ȥȥ
¿ͷӤƤޤ
ϼǿʧäƤޤ
׻ϤϤޤ󤬡ҤȤĤ˸ȥեܥʥå
ʤΤǡ٤Ϸ׻Ǥޤ
1028ڡ 0:11:00 23921
ԤԤΡά
޳ѷСʥ=a , ʥ=bȤ n(n1)ΰդĹF(n-1)a+F(n)b
ʣ(n)FibonacciF(0)=0,F(1)=1,F(n+1)=F(n)+F(n-1))

˭ο峲ۤϿ̡饯ǤסԤǤʤΤΤⲿǤ³Ǥ͡
ɤΤ顣
̤̪ 1028ڡ 0:12:48 MAIL:ishizaki@qa.so-net.ne.jp 23922
Ϥʤ
ǽŤΥߤˤʤäơ269,433ʤɤȤ㤤ˤʤΤ34,56ǤäƤȻפäԤäƤ顣
ԤƤɤԤƤɤܤʤ(ء`)Ρ׻ְäƤޤȤۤ

פAn=An-1ˡ3ݡAn-2ˤǡǤ
ȡ硡 1028ڡ 0:13:40 HomePage:http://hanau.daa.jp/blog2/23923
ȥȥ
˿٤Ʋεαƥ顼ѤޤäǤ衣
ܥ塼िäפΤ䤭Ӥߤǥ顼󤬣ߤȶäΰ¤
Τܤؤꤷ̤ιʵ򤷤Ƥޤ
1028ڡ 0:16:07 23924
Ϥʤ
եեܥʥåǤ͡ʤ˴㤤Ƥ

ǯϤɬʵꤷ˹Ԥޤ͡ʶˡ
ȡ硡 1028ڡ 0:17:07 HomePage:http://hanau.daa.jp/blog2/23925
ޥ
˺줿ΥեܥʥåȤȤ....(^^;;
MacOS X 1028ڡ 0:23:16 MAIL:masaru-y@kt.rim.or.jp HomePage:23926
uchinyan
ϤФϡ
եܥʥåǤ͡ñȤдñ :-)
ͥνȡ 1028ڡ 0:30:46 MAIL:uchi@sco.bekkoame.ne.jp 23927
ȥȥ
Фϡޥ뤵
¿Źī饹äƤޤ
ޥǡįƲǤĤͤƤޤ
18̤ϥ!!
1028ڡ 0:33:00 23928
ٶ
åϥեܥʥåʤǤ͡ʤ󤫼ʬǽ񤤤
ޤˤǤ餽ΤȤ˵դޤǤ޳ѷǤޤǤκȤ
10Ȼפäơǽ1597,2584פȻפäƤޤޤǤǹͤľ
ƵդޤȤˤǤƤ褫äǤǤϤ褦ʤ顣
繥ʹ(Ͽ) 1028ڡ 0:37:02 23929
tomh
#23926
> ˺줿ΥեܥʥåȤȤ....(^^;;

˺Ƥޤ (^^;
ѴؿǥꥴȤä㤤ޤ

ϡ˺줿ΥĤ? (^^;;
ԡ 1028ڡ 0:38:05 MAIL:tomh@yahoo.co.jp HomePage:H to M23930
tomh
#23930
׻Ϥäȡȥδطϡ

() = [(1+5)/2]x().

Ĺϡ[(123+555)/2]x()ʤΤǡ
NMȤơ

[(123+555)/2]x() = Nx()+Mx() = [(2N+M +M5)/2]x()

ȤʤäơȤӤȡ(N,M)=(34,55).
狼ȡϼߤʤȤƤʤȻפޤ (^^;
ԡ 1028ڡ 0:45:33 MAIL:tomh@yahoo.co.jp HomePage:H to M23931

ޡɽţǤ
줿Ϥդäƿ衣
ήлΥݥץ뤬դˤʤޤ
Ǥϡߤʤ󡣤褦
䤷Ƥ䤷Ƥä
äѤ餤ŷ񡡡 1028ڡ 0:54:50 MAIL:hopes@mba.ocn.ne.jp HomePage:ȣϣУţ23932
cm
ڥȤȥȤäƼȤDz򤭤ޤ
1028ڡ 1:02:49 23933
Ȥ
12̲Ǥ͡ʲʬʤβǤ
褺դ2ܤο޷
֤޳ѷ򺸱оΤʬξ¦AȤȿ׼˽B,C,D,E
Ĥ޷ü֤޳ѷ򺸱оΤʬκ¦
FȤȿ׼˽G,H,I,JȤ롣
ǢCGH,CHDλѷͤ
CľGH˿򲼤­KȤ
ľCDLȤ
cos36=CL/CH 衡CL=CH*cos36
sin18=KH/CH 衡KH=CH*sin18

CL : KH = cos36: sin18
18=Ȥ
CL : KH = cos2*: sin=1-2*(sin)^2 : sin

sin18=(5-1)/4ΤΤ
CL : KH = 1-2*((5-1)/4)^2 : (5-1)/4
=1-2*(3-5)/8 : (5-1)/4 =(5+1)/4 : (5-1)/4
=5+1 : 5-1
դν˽ФƤ5ѷ1դ
(5+1)/(5-1) =(6+2*5)/4 =(3+5)/2
դκǽθ޳ѷĹ1=Ȥ
10ܤθ޳ѷĹ((3+5)/2)^5=(55*5+123)/2
1=ꥤ
sin18=(5-1)/4=(1/2)/=1/(2*)
(5-1)/4=1/(2*)
5-1=4/(2*)=2/
=2/((5-1))=2*(5+1)/4=(5+1)/2
ȭ,
10ܤθ޳ѷĹ=34*+55*()
θ˭ԡ 1028ڡ 1:31:39 MAIL:nm528@ybb.ne.jp 23934
ҡΤ
礤ǿޤŬäƤʤȹͤޤ
٤ޤǿޤŬäƤ뤦ˤäȥեܥʥå˵Ĥޤʡ
ɤϳͤƱˤʤ櫓Ǥ
⼫ʬߴȤˤߤʬޤʾС
ɥ 1028ڡ 1:35:29 23935
mhayashi
=a(0), =b(0) Ȥơ
1. a(n)=a(n-1)+b(n-1)
2. b(n)=a(n)*b(0)/a(0)
δط a(5) ޤ
1028ڡ 1:42:30 HomePage:M.Hayashi's Web Site23936

a0b0Ȥȡ
a2=a0+b0b2=a0+2b0
a4=a2+b2b4=a2+2b2
a6=a4+b4b6=a4+2b4
a8=a6+b6b8=a6+2b6
a10=a8+b8b10=a8+2b8
ƤСa10=34a0+55b0Ȥʤ롣
ƽ 1028ڡ 4:48:39 HomePage:θ줳ߤ󡪡23937
ʤ
ȥӥ֡դϣˤʤ

Ĺϡºݤˤϣˤʤޤ
# ۤȤϡ122.99 cm
ơȤƤäݤΤϡǤϤޤ
̣ϡΣդĹ׻ƤߤƤ
̳ƻ 1028ڡ 7:56:49 MAIL:naka@sansu.org HomePage:naka's Home Page23938
ϥ饮㡼ƥ
ǤѴؿʤȤ߹碌MathematicaDz򤤤
ҤᤤƤʤΤݤä
̶彣 1028ڡ 11:07:48 HomePage:ĩ23939
kasama
äʤ(?_?äʤ(?_?ȻפäƤ顢áʬʤƤ(^_^;)
äȡǽΥĹa1b1Ȥȡ
b1=a1/(2sin(/10))
a2=a1cos(/5)/sin(/10)

b5=a5/(2sin(/10))
a6=a5cos(/5)/sin(/10)
ʤΤǡ
b1=a1(1+5)/2
a6=a1(123+555)/2
Ȥʤäơ
a6=34a1+55b1
Ǥ
1028ڡ 11:41:55 23940
uchinyan
#23927ؤμʥ쥹
եܥʥåˤʤ뤳ȤϡгϤΰդˤʿԻշͤС餫
#23938
= 1 ȤǤ͡ΤˤϡWindowsǡ
122.99186938124421665125227589011 cm Ȥʤޤ
= (1 + sqrt(5))/2 Ǥ顢׻С
䤽ơȤƤäݤΤϡǤϤޤ
ȤȴطΤʡ

ͥνȡ 1028ڡ 12:10:25 MAIL:uchi@sco.bekkoame.ne.jp 23941
uchinyan
#23941ˤäɲá(ΤǤʤ)
䥤 = (1 + sqrt(5))/2 Ǥ顢׻С
(10) = ( + 1)^5 Ǥ
ͥνȡ 1028ڡ 12:16:41 MAIL:uchi@sco.bekkoame.ne.jp 23942
M.Hossie
Фˤ㡣ȥδطĶͭ̾ʲʬ (1 + 5)/2 Ǥ͡
򣱤ޤꤹȡ A B Ȥ
A(n+1) = A (n) + B (n), B (n+1) = A (n) + 2B (n)
Ƥǡ n n = 5 34, 55 Фޤn = 5 äҾʤ󤫵Ǥ⤽Τޤ­㤤äƤʤȤ˺դۤäǤ

ط̵Ǥ㸩̱γޤˤ񤤿夲ޤĶα۸λ̵
Τꡡ 1028ڡ 13:17:51 23943
n
1028ڡ 16:55:12 23944
̾õ
פ֤ΥեܥʥåǤ͡

#23938
褯ʬޤ󤬡
ᣱʤСϲʬաʡʣܢ壵ˡˤʤΤǡ
+ᥤʣܦաա
ʥܥˡᥤաʡᣳܣա

եܥʥåνᣱ裲ᣳ֤Ȥ
󣱡ʥ奫
裱ᣱ

奫裱աܣա
աᣱʤΤǡաϣ˶ᤤ

1028ڡ 17:21:39 23945
оϩ
Ǥ޳ѷζä¸ߤջѷȡ
ӤȤƲȤ򤭤ޤ
䤡եܥʥåǤեܥʥåǤġġ
ͤޤǤorz
ǽ餬֥סθ夬֥ܥסġĤȡޤǤޤ񤤤ƤޤǤ
γ 1028ڡ 18:17:57 MAIL:pctakada@mail.goo.ne.jp HomePage:Ĥ줭23946
̾õ
Ǥ⾯񤤤ΤǤ
ᣱդȤȡĹϣբաѲޤ
աաܣΤǡ
աաաʦ+˦աᣲ+򷫤֤Ȥäơ
աᣳ+աᣳߥ+ߥ
ȵޤ
1028ڡ 18:24:50 23947
ʤ
#23945 ̾õ夵

äȤ򤹤äȽ񤤤Ƥޤ
Ǥ꤬Ȥޤ

ᣱᡡ
ᣲᡡ
ᣳᡡ
ᣴᣲ
ȡ˶ŤƤޤ

奫裱աܣա
ޤ޷Ūʶ̣ͶȤǤ
ա¦ܤѷΣդʤΤǤ顣
⡢οǤ礦
Muroran 1028ڡ 18:35:05 MAIL:naka@sansu.org HomePage:naka's Home Page23948

פ֤줿
1028ڡ 21:35:36 23949
uchinyan
#23945 and #23948
ʤۤɡ򤤤Ǥ͡ȤŪǤͤ
奫ȤΤΤޤǤ
ٶˤʤޤ :-)
ͥνȡ 1028ڡ 21:42:55 MAIL:uchi@sco.bekkoame.ne.jp 23950
DrK
ꥢ륿ǻäΤˡΡ
μξϡˤʤäƤ뤳Ȥ˵ŤФʤΤǤ
3ܤξ֤ˤʤäȤ޳ѷ˱Ӥ뻰ѷ2Ĥȸ޳ѷ޳ѷξʬˤʤ뤳Ȥ˵ŤޤΤȤդϡѷ2Ĥȸ޳ѷդ¤Ȥʤޤ
ѷޤ֤Ȥ޳ѷ1Ĥĺ˻ѷĺŤʤꡢդĹϥ1ʬȥ2ʬ¤롣
⤦1١3ܤνλˤǤѷܡ޳ѷ黰ѷ1ĿФʬټʳθ޳ѷդˤʤ롣ΤȤ޳ѷȼθ޳ѷդδطϸ޳ѷդȻѷ1ʬ¤Ȥʤ롣
顢򤿤ɤäƤȡ10ܤˤǤ޳ѷդ
34ʬȥ55ʬ¤ˤʤ롣
ϳڱफ?㤦ʡ 1028ڡ 22:47:26 MAIL:satoka@star.odn.ne.jp 23951
N.Nishi
A(n)=A(n-1)3A(n-2)â/2ʣܤǣ϶Τ߹ͤ롣
⤳μͤޤʤ޳ѷΤȤФäǹͤƤ롣
10ܤϣᣵβ˺ƷA(1)A(4)ƺǸA(5)򡣤ʤ˶ǤϤʤäǤ͡50ܤȤ줿ꤲФǤ()
1028ڡ 22:48:03 23952
DD
ƻ˷׻ƽФޤ
򤤤Ǥͤ
1028ڡ 23:23:12 23953
DrK
϶޳ѷǤǤ˸޳ѷ꤬ФΤʤȻפޤ
ҡ 1029ʶ 12:18:17 MAIL:satoka@star.odn.ne.jp 23954
⡼ޥ
{(3+5)/2}^5 = (123 + 555)/2
= A + B x {(1+ 5)/2}ȷ׻Ƶ᤿
̾õ夵βˡ˵Ťʤä
ʤ̲ʤ롦˶ᤤΤʤ
1029ʶ 16:56:59 MAIL:kennji72001@yahoo.co.jp 23955
̾õ
#23948 ʤ󡢤꤬Ȥޤٶˤʤޤ
#23950 奫Lucas numberˤΤȤϡ錄ΤޤǤ
奫֥ϥΥפκԤǤ뤳ȤΤäƤޤ

Ǥ⡢奫Lʣˤϸޤ
ʤĹAʣˤϡ
AʣˡLʣ+Fʣˡߢ壵ѡ
ͿޤFʣˤϥեܥʥåˡ
ȤСAʣˡʣ+壵ˡ⣱

Ѹ쥵Ȥˡ奫ڤҲ𤵤Ƥޤ

֥奫ڡLucas tree
ˡĤιʥΡɡˤޤ
ǯˡᤫ飱ĤĤȣĤ֤᤬ޤ
֤ϡǯФĤȡĤѤޤʣĤĤ᤬ޤˡ
ĤᤫϡǯˡĤĤȣĤ֤᤬ޤ
ǯ˽θĿϣ̡ʣΡˤˤʤޤ
1029ʶ 18:38:20 23956
uchinyan
(Ѥߤޤ󡣤Ĥޤʤߥޤޤ
A(n)ϡnĹʤΤǡA(1) -> A(0), A(2) -> A(1) ˤʤޤ)
#23956
奫֥ϥΥפκԤǤ뤳ȤΤäƤޤ
ؤޤΤޤǤ (^^;
䤹ʤĹAʣˤϡ
AʣˡLʣ+ Fʣˡߢ壵ѡ
Ǥϡ޳ѷггΰդˤʿԻշͤȡ
A(n+2) = A(n+1) + A(n)
Τǡ = A(0) = A(1) = (1 + sqrt(5))/2 * A(0)n >= 2 ǡ<-----
A(n) = F(n-1) * A(0) + F(n) * A(1) <-----
A(0) = 1 Ȥȡ<-----
A(n) = [{2 * F(n-1) + F(n)} + F(n) * sqrt(5)] / 2 = [{F(n-1) + F(n+1)} + F(n) * sqrt(5)] / 2
ʤΤǡ
L(n) = F(n-1) + F(n+1)
Ȥ񤱤ޤ͡
ޤ礷ȤǤϤʤΤǤ礦ä򤤤ʡȻפޤ
ɲ or ­ (^^;
δطϡA(n) ǡA(0) = 1, A(1) = 3 Ȥ礬L(n) = A(n-1) Ǥ뤳Ȥ⡢
L(n) = A(n-1) = F(n-2) * A(0) + F(n-1) * A(1) = F(n-2) + 3 * F(n-1) = F(n-1) + F(n+1)
Ƴޤ
ͥνȡ 1030ڡ 11:29:34 MAIL:uchi@sco.bekkoame.ne.jp 23957
̾õ
奫ΰ̹L(n)Ƥߤޤ
13471118294776123

䣲ΤȤL(n)L(n-1)+L(n-2)
L(n+)ݦL(ˡ¡L(nˡݦL(nݣˡѤ֤
L(n+1 )ʦ+¡L(n)ݦL(n-1 )Ӥơ
+¡ᣱ¡ݣ

L(n+)ݦL(ˡ¡L(nˡݦL(nݣˡ
¡ʣݣˡL(2) L(1)}
¡ʣݣˡʣݦˡ
ݦʣݦ++ʦ++¡ݦ¡¡ʦ¡ݦˤ
¡ʦ¡ݦˡ
Ʊͤˤơ
L(n+)ݦL(ˡL(nˡݦL(nݣˡ
ʦݦ¡ˡ

ݭ
ʦݦ¡L()ʦݦ¡ˡʦ+¡
äơ
Lʣˡʦ+¡
ա¡ݣդ֤ȡ
LʣˡЦա+ʡݣաˡ
ɽޤ

#23957 uchinyanȯ줿طȤȡեܥʥå
̹Fʣˡʦݦ¡ˡʦݦ¡
顢ˡ奫ΰ̹L(n)ޤ͡

#23947 ʥ쥹Ǥ
⤦ꤤˡϡ
աFʣ+Fʣ˦աͽۤ뤳ȤǤ
ʦա+ȤäơŪǼˡǾޤ

աաʣݣ+աʣݣ
ȤȤǡĤΥեܥʥåեܥʥåˤʤΤǤ

1030ڡ 21:37:49 23958
uchinyan
L(n) = F(n-1) + F(n+1), F(n) = (^n - ^n)/(-) 顢L(n) Ƥȡ
L(n) = (^(n+1) - ^(n+1) + ^(n-1) - ^(n-1))/(-)
ǡäȥȥåǤ = -1 ꡢ
L(n) = (^n * - ^n * - ^n * + * ^n)/(-) = (^n + ^n)(-)/(-) = ^n + ^n
= , = -1/ Ȥ
L(n) = ^n + (-1/)^n
ͥνȡ 1030ڡ 23:04:47 MAIL:uchi@sco.bekkoame.ne.jp 23959

ΥȽޤ줫1餤ǻäǤ
եܥʥåʤǤ͡Ĥ̾˺ƥեġ­Ƥޤ衣
Ϥ˲򤭤ǤǤ
1031 0:39:50 23960
emiko
η֤ǡ
111ʷ 19:35:27 23961