-Yeka ukukhangela! Siyifumene ekugqibeleni,' wadanduluka watsho uMkomishinala uMacCarnigan.
– Ngubani mhlekazi? wabuza uLieutenant weSibini uPierron.
“Kweyona ndlavini imtyibilizi onokuthi uyicinge. Kudala ndiyikhangela phantse iminyaka engama-50.
- Ndandingazi, uMkomishinala. Imalunga nabani?
-Inombolo yakhe ngu-Ein Stein kwaye indithathe phantse ubomi bonke ukuba ndiyifumane.
- Ngubani malunga? Ingaba unazo iifoto zakho phaya?
- Ewe, ndinayo apha, yile nto ikhangeleka ngayo, kodwa ungakhohliswa yimbonakalo yayo emsulwa, le ndoda ilapha isihlalele sikrokra phantse iminyaka elishumi.
Ke uMacCarnigan wabonisa iAgent Pierron ifoto ka-Ein Stein, le foto:
EStein.
Le mbali imfutshane yamapolisa isenokubonakala ngathi iyaqhula, kodwa ukuba sitshintsha abecuphi bezibalo, iba yenye yezona zinto zimangalisayo eziye zafunyanwa kwiminyaka yakutshanje. Kodwa ukuze siqonde ububanzi beli bali, kufuneka siqale sithethe ngenye yeenkalo apho imathematika kunye nobugcisa budibana khona: i-mosaics.
amaphepha-ndaba e-mosaic
Sonke sikhe sabona i-mosaic ngaxa lithile ebomini bethu. Le yimisebenzi emincinci yobugcisa okanye yokuhombisa eyenziwa kusetyenziswa amaqhekeza amancinci ahambelanayo.
Eminye imizekelo yeemosaics
Xa sithetha ngeemosaics kwimathematika, sidla ngokubhekisa kwinto eyaziwa ngokuba ziitessellations, eyindlela yokucwangcisa iziqwenga okanye iithayile ukuze ezi ziqwenga zibe nemiphetho efanayo kwaye zingashiyi imingxuma.
Kudala-dala iingcali zemathematika nezemathematika zaphakamisa lo mbuzo ulandelayo
Zeziphi iziqwenga endinokuthayela ngazo inqwelomoya?
Okokuthi, luhlobo luni lweengcezu endingazisebenzisayo kuloo nto, ndibeke ukuze iileyile zithintane kumacala aqhelekileyo, akukho zithuba kwindiza. Ngokucacileyo izangqa azikho kweli qela likhethiweyo, kuba ukuba ndifuna ukuthayela inqwelomoya usebenzisa izangqa kuphela ziya kundishiya nemingxuma. Yiza, ndiza kuphosa i-grout elungisiweyo.
izangqa zishiya izithuba
Nangona kunjalo, zininzi ezinye iimilo esinokuthi ngazo ithayile inqwelomoya, ezinje ngonxantathu, izikwere okanye iihexagons.
I-Tessellation enepoligoni enye eqhelekileyo
Okanye sinokuthayela indiza kunye neendibaniselwano zala okanye amanye amanani.
I-Tessellation eneepoligoni ezininzi eziqhelekileyo
Okanye unokuthayela inqwelomoya ngemidibaniso egqithisileyo:
Ezinye iithayile ezinokwenzeka
Kodwa uye wacingisisa ngeentlobo ezininzi zeethayile ozibonisileyo, zonke zinento efanayo, oko kukuthi, zibakho ngamaxesha athile. Igama elithi periodic libhekisela kwinto yokuba kukho inguqulelo ethile, ngaphandle kuka-zero, eshiya yonke imosaic efanayo. Ukusuka kwinto esiyiqondayo, ilingana nenyaniso yokuba ukuba sibeka i-tile yomhlaba, i-ceramic amehlo kwaye umntu uhambisa yonke i-mosaic kwicala elithile kwaye aphinde agqume amehlo kwakhona, asiyi kukwazi ukuwuxabisa umahluko phakathi kwe-mosaic yasekuqaleni. kunye nalowo ugxothiweyo.
i-mosaics ngaphandle kwamaphephandaba
Ngokuchaseneyo neethayile zamaxesha sifumana iithayile ezingezizo ezona zingenakuguqulelwa, hayi u-zero, ezishiya imosaic inkangeleko efanayo. Akunzima ukufumana i-mosaic ye-non-periodic, kwanele, umzekelo, ukuthatha i-tileng ye-periodic, makhe sicinge, umzekelo, enye eyenziwe ngezikwere kuphela, kwaye isikwere esinye se-mosaic yonke sahlulwe saba ngoonxantathu ababini. . Ngokucacileyo iseyi-tessellation yenqwelomoya, kodwa akusayi kubakho naluphi na uguqulelo oluya kuyishiya yonke i-tesserae ifana kuba siya kukwazi ukwahlula phakathi kwe-mosaic yoqobo kunye nesusiweyo ngokujonga indawo eguqulweyo ye oonxantathu ababini.
i-aperiodic tiling
Kodwa ngoku kuxa izinto ziba nomdla, kuba kuxa kuvela umbono we-aperiodic mosaic, ezo zithi, ngelixa zingekho ngamaxesha athile, zonelise imeko eyongezelelweyo yokuba zingabinayo imimandla emikhulu ebakho ngamaxesha athile. Ngendlela efanayo le ngcamango inokuvakala njenge-mosaic ye-aperiodic, ukuba sithatha isiqwenga esikhulu ngokwaneleyo, asiphindi kwakhona kwi-mosaic eseleyo. Qinisekisa ukuba isampulu ye-mosaic engakhange ichazwe ngokwexesha ngaphambili ayinakwenzeka kuba sinokufumana iingingqi ezinkulu ngokungenasizathu, thatha nje amaqhekeza amakhulu angaquki nokuba nguwuphi unxantathu.
Ke, umbuzo ovela ngokwemvelo ngulo ulandelayo:
Ngaba zikhona ii-aperiodic mosaics?
Lo mbuzo, owaqala ukufundwa kwisiqingatha sesibini senkulungwane yokugqibela, ngokukhawuleza wafumana impendulo eqinisekisiweyo kwaye omnye wabokuqala ukufumana i-aperiodic tessellation yayinguRaphael M. Robinson. I-mosaic echazwe nguRobinson ngo-1971 yayine-tesserae ezi-6 ezilandelelanayo.
iithayile zeRobinson
Kwiminyaka embalwa kamva, nangoo-70, uRoger Penrose wafumana iithayile ezimbini zeaperiodic ezinokwakhiwa, nganye kuzo isebenzisa iithayile ezimbini ezahlukeneyo kuphela. Eyokuqala kwezi tessellations yenziwa ziirhombusi ezimbini ezahlukeneyo:
Iithayile zePenrose (irhombuses)
Unokuvelisa i-mosaics ngolu hlobo:
Penrose ithayile
Eyesibini kwezi thayili zeaperiodic inikwa ziziqwenga ezibini ezaziwa njengekite kunye notolo, ngenxa yezizathu ezicacileyo:
Iithayile zePenrose (icomet kunye notolo)
Ewe, kukho ukuthandabuza ukuba i-plantar ingaba yinto elandelayo:
Ngaba zikhona iimosaic zeaperiodic ezenziwe ngethayile enye?
Le ngxaki yaziwa ngokuba yingxaki ye-Ein Stein (isuka kwisiJamani igama elithi "ilitye") kwaye phantse iminyaka engama-50 ihleli ingasonjululwanga. Kude kube ngoMatshi ophelileyo!
Ukufunyanwa kwe-Ein Stein
Ngomhla we-20 kaMatshi, izazinzulu uDavid Smith, uJoseph Samuel Myers, uCraig S. Kaplan kunye noChaim Goodman-Strauss abavela kwiYunivesithi yaseCambridge, eWaterloo naseArkansas bapapasha umsebenzi othi 'An aperiodic monotile' apho bachaza indlela enokwenzeka ngayo i-monotile efunwa kakhulu. emva kwetesserae evelisa i-aperiodic mosaic eneqhekeza elilodwa.
I-Tile echazwe nguSmith, Myers, Kaplan kunye noGoodman-Strauss
Ngale tile enye, ebonakala kum ifana kakhulu nesikipa, ubonisa ukuba i-aperiodic mosaics efana nale ilandelayo inokwakhiwa:
I-aperiodic mosaic yethayile
Ukuba ulangazelelo lwakho lokwazi malunga nalo mbandela, ungangena nzulu kolu lwazi lufunyenweyo kule vidiyo ilandelayo,
apho abafumani balo bathetha nabanye abantu abafanelekileyo kule ndawo, kubandakanywa neBhaso leNobel kwiFiziksi uRoger Penrose.
I-ABCdario de las Matemáticas licandelo elivela kwintsebenziswano kunye neKomishoni yokusasazwa kweRoyal Spanish Mathematics Society (RSME).
MALUNGA NOMBHALI
UVictor M. Manero
