ޥ
ޤż֤Ǥ

ƴοͤ⤤뤫ʡȻפĤġѤʤäΤɤФ뤫ġ(^^)

ȤꤢߥʤɤΤǤ
1117ڡ 0:10:48 26163
ߥƥ
顢ΩΤȻפǤޤäˡ
ͤФޤǤ||
1117ڡ 0:15:01 HomePage:ߤ26164

ǽ򴪰㤤ޤƱä褦Ǥ
ģСܣУƤ褯ҥŽդȻפäŸޤ
ǣǤʴñǤΤȻפĤޤ
褯ɤȣģФ̾ǤϤʤΩΤʤǤ͡
顼θ 1117ڡ 0:15:03 HomePage:26165
ߤ
Фϣţͤ򣲡ʬȤͽۤϳ줿ߤ

㤢Τɤʤ
1117ڡ 0:20:48 26166
ޥ
𤷤ޤ

#28165ʤۤɡȤ⤢Τ...

Ȥʤȡ⤷ȻνФޤߥäƤǽ⤢ȤȤ...԰
PowerBook G4 1117ڡ 0:22:50 MAIL:masaru-y@sansu.org HomePage:26167
tomh
#26166
EM4:1ʬǤ͡
ԡ 1117ڡ 0:23:55 MAIL:tomh@yahoo.co.jp HomePage:H to M26168
ޥ
#26167
ǤǤۤáɤߥǤϤʤǤ...
PowerBook G4 1117ڡ 0:26:18 MAIL:masaru-y@sansu.org HomePage:26169
ShinKoba
äϡʿȤäгʬ˻ɤΤȻפΤǤϤ껻򤭤ʤɤȡ餽˹ͤƤޤޤ˾ܤƤƹͤȡʳˤޤ򤱤ΤȵŤޤģĹ̤ȤơޤĺȾդӡθ庸ĺ麸أأԤäȤĺäۤɤΣȷ٤СξƤϤޤΩΤŸޤΰ񤱤ȤˤʤޤθϡֺȱĺӡԥߥåɷȤСƳΤǤ礦͡
1117ڡ 0:30:03 26170
CRYING DOLPHIN
ϥӥĤǤˤƤߤ
http://www7a.biglobe.ne.jp/~cdcdcd/q477tenkaijaaa.GIF
⤦칩פȤ鷺Ȥ򤱤뤱ɡޤ
ƬʤڤǤä
ǯԥ奦ȡ 1117ڡ 0:40:17 HomePage:θ³äƤɤΤ餤26171
holden
ҥŽդȻפäŸޤ񤤤Ʋ򤤤Ƥޤġ񤷤!!
1117ڡ 0:48:23 26172
ȥȥ
#26171
դ򣲡ߣˣĤʤ٤ơˢţͣƤȢģţͤ
ƣĤȣƤӤޤ̤ȤƣãĤοޤƱǤ͡
ʼ˸лԡ 1117ڡ 0:54:06 MAIL:h-sakai@zb3.so-net.ne.jp 26173
hin Koba
ѵ줿ȤȤǤФ餯ĤƤޤ
1117ڡ 1:03:33 26174
ߤ
#26171
ޤλѷäΩΤڤȤǤ褯
ѥ󤸤ʤ˵ŤʤäƤȤϤޤޤʤ
1117ڡ 2:34:50 26175
Ȥ
ƴǤʤȤʬβˡǤ
褺դοޤD(0,10,20),F(20,0,0)
ľEM:y=x,z=0Ȥ
ľEMx=tȤP(t,t,0)Ȥ
D(0,10,20)ȤεΥ
DP=sqrt(t^2+(t-10)^2+20^2)=sqrt(2*t^2-20*t+500)
F(20,0,0)ȤεΥ
FP=sqrt((t-20)^2+t^2)=sqrt(2*t^2-40*t+400)
ȭȤ¤
DP+FP=sqrt(2*t^2-20*t+500)+sqrt(2*t^2-40*t+400)
ʬƶ˾ͤ(ʲmupad light 2.5.3Ǥ⤦proʤ
С3.ͭߤǤ)
diff(sqrt(2*t^2-20*t+500)+sqrt(2*t^2-40*t+400),t):
factor(%):
numer(%):
solve(%):
{8}
sqrt(2*8^2-20*8+500)/sqrt(2*8^2-40*8+400);
{3/2}()
ϰʲ
solve(2*(t*sqrt(t^2-10*t+250)-10*sqrt(t^2-10*t+250)+t*sqrt(t^2-20*t+200)-5*sqrt(t^2-20*t+200)),t);
mupad ǰȯDz򤱤maxima2褷sqrtϤ13ޥ
5ޥɤǤߤޤβˡϤޤˤǤޤ
֤ꤹΤˤǤǤĤؤǤߤޤ
˭ԡ 1117ڡ 3:15:12 MAIL:fttnm528@ybb.ne.jp 26177
⡼ޥ
դ򣲣¤٤ơгͤޤ
(2,0),(-1,2)
y=x
y-0=-2/3(x-2)
θx=4/5
Ĥޤꡢ(1+4/5)/(2-4/5)=9/6=3/2
ŪǤϤʤ
1117ڡ 4:03:33 MAIL:kennji72001@yahoo.co.jp 26178
kasama
Ϥ褦ޤCADˤ餻ޤ(^_^;
DEMʬEMΤޤ˲žơFEMƱʿ̾ˤäƤơDFǡȤޤ
1117ڡ 9:29:48 26179
ϥ饮㡼ƥ
¾οͤǤޤ
̶彣 1117ڡ 11:13:04 HomePage:ĩ26180
uchinyan
Ϥˤϡ
ϡɬñǤϤʤȻפޤ褯ѥȹ礻ʡȤǤ͡
ΩΤޤĹκǾʤΤǡʿ̤ˤƹͤޤä񤷤ʤޤȤδطǡΤ褦ˤޤ
ޤD ED MM F Ӥޤդδط٤δطʤɤĴ٤ȡDE = DMEMF = 90١EM = FM ʬޤ
ǡEMF EM 򼴤ˤƲžDEM Τʿ̤ˤΤ褦ˤޤF ΰư F' Ȥޤ
ȡDP + PF = DP + PF' ʤΤǡD PP F' ǺǾˤФ褯Ǿľ DF' ˤʤޤ
ʲǤ P ϡΤȤ P Ȥޤ
D EM ˿򲼤­ N ȤȡDNP = F'MP = 90 ʤΤǡDN//F'M ǡDPPF = DPPF' = DNF'M Ǥ
ȤF'M = FM = EM ʤΤǡɡDPPF = DNEM ˤʤޤĤޤꡢDEM ι⤵դȤǤ
ǡDEM = 1/2 * DN * EM ꡢDPPF = DNEM = (1/2 * DN * EM)(1/2 * EM * EM) = DEMMEF Ǥ
ǡޤMEF = 1/2 * HEFG = 1/2 * 2 * 1 = 1 cm^2 Ǥ
ˡDEM ϡDEHDMHHEM 򤽤줾 DEM ȶͭդ򼴤ˤƲžơDEM Τʿ̾ˤΤƤߤȡ
٤δط顢礦ɡ 2cm DEHDMHHEM ΤˤʤäƤ뤳Ȥʬޤ
ǡDEM = 2 * 2 - DEH - DMH - HEM = 2 * 2 - 2 * 1/2 * 1 * 2 - 1/2 * 1 * 1 = 3/2 cm^2 Ǥ
äơDPPF = DEMMEF = 3/21 ˤʤꡢDP PF 3/2 ܤˤʤޤ
ʤDEM ѤεϡϲΥȤٶޤ ^^;
ͥνȡ 1117ڡ 11:14:01 MAIL:uchi@sco.bekkoame.ne.jp 26181
uchinyan
Ǽɤߤޤ
ŪˤƱǤCRYING DOLPHIN#26171οޤʬ䤹ơβˡñǤǤ͡
ʤP ϡΤ EM 41 ʬǤ
ͥνȡ 1117ڡ 11:27:40 MAIL:uchi@sco.bekkoame.ne.jp 26182
粬ҹ
ڤޤƤ餤ޤʡ
DEMѤǵޤFPPD23
äơ3/2
ŤʤäճˤʤꤨǤ͡
1117ڡ 14:57:32 MAIL:toshi009@land.hokuriku.ne.jp 26183
kazsyun
ޤλѤ-ȣţͣ͡ţƣǤŸޤ
1117ڡ 16:44:48 26184
uchinyan
ʬǶ̤Ǥ
#26028
???
1+2+3++11=66
1+2+ġ+36=666
1+2+3+4++=666
˴ؤơ伫Ȥϲ򤱤ƤʤΤǤ轵轵γĥǥΤȤȤĴ٤ƤȤˡΤȤ򸫤Ĥޤ
㤨Сhttp://mathworld.wolfram.com/TriangularNumber.html 򸫤ȡʤ겼Ǥ
The beast number 666 is triangular, since
T_6*6 = T_36 = 666(28)
In fact, it is the largest repdigit triangular number (Bellew and Weger 1975-76).
Ȥꡢ666 repdigit Ǥ뻰ѿȤޤϡBellew and Weger 1975-76 ˹Ԥä褦Ǥ
ǡrepdigit ȤϡƱ¤ֿΤȤǡ111..11, 222..22, ..., 666..66, ..., 999..99 ʤɤǤ
ѿϤǤ͡פϡ1 + 2 + 3 + ... + n = n(n+1)/2 ΤȤǤ
ʸϡ
Bellew, D. W. and Weger, R. C. "Repdigit Triangular Numbers." J. Recr. Math. 8, 96-97, 1975-76.
J. Recr. Math. ϡĴ٤ȤJournal of Recreational Mathematics Τ褦Ǥ
ǰʤ顢ŻŪˤ̵褦ǡޤ󥿡ͥåȻʤϸƤޤ󡣾ߤʡ
ʤ⡼ޥ󤵤#26033ʬŪ䤬#26035ǥĤޤѤߤޤ (^^;ȤС
ʤȤ⡢1 + 2 + 3 + ... + n = ddd..dd ȤȤˡ
d = 2, 4, 7, 8, 9 ϲ򤬤ʤȡ
d = 3 1 + 2 = 3 ˸¤뤳ȡ
ϡưפʬޤd = 1, 5, 6 ξϡη夫碌Ƥ⡼ޥ󤵤ˡȡ
#26035ǻŦ褦˷η׻Ǥڤ꤬褯ʬ餺̤ m ξǾʤȤޤʤƤޤ
ʤץĴ٤¤Ǥϡ
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + ... + 10 = 55
1 + 2 + 3 + ... + 11 = 66
1 + 2 + 3 + ... + 36 = 666
ʤǤΤۤɤʸȻפޤ⤷ɤʤ¸ΤǤ顢Τ餻ĺȹǤ
ޤޤǡ
ͥνȡ 1117ڡ 20:59:29 MAIL:uchi@sco.bekkoame.ne.jp 26185
ۤ
#26171
...󤼤Ҥᤫʤä...ѷDEMݤDPFľ
ȤʤȻפĤ...
褦ͤȡޤäƻȤ빽ͭ̾ѷˤʤäƤ櫓Ǥ

Ѥ򤷤Τǡα...

HȤơP(x,1-x,0)Ȥ
DP+PF=(x^2+(1-x)^2+4)+((x-1)^2+(x+1)^2)
=2ߡТ((x-1/2)^2+9/4)+(x^2+1)
μ΢2ʹߤϡʿ̤ˤxP(x,0)Ȥä
K(1/2,3/2)ȡL(0,-1)顡PޤǤεΥKP+LP
ǾͤK,P,LľΤȤ
äơ3/2:1=3:2

βǽˤҤᤤΤǡ
ɤˤơʸFLˡDKˤʤ褦ޤ֤ʤȹͤ
ϤޤäƤޤޤ
̤αȡ 1118ʶ 16:36:44 MAIL:micci@sansu.org HomePage:ߤäα26186
uchinyan
ޤ礷äǤϤʤǤ#26181ϼ˳ĥǤơDPPF = DEMMEF ϡ̤Ω褦Ǥ
ȤȡǤϤʤǤDPPF = DEMMEF = sqrt((HM/AB)^2 + (1 + (HM/AD)^2) * (AE/AB)^2)1 ˤʤޤ
ξϡABADAEHM = 2121 ʤΤǡ
DPPF = sqrt((1/2)^2 + (1 + (1/1)^2) * (2/2)^2)1 = = sqrt(1/4 + 2)1 = sqrt(9/4)1 = 3/21
ȤʤꡢǤƸޤ
ͥνȡ 1118ʶ 23:25:36 MAIL:uchi@sco.bekkoame.ne.jp 26187
⡼ޥ
ˤʤǡͼޤľ
ͧС

45ɤΥ쥪󤬤ơΤ17ɤ
15ɤ13ɤĿȤ롣
餬ˤ2ɤв񤦤ȤƱƱΤξο
Ѳۤʤ뿧ƱΤξˤ3ο2ɤȤ
ѲΤȤ롣
ִ֤ˤ45ɤ٤ƤΥ쥪ƱȤʤ뤳Ȥ
ꤦ뤫Ƚꤻ衣ɬ2ɤǽв񤦤ΤȤ롣
1119ڡ 22:42:29 MAIL:kennji72001@yahoo.co.jp 26188
weapon
#26188
ꤨʤ
٤ƤΥ쥪ƱȤʤˤϡο=οޤ
ο=Ŀοޤϳο=ĿοȤʤִ֤ʤФʤʤ
(ο-ο)Ͼ2(3ܿ)0ˤʤ뤳ȤϤʤ
(ο-Ŀο)(ο-Ŀο)ˤĤƤƱ͡
1120 3:04:29 26189
uchinyan
#26188
weapon#26189Ȼפޤ
פϡɤκϽв񤤤ˤäơ3 dzä 1 2 ;Ѳޤ
45ɤ٤Ʊξϡ 3 ܿʤΤǡꤨʤȤȤǤ͡
ͥνȡ 1120 8:14:49 MAIL:uchi@sco.bekkoame.ne.jp 26190
⡼ޥ
#26189,#26190
weaponuchinyan󡢤̾ʤߤʤˤϴñޤ
ͧͤβ

kνв񤤤äβĿΥ쥪
ykgkbkȤ(y0g0b0)=(171513)
(y(k+1),g(k+1),b(k+1))=(yk-1,gk-1,bk+2)(yk-1,gk+2,bk-1)
(yk+2,gk-1,bk-1)
Τ줫Ω

y(k+1)-g(k+1)=yk-gkyk-gk3
äy(k+1)-g(k+1)yk-gk(mod3)
y0-g0=2äơyk-gk2
ִ֤45ɤ٤ƤƱˤʤ
yk-gk=045
äyk-gk0
Ȥʤ̷⡣

ʤߤˡ錄ϡ
줾οκϤ٤ƣ顢
ɤǹͤƤ⤤
-ܣᣱ-ܣ
ܣᣳ
Ϥʤ̵

1120 9:04:20 MAIL:kennji72001@yahoo.co.jp 26191
july
DEMEMޤäơD'Fľˤʤ褦ˤD'FEMεΥǻС
ʬǤȤΤΡ롼ȤʤΤǡǰʬ躹ȤǽХ롼ȤϾä뤬3ǤƤƤޤuzeeeee
ȤޤʴǤmasaru
äơ餺󥹤͡ʡ
1121ʷ 0:55:49 26192
ޥ
#26192
Ϥɡ⡣ʤäƵǤ͡ˢ
PowerBook G4 1122ʲС 9:13:22 MAIL:masaru-y@sansu.org HomePage:26193
⡼ޥ
ver3 򤱤ʤ
ʤʤ

ˤʤǡ
ͧͤΤǤ
ꡡʿ̾100ĤȤޤ¦50Ĥ褦
ľȤǤ뤳Ȥ򼨤
1122ʲС 17:18:28 MAIL:kennji72001@yahoo.co.jp 26194
uchinyan
#26194
ꡡʿ̾100ĤȤޤ¦50Ĥ褦
ľȤǤ뤳Ȥ򼨤
롢ͤƤߤΤǤɤ⤦ޤˡפĤ¾˾ȻפäΤΡ
ɤʤ񤭹ޤʤ褦ʤΤǡۤť򡣸Ȥ뤫⤷ޤ (^^;

ޤʿ̤ŬľɸϤƳ˺ɸͿޤ
κɸ y ɸͤ礭Τ֤ˡy ɸͤˤ x ɸͤΤ֤ˡ
ֹ򿶤äƤ50 ܤ P(p,q)51ܤ A(x0,y0) Ȥޤ
⤷q > y0 ʤСq > c > y0 Ȥʤ c ȤäƤơy = c ȤСľդޤ
ֹͿ顢q < y0 Ϥꤨޤ󤬡q = y0 ϲǽǤΤȤϼΤ褦ˤޤ
A ȡ1 ܡ...50 ܤȤľη׻ͤФκǾΤΤ a1 Ȥ
ͤʤ a1 = 1 Ȥޤ
Ʊͤˡ A ȡ52 ܡ...100 ܤȤľη׻ͤФκǾΤΤ a2 Ȥ
ͤʤ a2 = 1 Ȥޤ
ơa1, a2 Τɤ⾮ a ȤäƤơľ y = a * (x - x0) + y0 Ĥޤ
줬(ξ¦ǤϤʤ)¦50ĤפȤդޤ
ʤ1 ܡ...50 ܤ (x,y) ФƤϡy >= y0 ʤΤǡ
x > x0 ʤСֹο顢y > y0 ǡ(y - y0)/(x - x0) > a ꡢy > a * (x - x0) + y0
x = x0 ʤС餫ˡy > y0 = a * (x - x0) + y0
x < x0 ʤС̤ y >= y0 Ǥa > 0 >= (y - y0)/(x - x0) ꡢy > a * (x - x0) + y0
Ȥʤꡢ1 50 ܤΤ٤Ƥϡľ y = a * (x - x0) + y0 ˤޤ
ޤ52 ܡ...100 ܤ (x,y) ФƤϡy <= y0 ʤΤǡ
x > x0 ʤС̤ y <= y0 Ǥa > 0 >= (y - y0)/(x - x0) ꡢy < a * (x - x0) + y0
x = x0 ʤС餫ˡy < y0 = a * (x - x0) + y0
x < x0 ʤСֹο顢y < y0 ǡa > (y - y0)/(x - x0) ꡢy < a * (x - x0) + y0
Ȥʤꡢ52 100 ܤΤ٤Ƥϡľ y = a * (x - x0) + y0 겼ˤޤ
ʤ51 ܤϡľ y = a * (x - x0) + y0 ˤΤäƤޤ
줬ϡ꤬ľξ¦ 50 ĤĤפξǤ⡢1 50 ܤΤ٤Ƥ y ɸȡ
ľ y = a * (x - x0) + y0 x 1 50 ܤ x ɸ˰פȤ y ͤȤ 50 ȤӤơ
ΡֺפκǾ ymin Ȥȡymin 0 ǤϤʤΤǡ0 < b < ymin Ȥʤ b Ȥ뤳ȤǤޤ
ǡľ y = a * (x - x0) + (y0 + b) ȤС51 ܤϤľβˤơ¾ѤʤΤǡ
ľξ¦ 50 ĤĤפξǤפǤ

ʤξϡ˥ʥ֤ۤˡǤ50 Ȥ 100 Ȥˤϰ¸ޤ
äơξ򤽤Τޤ޳ĥơ̤ˡ
ʿ̾ n ĤȤꡢ¦ m Ĥ褦ľȤǤ롣
ʿ̾ 2n ĤȤꡢξ¦ n ĤĤ褦ľȤǤ롣
ʤɡΤȻפޤ
ͥνȡ 1123ʿ 13:46:43 MAIL:uchi@sco.bekkoame.ne.jp 26195
⡼ޥ
#26195 uchinyan 󡢤Ĥ꤬Ȥޤ

ͧͤβϰʲ˼褦ʤäƥץʤΤǤ

Ǥդ2Ф2ľ򤹤٤ư
ľοͭ¡100C2ˤǤ뤫顢餹٤Ƥľ
ʿԤǤʤľL롣Lʿ԰ư
11ȿ¦˰ܤäƤ2ƱˤȤӤ뤳ȤϤʤˡ
ŬʤȤǻߤСǤդοʬ롣

Ǥ뤫ɤ¬ʤΤǡ˽񤤤Ȥޤ
1123ʿ 19:12:19 MAIL:kennji72001@yahoo.co.jp 26196
ȥȥ
ϣȾǻŻ򤷤ۤɵ𤷤ޤ
ޤǵƤ뤳Ȥ̵Τ褦Ǥ
䤹ߤʤzzz
ʼ˸лԡ 1123ʿ 20:41:21 MAIL:h-sakai@zb3.so-net.ne.jp 26197
ޥ
֥֥ŵMAXפΣ渶Ƥ񤭤ޤʴǤ(^^;;

ᤤΤǺǯ⤽󣱥ĤΤߤȤʤޤĿͤȤƤϡΩʤƤ祮֥˽ФƤޤäǯȤȤ⤢äơǯȤ˿ǯǤäȤ顢2005ǯ1ΩƲҤ򵯤פʡƽ񤯤ȤˤʤΤϴְ㤤ʤȤäȤޥ륹ȡĤǯȤȤˤʤꤽǤ󡢤ǯˤϡ19xxǯФפȤ200xǯѥǣ祪СζǤΩƤפʤƤΤ¤äƤ櫓Ǥʾ
ƺǤ

䡧ޥ뷯ͤǯ̤򥿥˥֥򤹤뤳ȤˤޤͤǤ󤱤򤷤ƾäꡢȤʥ롼ǤȤͤǤ󤱤򤷤Ƥʤʤ餬ޤʤΤǡ֤ޤϣͤȣͤʬơ줾Υ롼פξԤ辡ԤפȤˤޤơޥ뷯ϤɤάȤɤǤ礦

ϴñǤ͡ɤϤŤȻפޤĤΥ롼פʬȤˡͤΤۤäۤŪͭʤǤͤΤۤäƾԤȤʤΨϣǤͤΤۤȣǤ͡ޥ뷯ΤȤ٤άϡ֤ʤȤƣͤΥ롼פפȤȤˤʤǤ

ơǽꤸ㤢åꤷǤ͡ؤʡˤ˼ΤǤ顢ּʤפȤä뤳ȤǤ礦㤢ʤ餤

ƱǤϡԸʿפȤ夬äᡢ֤ޤϤ줾Υ롼פǤ󤱤򤷤ơä͡ʣͤǤʤƤ⹽ޤˤ辡˿ʤפȤˤޤǡͥ롼פϣͤη辡ʽмԤФ뤳Ȥ⤢뤳Ȥˤʤꡢʿˤʤäޤ͡ǤϡΤȤޥ뤵ΤȤ٤άϡ

ϴŪˤʬʤǤָ͡ʿˤʤäפ褦ʵ⤷ޤ֣ͥ롼פΤۤͭˤʤäפ褦ʵ⤷Ƥޤޤ
ޤͥ롼פä硢辡˿ʤΨϣǤͥ͡롼פΤۤ⡢ΨϣǤ֤㤢ƱפȤȤǤϤʤǤͥ롼פη辡ʽмԤϣͤޤϣͤǤͤˤʤ뤫ͤˤʤ뤫Ϥ줾죱Ǥͥ롼פˤͤͥΨϡʣˡߡʣˡߡʣˡܡʣˡߡʣˡߡʣˡᣵȤʤǤϡͥ롼פ飱ͤ辡˽ФƤȡͤФƤ򤽤줾Ƥιפ򻻽ФƤǤȡͥ롼פˤͤͥΨϡʣݣˡࣳ᣷Ȥʤޤ˥ӥߥ硼ǤϤޤͥ롼פΤۤͥ䤹Ǥ͡Ȥ櫓ǤǤޥ뤵ΤȤ٤άϡ֣ͤΤۤ˹Ԥ٤פȤʤǤ

Ȥ櫓ǡǯ᤯ϤʤȤߤߤäάȤȤˤʤäƤޤޤǤޤ֥äƤΤϡʳΨκѤ߽ŤͤǥäƤΤܼʤ櫓ǡХˤϽʤǤ͡ȤĤġƥȡ˥ѥŹʤƤΨ˰֥ǯäƤޤä櫓Ǥʾ
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