡ 11:22:20 HomePage:ĩ25335
ޥ
#25335
C-D#25309ǤƤƤޤ

http://www.sansu.org/456.gif

ʴβˡꤷƤޤʿޤϣޤǤǤ
PowerBook G4 623ڡ 11:45:09 MAIL:masaru-y@sansu.org HomePage:25336
uchinyan
#25336ڤ#25309
ʤۤɡ#25334οؤäݤˡ򤦤ޤˤƤޤ͡
ϻޤ
顢ǼĤɤߤޤ
ͥνȡ 623ڡ 11:57:37 MAIL:uchi@sco.bekkoame.ne.jp 25337
uchinyan
ǼĤɤߤޤ
ʤ#25334οؤäݤˡߥäƤޤѤߤޤ󡣽ޤ
ޤˡޥ뤵󤫤ŦäΤǺǤC-Dβˡޥ뤵ˡǤ͡
#25334οؤäݤˡƱǤȤƤäȲ򤫤ƤΤϡϤæ˹Ǥ ^^/
ࡢʤٸƤ⡢ޥ뤵οޡ
ͥνȡ 623ڡ 12:51:20 MAIL:uchi@sco.bekkoame.ne.jp 25338
ޥ
#25338
ޤϡ¾긫Ƥդ⤫פäƤǤ顣򸫤Ƥˤβˡפ⤫C-DˤϤӤäǤ

ȤǺ󡢱߼Ψ򣳤ˤƤߤޤޤʤˤäƤְ㤤ޤ˷׻ѤˤʤΤǡˤƤɤȡ3.14ǤѤʤǤɡ޷Ūꤸ㤢ʤǤ߼ΨǤ3.14ǤܼŪˤϤɡǤ⤤ȤʤΤǡʤñʤۤɤʡä٤ιͤǤ
PowerBook G4 623ڡ 13:17:40 MAIL:masaru-y@sansu.org HomePage:25339
uchinyan
#25339
#25338
䤦ࡢʤٸƤ⡢ޥ뤵οޡ
䤬㤷Τϡ󺣲βˡȤͥƤΤǤ
ޥ뤵οޤ䤬ȤäƳեܥʥå¤μμʷξˤʤäƤ⤢ޤ
⡢ˤʤäƤ뤷
եܥʥåäơԻ׵ġŪǤ͡
ñʤɡճʤȤ˴ФΤäƤꡣ
߼Ψ˴ؤƤϡޤϤۤɽפǤϤʤޤȤȤǡ
ͥνȡ 623ڡ 14:02:16 MAIL:uchi@sco.bekkoame.ne.jp 25340
M.Hossie
Фˤ㡣Fibonacci Σ¤ޤ˷׻ʤǤޥβˡޤˤϻޤ

ȤǡϣޤΥСǡ (JAL, ANA) ȯǤ (֤ϣΣ)οͤΣ֤˽󤵤ƤơƵ٤ߤ˳ݤ٤꤫̾ʤˤǤǤƤβϩĶǤȤʬ ANA 121 ƹԤ̵פޤǣؤä겡ΤϸޤǤ̵Ǥ뺢ˤʤääơǯߤ­ߤ餤ʰ
ϡ 623ڡ 19:04:43 25341
N.Nishi
excelϤڤޤ
624ʶ 1:12:16 25342
N.Nishi
excelϤڤޤ
624ʶ 1:12:16 25343
Ȼ
եܥʥå٤礦Ѥ׻ޤ.
624ʶ 17:40:38 25344
ݣ椿
ץDz򤭤ޤjavaͤơ

public class ex456 {

public static void main(String args[]){
answer_body ab = new answer_body(); //answer_bodyν
ab.answer(1,1);//
}
}

class answer_body{
private int child , parent;
private int time = 0;
private int area , tarea = 0;

answer_body(){//ʤ󥹥ȥ饯
}

public void answer(int now, int before){//ʬ

area = now*now*3;//ѷ׻
tarea = area + tarea;//­

if(tarea > 100000){//߷100000Ķޤ
System.out.println("߷Ѥ10cm^2ĶΤ"+ time +"ø");//ɽ
}else{
this.child = now + before;//ҶȾ»
this.parent = now;//Ƥ򸽺ߤȾ¤
time++;//֤򥫥ȥå
answer(this.child , this.parent);//Ƶʥեܥʥå
}
}
}
624ʶ 22:06:36 25345
ʤʤ
ꥢ륿ǤȤФ褫ä
棳ΤȤˡعȤοؤǥեܥʥåȲ桩ȿʪä褦ʡ
ѥʥåץȤҤޤȤϥեܥʥåˤʤäƤȤĤ褯ФƤʤɡ
624ʶ 22:59:06 HomePage:椫Ť25346
ҡΤ
...ꥢ륿ǻäǤʤä
ιԤäΤǤʲ

...Ͻֻ˥ץޤ
ץȸäƤʰ׸JavaScriptǤ...

<script language="JavaScript">
m=0;n=6;a=1;b=1;
for(i=0;n<=100000;i++){m=a+b;n+=m*m*3;a=b;b=m;}
document.write(""+i+"ø塩");
</script>

ޤʡˡhttp://www.sky.sannet.ne.jp/bomb/SSS.html
ޤ礭ʿȸǤƤޤʶС

9ߤ濴 625ڡ 8:45:08 HomePage:25348
粬ҹ
꼫ΤϥեܥʥåȤ狼äǤޤʡ
ʤߤ˰̹ᣱ壵Сʣܢ壵/ˡʣ壵/ˡѤˤƤϤ褦ȤޤݽʤޤʡϾǮɤäݤʤäƤޤäΤǽޤǥå֤Ǥ
626 22:08:49 MAIL:toshi009@land.hokuriku.ne.jp 25349
ݤ
HAPPY BIRTHDAY
ޥ뤵󡣤ǤȤ޼
åŷ񡡡 628ʲС 0:05:45 MAIL:hopes@mba.ocn.ne.jp HomePage:HOPES褤Ȥ٤Ϥ25350
ޥ
#25350
䡢ޤǤ...Ǥʡ(^^;;

Ǥ⡢줷ǯ𤸤ʤʤäƤޤޤ...orz
PowerBook G4 628ʲС 0:45:31 MAIL:masaru-y@sansu.org HomePage:25351
ݤǡ
ջޤ
ޥ뤵褪ᤧ
628ʲС 1:03:31 25352
ݤ
#23351
ʤ
ޡߤʤޤˤΤ餻ȸȤǡ
䤷Ƥ䤷Ƥä
åŷ񡡡 628ʲС 6:23:13 MAIL:hopes@mba.ocn.ne.jp HomePage:HOPES褤Ȥ٤Ϥ25353