鯤ο
BETGQPDθUȤȡΩΤϡB-QTPU-Eˤʤޤ

ݥȤBDEGǹͤ뤳ȤǤ
DBEPEGBQϤΤˤޤ
ΩΤʿDTGǤȡGQPDʿ̾ˤꡢθU⤳ʿ̾ˤ뤳Ȥ顢
QTPUΩΤʿDTG̤Ȥ狼ޤ
ơΩΤB-QTPU-EȤ狼ޤ
BDE濴RBEG濴SȤȡ
RS//QP//DGǡRS:QP:DG=1:1:3Ǥ뤳ȤĴ٤Ȥ狼Τǡ
ѤƤĴ٤ȡQTPU1/2QTG狼ޤ
ΩΤѤϡQEBG1/2ǤꡢDEBG1/4ǤꡢABCD-EFGH1/12Ǥ뤳Ȥ狼ޤ
äơV6*6*6*1/1218
//
84ڡ 3:49:30 51716

m(_ _)m
ABCD-EEGH=666=216
A-BDE=2161/21/3=36
A-BDE-G=216-363=108
A-BDE-P=1082/3=72
4ʬˤΩΤ
724-216=72
ŤʤBDE-Gĺο(4ս)1ĤʤΤ
724=18cm^3

ȤΤǤ4սνŤʤƱΤ˽Ťʤ̵꤬ȤȤ򤭤ȼʤȤʤȻפΤǤɤФ褤Ǥ礦ġ
84ڡ 4:25:36 51717
ֿء׾ι
Τˡ⤵Ⱦʬλѿ٤碌˺äơζͭʬȸޤ
84ڡ 6:28:36 51718
ֿء׾ι
geogebraǻͿޤޤ
https://www.geogebra.org/m/tmjmeeja
84ڡ 7:00:37 51719
ߥȤ
ֿͤء׾ιԤƱ褦٤碌˺äƶͭʬ򸫤ޤ
Ϸϡ 84ڡ 7:46:06 MAIL:manato-yo-da@jcom.zaq.ne.jp 51720
鯤ο
#51717
Τˡ̤̤ˤơ̤濴ȸ礦ĺĤĺȤ뾮ѿ
Τ̤줾бƣĹͤȤˡνŤʤ꤬ɤȤƱǤ
٤礦ΩΤȤ߹碌ϡĤǤʤΤȶͭͤοбƣĤȻפޤ
ơĤνŤʤѤV2ĤνŤʤѤV3ĤνŤʤѤV4Ȥȡ

ΤѤ72ǡƾѿѤ36顢

7236*4-6*V2+4*V3-V4
δطΩ顢V3V4ñ˵ʤСδطȤäơV2줽
v3v4ϴñǤʤ顢Υץ񤷤Ȼפޤ

84ڡ 19:52:32 51721
ǯ
2:1ǤϤʤP,QĺΤʤ顢2Ĥϰפ롲6*6*6/3=72
21/2ˤΤǡ72*1/2*1/2=18
ȤϻפޤϹäƤ褦Ǥ
פΤϡɬ
84ڡ 20:10:10 51722
鯤ο
51721
ΤABCDѿaBCDAbCDABcDABCdȤȡ
aBCDAbCDνŤʤϡabޤߡ
aBCDABcDνŤʤϡacޤߡ
aBCDABCdνŤʤϡadޤΤǡ
Ĥξѿaͭ롣
ƱͤˤơĤb,c,dͭ롣
顢ѿĤνŤʤϡ4ΤߤabcdޤͽۤǤ롣

84ڡ 20:20:02 51723
baLLjugglermoka
޷ľʬޤѤη׻ιפɬפǤ
84ڡ 20:20:58 51724
鯤ο
»ޤ
ΤABCDѿaBCDAbCDABcDABCdȤȡ
aBCDAbCDνŤʤϡabޤߡ
aBCDABcDνŤʤϡacޤߡ
aBCDABCdνŤʤϡadޤΤǡ
ĤνŤʤ꾮ѿaͭ롣
ƱͤˤơĤνŤʤb,c,dͭ롣
顢ѿĤνŤʤϡ4ΤߤabcdޤͽۤǤ롣
84ڡ 20:21:12 51725
鯤ο
ޤޤ
ΤABCDѿaBCDAbCDABcDABCdȤȡ
aBCDAbCDνŤʤϡabޤߡ
aBCDABcDνŤʤϡacޤߡ
aBCDABCdνŤʤϡadޤΤǡ
ĤξѿνŤʤaͭ롣
ƱͤˤơĤξѿνŤʤb,c,dͭ롣
顢ѿĤνŤʤϡ4ΤߤabcdޤͽۤǤ롣
84ڡ 20:22:33 51726
鯤ο
#51724
̤ͳˡȡμɬפˤʤΤǤؼˤϴΤʤǤ礦
Τĺ̤˲ϡ礦̤νſˤ롣
ſϡ򣲡ʬ롣

84ڡ 20:34:51 51727

#51721 鯤οͤ
ܤ⤤꤬Ȥޤ
7236*4-6*V2+4*V3-V4
ˤV2Τ()бΤ6ġ
V3ĺб4ġV4Τ濴1(餯#51726 ˤabcdޤΰ)¸ߤͻҤʤΤǤ͡
V3,V4ޤʤȤˤ񤷤Ǥ͡
ˤ꤬Ȥޤ
84ڡ 23:54:40 51728
鯤ο
#51728
7236*4-6*V2+4*V3-V4
Ͻn=4ξ礫ΥʥǤ

n(ABCD)
n(A)+n(B)+n(C)+n(D)
n(AB)n(AC)n(AD)n(BC)n(BD)n(CD)
n(ABC)n(ABD)n(ACD)n(BCD)
n(ABCD)

ޤޡ޷
aBCDAbCDABcDABCdǤꡢоꡢŽ碌ABCDˤʤطˤꡢƱξѿνŤʤʬƱˤʤꤽ顢δطʤꤿȹͤǤ

Ʒΰ̣ϡV1ᾮѿѡV0ABCDѤȤȡ

V0V1*1C4-V2*2C4+V3*3C4-V4*4C4
Ǥ

2ĤνŤʤ꤬4C26ĤꡢɤνŤʤߤ˰ۤʤĤͤͭطˤ뤳Ȥ顢2ĤνŤʤˤĤƤϡޤбĤƤޤޤ¾2෸ˤĤƤ޷ŪбĤޤǤϤ狼ޤ
V3ηϤ褯狼ޤ󤬡V44(ѣ)ˤʤΤΤˤʤΤ(դ狼äƤΤǡ׻ǽ)ǤСμV3狼äƤޤȤˤʤޤ
V4ˤĤ4ޤޤǤˤϤ狼ʤΤǡV4ǤʤΤϻǰ
ΩΤΩΤζΩΤˤʤꤽ顢ΤޤߣˤϤʤʤޤ
85ʶ 1:29:00 51729
ֿء׾ι
#51718ɽԽʬǤΤǡΤ褦ˡޤ٤碌ɬʤΤǡפޤǤ
ΩΤϡΤΡ¦̤̤Ȥ⤵ΤȾʬˤʤ룲ĤλѿζͭʬǤȸޤ
85ʶ 5:13:07 51730
鯤ο
#51729
V44(ѣ)ˤʤΤΤˤʤΤ

abcdޤΤϳμ¤Ǥ켫ȤˤϤʤʤޤ
ȤΤϡ򣲤Ȥ3ĤξѷνŤʤޤƤߤ顢
ѷǤϤʤѷޤϻѷˤʤäǤ
顢V4ϡΤγ̤˻ѿ򤯤äĤ޷ˤʤΤǤʤ
פޤ줬ΩΤä餹ΤǤ
ïCADV4ηǧǤޤ
85ʶ 20:02:56 51731
鯤ο
51731
ѷޤϻѷˤʤäǤ
ǤϻդĹϻѷǤϻѷǤϤޤ
85ʶ 20:08:54 51732
鯤ο
#51722

>2:1ǤϤʤP,QĺΤʤ顢2Ĥϰפ롲6*6*6/3=72
>21/2ˤΤǡ72*1/2*1/2=18
>ȤϻפޤϹäƤ褦Ǥ
>פΤϡɬ

ΰפǤ
ʥѡˡΤȻפޤ㤦褦Ǥ
⤷βˡΩʤС2Ȥơͤ⡢
1/4ˤʤϤǤºݤϡ1/5ˤʤޤ

ѷABCBCMACNAMPBNQȤ롣
λPBCȢQACνŤʤʬѤϡABCѤβܤ

ǤϡɤäȤȡ
֤ˤơο޷2ܤ˰ФäƤȤȤǤΤ礹ɬפޤ

ΤĤ̤ʿ̤֤ơŤʤ룲ĤξѿΰV1Τ̤̤ȤΤȤ
⤦ĤξѿV2Τ¦̤̤ȤΤȤʤС
ǹͤ硢β줫ǹͤʤФʤޤ
V1V2򶦤˱ľ(V1ι⤵)˳礷޷ǹͤζʬѤ1/2ˤ롣
V1V2򶦤˱ľ(V1ι⤵)ȡV2ι⤵2˳礷޷ǹͤζʬѤ1/4ˤ롣

ΰФ޷ǹͤơ᤹ˡϡʱߤߤ˵夵Ȥ˻Ȥޤ
ξ⡢ʿΤѴ򤫤ƤϤǤ
86ڡ 7:56:37 51733

鯤οͤ

Ȥ꤬Ȥޤ
https://ibb.co/Y70FM1m

ȤμԤ񤤤ΤǤޤ褦ˤʤäƤǤ礦
PDFեǤ

Τγ̤⤵ȾʬλѿͤȤ4ĤΩΤζͭʬΤ4Ĥa,b,c,dΤꡢġaȡΤλܤͤȤǺ3Ĥγ٤ľѤˤʤ뤽Ǥ
򤬤øʤΤǡեͤΤȡġ
Τ4Ĥ黰ؿľդФȡΩΤˤʤޤαФʬV4ΰ褫鳰ʤɤϡɸˤ׻ʤɤˤǧɬפȻפޤ

Ϥ褯ʬäƤʤΤǤ䤤ޤԤʹȤϤǤޤ
ɤꤤޤ

87 1:52:35 51734

aȡΤλܤͤȤǺ3Ĥγ٤ľѤˤʤ뤽Ǥ


a롢Τ3ܤͤɤ٤ľѤˤʤ뤽Ǥ

ޤ
87 2:00:12 51735

ƤϤۤ񤷤ǤϤʤä⤷ޤ󡣤褬ѤʤΤǤ礦
򤤤ޤ
ʤߤ˹äƤ뤫ʬޤ󤬡abcdΰդϡΤΰդ1/3ˤʤΤǡV4ΩΤȤСξV4=2*2*2=8 cm^2Ǥ礦V3=11ˤʤΤǤ礦(?
87 2:27:43 51736

ޤߤޤ
abcdΤϸ礭ΤʰִطʤΤˡ3ܤͤĤϡ礭ΩΤȤ㤦ΤǡФƤΩΤˤʤȸƤʤǤ͡
ŤͽŤͼ餷ޤ
񤷤Ǥ()
87 2:57:18 51737

עʿԤʡ
m(_ _)m
87 3:20:52 51738
鯤ο
#51734

JޥޤοޤǡQEF3:1ʬǤEF1:3ʬR(2,2,3)/4Ȥȡ
ѿaBCDAbCDνŤʤϡ8C-EaQb-D
ѿABcDABCdνŤʤϡ8A-FcRd-B
ΣĤ8ΤνŤʤ꤬V4
RC-EaQb-DˤޤޤΤǡRV4˴ޤޤޤ
ƱͤQV4˴ޤޤޤ
V4̤顢QRV4˴ޤޤޤ

ʤȡо顢P濴Ȥơ岼ˡΩΤ
⤵ȾʬȬΤޤळȤˤʤޤ
ĺϡ
1/4(2,2,1)
1/4(2,2,3)
1/4(1,2,2)
1/4(3,2,2)
1/4(2,1,2)
1/4(2,3,2)
ޤ줬V4Ρ

87 6:27:00 51739
鯤ο
#51736

>abcdΰդϡΤΰդ1/3ˤʤΤǡ

ϹäƤޤ51716Ǥ⿨Ƥޤ
RS//QP//DGǡRS:QP:DG=1:1:3Ǥ뤳ȤĴ٤Ȥ狼Τǡ

ʤθΡV1ѤΩΤ1/12Ǥ뤳Ȥ⡢51716ƳФƤޤ
#51716ˤQTPUʥޥޤοޤǤaEbQޤ

V4ΩΤȤСξV4=2*2*2=8 cm^2Ǥ礦

ϰ㤤ޤ
䤬Ƥ᡼Ǥϡ
abcdγͤ"Ω"ͤΰˤʤΤǤʤ
ABCDnotabcdˤγ̤γ¦˻ѿ(㤨OABC)򣴤Žդ鸵ΩΤǤ褦ˡ
abcdγ̤γ¦V4˴ޤޤ뻰ѿꡢ򣴤ŽդabcdޤΩΤˤʤΤ
ͽۤƤޤ
Ĥޤꡢa,b,c,dγ̤γ¦4ɲäơa,b,c,dȡɲä4ĺȤ8
ΩΡɡʤ뤤ʿϻΡˤĺˤʤΤǤʤƤޤ
(ΤΰĤQ)

ɤ㤦ΤǤϡȤˤʤäȤΤ#51739Ǥޤ

JޥޤοޤǡQEF3:1ʬǤEF1:3ʬR(2,2,3)/4Ȥȡ
侮ѿaBCDAbCDνŤʤϡ8C-EaQb-D
侮ѿABcDABCdνŤʤϡ8A-FcRd-B
䤳ΣĤ8ΤνŤʤ꤬V4

ʤΤǤ#51739ιͻ顢abcdγ¦ϡȬΤˤʤäƤΤȡ

8C-EaQb-D8A-FcRd-BγĺκɸϡƤ狼äƤΤǡ
򺵿޷륽եȤСǧǤΤǤ礦
ŪˤϡƱΤθ򺵤׻ФʤǤɡ

O(0,0,0)
A(1,0,0)
B(0,1,0)
C(0,0,1)
D(1,1,1)
Ȥȡ
a(2,1,1)/3
b(1,2,1)/3
c(1,1,2)/3
d(2,2,2)/3
Q(2,2,1)/4
R(2,2,3)/4

87 10:45:41 51740

鯤οͤ

ŪǤ餹ߤޤ
Υ᡼ǤդĹ1/3ΩΤȡ1/2ΩΤҾ˽񤤤ơ
1/3abcdȤꡢ1/2ϡ̤濴ȬΤޤ
ȡabcdγĺȬΤγ¦¸ߤ
Ȭ(Qʤ)γĺabcdγ¦¸ߤƤޤ
ޤabcdγĺϡȬΤγ٤ʤ̤γ¦¸ߤޤ

ΩοޤʤȤʤ᡼ΤϡV4ϡΤĺȬΤĺȤΩΤʤΤǤϤʤȤȤǤ

⤷⡢Ĺ1ΩΤ⤦ĺΤͤơͭΩΤͤСΩΤΤ褦ʴоΤʷʤΤʤȡġ
ΤʤΤǡʬɤäƤ뤫Ĥޤ󤬡

⤽⤳󤬸Ǥ顢ѿޤ
87 16:05:54 51741
٥륯åĥ
̲­ΤȤ񤷤äΤǤʤʤĤ줺βˤʤޤ
BDEGΩΤ4ĤγѤڤäѤ1-1/641/3
BCHG˴ؤоΤǡ̤Ȥѿ2ĤȤƸȡѤ3/4⤵1/3ʤΤǡ
666ߡ1/3ˡߡ3/4ˡߡ1/3ˡ18Ȥʤޤ
줾ˤĤƤϡΩΤ򤤤鸫ʿ̿ޤݽѤޤ
פ֤εǿ­áޤŻǤ
87 22:28:12 51742
鯤ο
#51741

geogebra򥤥󥹥ȡ뤷ơ
O(0,0,0)
A(12,0,0)
B(0,12,0)
C(0,0,12)
D(12,12,12)
E(6,6,12)
F(6,6,0)
Ȥȡ
a(8,4,4)
b(4,8,4)
c(4,4,8)
d(8,8,8)
Q(6,6,3)
R(6,6,9)

ѿaBCDAbCDνŤʤϡ8C-EaQb-D
ѿABcDABCdνŤʤϡ8A-FcRd-B
褷ơžơʳ٤V4įƤޤ
ʣʿ޷˴ޤ
鸫ϻѷ̤鸫8ѷ˸ޤ

87 23:33:03 51743
鯤ο
#51742
BCHG˴ؤоΤ

ޤεǹԤȡBCGHƱʿ̤ˤޤ󡣤Τᡢտޤ狼ˤǤ

ϡBETȤơDEBGʿDTGǤơΤȵΩV2˹⤵BTETͭ2ĤŽ碌ǡ̡ɤʢDTGQTPUUPDGQθˤ4:1ǤȵŤˤޤ
87 23:49:17 51744
鯤ο
#51743
̤ͳѷ12ΤˤʤäƤ褦Ǥ
88ʷ 0:06:36 51745
鯤ο
#51745
̤ͳѷ12ΤˤʤäƤ褦Ǥ
8ΤǤ
88ʷ 0:09:06 51746
鯤ο
#51741

¿ʬǡFAȡ

>ΩοޤʤȤʤ᡼ΤϡV4ϡΤĺȬΤĺȤΩΤʤΤǤϤʤȤȤǤ

Τ褦Ǥĺ10168ΩΤˤʤޤ

ȬΤĺȸ礦ĺľˤʤV4򸫤ȡѷ˸ޤ
8ѷγĺϡȬΤλĤΣĺΤΣĺǤ
88ʷ 0:56:16 51747
鯤ο
#51744

ϡBETȤơDEBGʿDTGǤơΤȵΩV2˹⤵BTETͭ2ĤŽ碌ǡ̡ɡʢDTGQTPUUPDGQθˤ4:1ǤȵŤˤޤ

¿ʬƱȤͤƤΤȡ
PDGQθUDGVȤȡ
λDEBGDTGѤϡDG*TV/2
ΩΤQTPUѤPQ*TU/2
ǡ
PQDG1/3
TUTV3/4
顢QTPUDTG1/3*3/41/4
88ʷ 2:00:50 51748
٥륯åĥ
#51744
Ŧ꤬ȤޤBCHEδְ㤤Ǥ
88ʷ 15:12:25 51749

#51747
鯤οͤޡ
Ĺˤ錄ꡢ͡­ۤʬäƤŸȯŸƤޤˤ꤬Ȥޤ̤ɤ졢פǾߤȤäޤ
88ʷ 18:12:50 51750
鯤ο
#51750

б˱ʤФȡǾߤȤޤʤ񤭴ְ㤨ʤɤ¿Ӥ餷Τ褦ˤʤäƤޤäƤΤϳͤ˿ʤȻפޤ
᡼ǧ褦ȰCADƳͤߵ郎⤯Ƥ󡢲ǾҲ𤵤ƤgeogebraƳƤߤȤǤȤߵ㤵äΤǡκȤ򤭤äʤΤȴդƤޤ
88ʷ 18:34:09 51751

鯤οͤ

äˤʤäƤޤ
ʤ˷ФޤΤǵϿȤƻĤƤޤ
V4ΩΤηͳѷνΤˤʤޤ
ĺ14, 12, 24ܤǤ

ȬΤ̤ΤΤĺʤ̤ˤĤơ
̤ξ3Ĥ̤θ1Ĥޤ
ȤСΩΤΰդĹ1ΤȤ
Τĺ
(1/6,1/6,1/6)
(-1/6,1/6,-1/6)
(-1/6,-1/6,1/6)
̤ˤĤơ
ȬΤĺ
(0,1/4,0)
(-1/4,0,0)
(0,0,1/4)
ȡ
(-1/10,1/10,1/10)
äơ3̤Ǹޤ

λͳѷνĤȲĹϢ2/5Ȣ2/4ǡ
ΩΤ濴OλͳѷޤǤεΥ1/6ǡ
Ѥϻͳѿ12ʬʤΤ
12ߢ2/5ߢ2/41/21/61/3=1/30
Ȥʤޤ

ǤΩΤΰ6cmʤΤ
V4=6661/30=36/5=7.2cm^3
ˤʤ뤳Ȥˤʤޤ

ʿ̤θθ餳Τ褦ˤʤޤ
ɤġ
Ȥ⤢졢ˤ꤬Ȥޤ
89ʲС 13:00:46 51752

#51752λͻǤ
ȤμԤ˺ä㤤ޤ

https://ibb.co/k5vYCHs

m(_ _)m

89ʲС 14:28:09 51753

#51753
ˤΩΤ濴OǤϤʤP(0,0,0)Ǥ狼Ť餯Ƥ򤪤ޤ
89ʲС 14:36:51 51754

#51752
ȬΤ̤ΤΤĺʤ̤ˤĤơ
̤ξ3Ĥ̤θ1Ĥޤ

־ˡעΩΤ濴鸫Ƴ¦ˡ

Ȥ̣Ǥߤޤ
ͭ񤦤ޤ
89ʲС 17:42:53 51755
鯤ο
#51753
ϺɤǤ
ϸƤ⡢ǸϤȷ׻ʤȡȤȤǤ͡
꤬Ȥޤ
Ȥ줿ȤȤɩˤϤʤäƤʤȤȤǤ
ͭ̾ɩΤ򾯤ˡѤˤʤΤʡ
89ʲС 22:28:12 51756

#51756
Ϥ
Deltoid dodecahedron ɩΡˤʤ褦Ǥ
https://etc.usf.edu/clipart/20200/20216/deltdodeca_20216.htm

14ĺϡΤ4ȬΤ6Τۤˡɩû2դˤäƺĺ4Ȥ̤ˤʤޤ
ߤĹ2դդΤĺȬΤĺΤˤʤޤ

810ʿ 0:01:20 51757
鯤ο
#51757
Deltoid dodecahedron ɩΡˤʤ褦Ǥ

̾ĤƤǤ͡
οȯɽ˷夷Ƥ褫äǤ
810ʿ 18:23:48 51758
̵̾
ֿء׾ι
ɤ⻰ѿѤ狼ޤGeoGebraѤƤäƤΤǤ
811ڡ 17:37:19 51759
kyorofumi
DPDQθXΩΤ濴(1/2,1/2,1/2)
BEXPĺȤΤΣܤѤȻפäB(0,0,0)
E(1,0,1), X(1/2,1/2,1/2), Q(1/3,2/3,2/3)
׻顢1/36 줬Ĥǡ216ܤ12ˤʤäǤɤְäƤ뤫狼ޤ...

äƤʬѤäƤλΣĤǤϤʤǤ
817ʿ 1:48:28 51760
kyorofumi
DPGQθΩΤ濴*
817ʿ 1:49:37 51761