- Misa ukusesha! "Ekugcineni sesiyitholile," kubabaza uKhomishana uMacCarnigan.
– Kubani mnumzane? -kubuza uLieutenant Pierron Wesibili.
- Komunye wama-scoundrels anzima kakhulu ongawacabanga. Sekuyiminyaka ecishe ibe ngu-50 ngiyifuna.
– Bengingazi, Commissioner. Imayelana nobani?
- Inombolo yakhe ngu-Ein Stein futhi kungithathe cishe impilo yonke ukumthola.
- Imayelana nobani? Ingabe unazo izithombe zakho lapho?
- Yebo, nginayo lapha, ibukeka kanjena, kepha ungakhohliswa ukubukeka kwayo kungenacala, lo mnumzane omncane lapha uye wasigcina singabazeki cishe amashumi eminyaka ayishumi.
UMacCarnigan wabe esekhombisa u-Agent Pierron isithombe sika-Ein Stein, lesi sithombe:
E-Stein.
Le ndaba emfushane yamaphoyisa ingase ibukeke njengehlaya, kodwa uma sishintsha abaseshi bochwepheshe bezibalo, iba ngenye yezinto ezinhle kakhulu ezitholakele zezibalo eziye zatholakala eminyakeni yamuva nje. Kodwa ukuze siqonde ububanzi bale ndaba kufanele siqale sikhulume ngomunye wemikhakha lapho kuhlangana khona izibalo nobuciko: ama-mosaics.
Amaphephandaba kaMose
Sonke sike sabona i-mosaic ngesikhathi esithile ezimpilweni zethu. Lena imisebenzi yobuciko emincane noma yokuhlobisa eyenziwa kusetshenziswa izingcezu ezincane ezihambisanayo.
Ezinye izibonelo zama-mosaics
Uma sikhuluma nge-mosaic ku-mathematics ngokuvamile sibhekisela kulokho okwaziwa ngokuthi ama-tessellations, okuyindlela yokuhlela izingcezu noma amathayela ukuze lezi zingcezu zibe nemiphetho efanayo futhi zingashiyi izimbobo.
Esikhathini eside esidlule, izazi zezibalo zazibuza lo mbuzo olandelayo:
Yiziphi izinhlobo zezingcezu engingahlanganisa ngazo indiza?
Okungukuthi, yiluphi uhlobo lwezicucu engingazisebenzisa kulokho, ngizibeke ukuze amathayili athinte ezinhlangothini ezivamile, azikho izikhala endizeni. Ngokusobala imibuthano ayikho kuleli qembu elikhethiwe, ngoba uma ngifuna ukuthayela indiza ngisebenzisa imibuthano kuphela kuzosala izikhala. Woza, kuzomele ngifake i-fixed grout.
Imibuthano ishiya izikhala
Kodwa-ke, kunezinye izibalo eziningi esingazenza ngazo i-tessellate indiza, njengesibonelo, onxantathu, izikwele noma ama-hexagon.
I-Tessellation enepholigoni eyodwa evamile
Noma singathayela indiza ngezinhlanganisela zalezi zibalo noma ezinye.
I-Tessellation enamapholygoni amaningana avamile
Noma ungakwazi ngisho nokwenza i-tessellate indiza ngezinhlanganisela eziwubukhazikhazi kakhulu:
Amanye ama-tessellations angenzeka
Kodwa uye wacabangela ukuhlukahluka okukhulu kwama-tessellation awethulile, wonke kunokuthile afana ngawo, okungukuthi, atholakala ngezikhathi ezithile. Igama elithi periodic libhekisela eqinisweni lokuthi kukhona ukuhumusha okuthile, ngaphandle kukaziro, okushiya yonke i-mosaic ifana. Ngokwalokho esikuqondayo, kulingana nokuthi uma sithayela indawo engaphezulu, i-ceramic amehlo futhi othile ehambisa yonke i-mosaic ngendlela ethile abese evala amehlo futhi ngeke sikwazi ukubona umehluko phakathi kwe-mosaic yokuqala kanye ne-mosaic esusiwe. eyodwa.
Ama-mosaics ngaphandle kwamaphephandaba
Ngokuphambene nama-tessellations we-periodic sithola ama-tessellations angewona ama-periodic, okuyilawo angenawo ukuhumusha, hhayi okuyize, ashiya i-mosaic inokubukeka okufanayo. Akunzima ukuthola ama-mosaic angewona ama-periodic, kwanele, isibonelo, ukuthatha i-tessellation ngezikhathi ezithile, ake sicabange ngokwesibonelo eyodwa eyakhiwe ngezikwele kuphela, futhi sihlukanisa isikwele esisodwa se-mosaic yonke ibe ngonxantathu ababili. Ngokusobala kuseyi-tessellation yendiza, kodwa ngeke kube khona ukuhumusha okushiya yonke i-tessera ifana njengoba sizokwazi ukuhlukanisa phakathi kwe-mosaic yasekuqaleni kanye nesusiwe yayo ngokubheka indawo eguquliwe yabonxantathu ababili.
Imidwebo ye-Aperiodic
Kodwa manje yilapho izinto ziba mnandi, ngoba yilapho kuvela khona umqondo we-aperiodic mosaic, okuyilabo okuthi, ngokuba ngezikhathi ezithile, banganeliseki isimo esingeziwe sokuthi abanazo izifunda ezinkulu ngokuzenzakalelayo eziba ngezikhathi ezithile. Ngendlela efanayo lo mbono ungazwakala njenge-mosaic ye-aperiodic, uma sithatha ucezu olukhulu ngokwanele, aluphindaphindi kuyo yonke i-mosaic. Qiniseka ukuthi isampula ye-mosaic okungekho periodical echazwayo ngaphambilini ayisebenzi ngezikhathi ezithile njengoba singathola izifunda ezinkulu ngokunganaki ngezikhathi ezithile, vele sithathe izingcezu ezinkulu ngokunganaki ezingabandakanyi noma yimuphi unxantathu.
Ngakho umbuzo ophakama ngokwemvelo uthi:
Ingabe akhona ama-aperiodic mosaics?
Lo mbuzo, owaqala ukuxoxwa ngawo engxenyeni yesibili yekhulu leminyaka elidlule, ngokushesha wathola impendulo yokuqinisekisa futhi omunye wabokuqala ukuthola i-aperiodic tessellation kwakungu-Raphael M. Robinson. I-mosaic eyachazwa uRobinson ngo-1971 yakhiwe ngamathayili angu-6 alandelanayo.
Robinson tile
Eminyakeni embalwa kamuva, futhi ngawo-70, uRoger Penrose wathola amathayili amabili e-aperiodic ayengakhiwa, ngalinye lisebenzisa amathayela amabili kuphela ahlukene. Eyokuqala yala ma-tessellations yenziwe ngama-rhombuse amabili ahlukene:
I-Penrose tesserae (i-rhombuses)
Ungakwazi ukukhiqiza ama-mosaic kanje:
I-Penrose Mosaic
Okwesibili kulawa ma-aperiodic tessellations anikezwa izingcezu ezimbili ezaziwa ngokuthi inkanyezi enomsila nomcibisholo, ngenxa yezizathu ezisobala:
I-Penrose tesserae (ikhayithi nomcibisholo)
Nokho, kunombuzo wokuthi i-plantar ingaba kanjena:
Ingabe akhona ama-aperiodic mosaics enziwe ngethayela elilodwa?
Le nkinga yaziwa ngokuthi inkinga ye-Ein Stein (elisuselwa kwelesiJalimane elisho “itshe”) futhi cishe iminyaka engu-50 ibilokhu ingaxazululiwe. Kuze kube ngoMashi odlule!
Ukutholwa kuka-Ein Stein
Ngomhla zingama-20 kuNdasa, ososayensi uDavid Smith, uJoseph Samuel Myers, uCraig S. Kaplan kanye no-Chaim Goodman-Strauss baseNyuvesi yaseCambridge, e-Waterloo nase-Arkansas bashicilela umsebenzi othi 'An aperiodic monotile' lapho bachaza khona uhlobo olungenzeka lwalolu hlelo olufunwayo. -ngemuva kwethayela elidala i-aperiodic mosaic enesiqephu esiyingqayizivele.
Uthayela ochazwe nguSmith, Myers, Kaplan noGoodman-Strauss
Ngaleli thayela elilodwa, ngokubona kwami libukeka lifana kakhulu nesikibha, likhombisa ukuthi kungakhiwa ama-aperiodic mosaics afana nalawa alandelayo:
I-aperiodic mosaic yethayela
Uma ufuna ukwazi ngesihloko, ungangena ujule kulokhu kutholwa kuvidiyo elandelayo,
lapho abavumbululi bayo bekhuluma khona nabanye abantu abafanelekile endaweni, okuhlanganisa noMklomelo KaNobel kuPhysics uRoger Penrose.
I-ABCdario de las Mathematics iyisigaba esivela ekusebenzisaneni neKhomishini Yokusabalalisa ye-Royal Spanish Mathematics Society (RSME).
MAYELANA NOMBHALI
UVictor M. Manero
