Flexagon hack. Yuav ua li cas yuav ua rau ib tug peb-dimensional crafts?

Cov khoom ua los ntawm daim ntawv - yog ib tug tag nrho lub ntiaj teb no uas muaj tswv yim ntau haiv neeg. Muaj ntau daim ntawv yees ua los ntawm mathematicians. Piv txwv li, lub npe hu thoob ntiaj teb hack flexagon kuj yees lej menyuam kawm ntawv nyob Princeton University Arturom Stounom nyob rau hauv 1939. Lub entertaining flexagon? Yuav ua li cas yuav ua rau ib tug ntau yam ntawm flexagon thiab thov cov me nyuam?

Muaj kev lom zem crafts tawm ntawm daim ntawv

Needless Latin lo lus (flectere), tsim lub hauv paus ntawm lub npe, nws yog bent los yog daim ntau quav tso. Yog li ntawd flexagon - ib tug polygon, uas yuav tsum tau tsim los ntawm cov ib txwm sawb ntawv dawb. Txhua lub sij hawm, dabtsi yog khoov lub polygon, peb nrhiav tau ib tug tshiab lub dav hlau.

Flexagon dab tsi nws yog zoo li cas? Yuav ua li cas ua nws txoj cai no daim duab? Feem ntau ua ib tug hexagonal tiaj flexagon, raws li nws yog ib qho yooj yim. Siv ib tug ntau yam ntawm cov qauv ntawm cov dav hlau, peb yuav thov cov me nyuam ntawm txawv txawv crafts, thiab cia lawv nyob rau hauv cov creation ntawm ob planar thiab ntim cov nuj nqis kuj pab tau.

Flexagon: yuav ua li cas yuav ua rau daim ntawv?

Pib qhov twg? Yog li ntawd, peb yuav txiav txim siab los mus tsim flexagon. Yuav ua li cas yuav ua rau ib tug ceev hack? Polygon yuav sai sai thiab yooj yim los ntawm ib tug ntawv ntawm daim ntawv yog, tab sis nws yog advisable tsis xaiv ib yam nkaus thiab mos mos. Flexagon quadrangular hu ua tetrafleksagonami. Ib tug daim duab muaj lub luaj li ib cov hexagon, hu ua geksafleksagonom. Txhua nto nws muaj nws 6-sectors cov vajvoos peb sab. Tseem muaj oktafleksagony (8 sab) thiab dodekafleksagony (10 sab). Yuav ua li cas ua flexagon ntawm daim ntawv? Scheme yog heev ntau haiv neeg. Xav txog ib tug heev yooj yim, uas yog ua los ntawm zoo tib yam geksafleksagon. Qhov no tswvyim yog siv feem ntau.

Nws yog ib qho yooj yim mus kos rau lawv tus kheej, vim hais tias nws muaj xwb ntawm ib pab pawg neeg ntawm txoj cai cov vajvoos peb sab. Tab sis koj muaj peev xwm siv tau ib qho ornamented tswvyim nyob rau hauv uas rau cov thawj lub sij hawm nws yog yooj yim los mus sib sau ua ke crafts. Thaum cov Circuit Court yog txiav, daim ntau quav tso nyob rau hauv ib nrab thiab stacked nplooj theem, dabtsi yog khoov txhua txhua daim duab peb sab txoj kev ua ib feem ntawm ib tug nyias muaj nyias ib lub dav hlau. Thaum flexagon yog siab tau koom ua ke, muab lub xeem kom meej.

Nyob rau txhua qhov ntawm plaub chaw yuav muaj koj duab. Tom qab kev kawm no tswvyim, ces koj yuav mus ua hauj lwm creatively. Nyob rau lub tiaj ntawv kos tib yam daim duab peb sab. Ces tus xov tooj lub sectors uas tsim ib lub dav hlau. Cov vajvoos peb sab, raws li cov lus qhia, koj yuav tsum khoov cia, tsim tus yam polygon. Tab sis txhua leej txhua tus xaiv lawv tus kheej txoj kev, raws li cov yooj yim tshaj rau quav. Ib yam li ntawd, qhov no tswvyim yog yuav tej polygon-flexagon. Ntau txoj schemes ntawm cov nuj nqis zoo tsim maj.

Ntawv-flexagon

Lej qauv-flexagon tus me nyuam yuav yeej yuav txaus siab. Qhov no yog ib qho amazing khoom teejtug uas yog daim ntawv yuav tsum muaj ntaub ntawv diversely. Nyob rau saum npoo ntawm lub tiav lawm daim depict lub cim ntawm cov me nyuam tas lauv thiab pib tus me nyuam ntse heev ua pov thawj tias zauv qauv tej zaum yuav ntawm kev txaus siab.

Thiab koj yuav los nrog ib tug zoo heev thiab txawv txawv ntawv, thiab nws tsis yog ib tug dag. Yuav ua li cas yuav ua rau ib daim ntawv-flexagon? Yog hais tias koj kos rau qhov chaw ntawm lub tos txais lus rau tus me nyuam thiab lub Christmas decorations, nws yuav tau ib tug zoo khoom plig rau lub xyoo tshiab. Tiam sis yog tias koj tau phem nuj nqis tau, nrhiav lwm txoj kev tawm. Koj muaj peev xwm tsuas txiav tawm koj nyiam daim duab thiab phua rau hauv sib npaug zos cov vajvoos peb sab, uas ces yuav tau ua tib zoo glued rau txhua txhua sector ntawm crafts

Tej khoom - ib tug ntau yam ntawm kev sib raug zoo

Muaj peb-dimensional nuj nqis. Yuav ua li cas ua flexagon volume ntawm daim ntawv? Ua li no, siv sij hawm piv txwv li lub tiav lawm tswvyim, uas muaj 10 equilateral cov vajvoos peb sab pab sectors. Qhov no xam yog hu ua trigeksafleksagon - uas yog, lub ib thooj ntawm cov hexagon yuav ua tau peb tej chaw. Ntawm cov hoob kawm, qhov no tsis yog cov kev txwv. Tus qauv tej zaum yuav muaj 4, 5, thiab tej chaw, thiab 10. Cov flexagon txawm nthuav ntau, tab sis yog raws li nyob rau hauv tib lub tswv yim. Tab sis mus sau xws li ib tug txuj ci tseem ceeb tsis yog li ntawd yooj yim. Lub ntsiab txoj cai thaum tsim tau ib tug qauv - ua raws li cov lus qhia. geksafleksagona Scheme 4 chaw yuav zoo li no:

Ntawm no yog ib qho piv txwv ntawm cov uas yuav txawm ntau daunting daim duab - nonageksafleksagon. Hais tias yog, qhov ntim flexagon nrog rau cov ces kaum, thiab tej chaw no twb 9. Qhov no qho khoom ua si yog twb laus, tus me nyuam xws qauv tsis muaj hwj chim dhau, nyob rau hauv txhua rooj plaub, tsis muaj kev pab los ntawm cov niam txiv.

Yuav kom nkag siab txog cov intricacies ntawm lub tswvyim uas lub ntim cov nuj nqis nws yuav siv sij hawm. Lub preform yog zoo dua rau decorate nrog sib txawv xim kom tsis txhob tsis meej pem thaum lub sij hawm los ua ke. Sim!