– Hooki i ka huli! "Ua loaʻa iā mākou," wahi a Komisina MacCarnigan.
– I ka haku ia wai? - i ninau aku ai o Lutanela Pierron.
- I kekahi o nā mea ʻino loa i hiki iā ʻoe ke noʻonoʻo. Ua ʻimi au iā ia no aneane 50 makahiki.
– ʻAʻohe oʻu manaʻo, e Komisina. E pili ana ia wai?
– ʻO Ein Stein kāna helu a ʻaneʻane hoʻokahi o koʻu ola ʻana e ʻike iā ia.
- E pili ana ia wai? Loaʻa iā ʻoe kekahi mau kiʻi o ʻoe ma laila?
– ʻAe, loaʻa iaʻu ma ʻaneʻi, ʻo ia ke ʻano o kona ʻano, akā, mai hoʻopunipuni ʻoe i kona helehelena hala ʻole, ua hoʻopaʻa kēia keonimana liʻiliʻi iā mākou i kahi kānalua no ka aneane ʻumi makahiki.
Ua hōʻike ʻo MacCarnigan iā Agent Pierron i ke kiʻi o Ein Stein, kēia kiʻi:
Ma Stein.
He ʻakaʻaka paha kēia moʻolelo mākaʻi pōkole, akā inā mākou e hoʻololi i nā mākaʻikaʻi no ka poʻe makemakika, lilo ia i kekahi o nā ʻike makemakika maikaʻi loa i ʻike ʻia i nā makahiki i hala. Akā, i mea e hoʻomaopopo ai i ke ʻano o kēia moʻolelo, pono mākou e kamaʻilio mua e pili ana i kekahi o nā kahua i hoʻohui ʻia ai ka makemakika a me ke kiʻi: mosaics.
Na Nupepa Mosaic
Ua ʻike mākou i kahi mosaic i kekahi manawa o ko mākou ola. He mau hana noʻeau liʻiliʻi kēia i hana ʻia me ka hoʻohana ʻana i nā ʻāpana liʻiliʻi i hui pū ʻia.
ʻO kekahi mau laʻana o nā mosaics
Ke kamaʻilio mākou e pili ana i nā mosaics ma ka makemakika, ʻike mākou i ka mea i kapa ʻia ʻo tessellations, ʻo ia ke ʻano o ka hoʻonohonoho ʻana i nā ʻāpana a i ʻole nā tile i loaʻa i kēia mau ʻāpana nā kihi maʻamau a ʻaʻole e haʻalele i nā lua.
I ka wā kahiko, ua nīnau ka poʻe makemakika iā lākou iho i kēia nīnau:
He aha ke ʻano o nā ʻāpana hiki iaʻu ke hoʻokaʻawale i ka mokulele?
ʻO ia hoʻi, he aha ke ʻano o nā ʻāpana e hiki iaʻu ke hoʻohana no ia mea, e kau ana iā lākou i paʻi nā tile i nā ʻaoʻao maʻamau, ʻaʻohe wahi āpau o ka mokulele. ʻIke maopopo ʻaʻole nā pōʻai i loko o kēia pūʻulu koho, no ka mea, inā makemake wau e hoʻopololei i ka mokulele me ka hoʻohana ʻana i nā pōʻai wale nō e waiho ʻia nā āpau. E hele mai, pono wau e hoʻokomo i ka grout paʻa.
Haʻalele nā pōʻai i nā āpau
Eia nō naʻe, he nui nā kiʻi ʻē aʻe e hiki ai iā mākou ke tessellate i ka mokulele, e like me ka laʻana, triangles, squares a hexagons.
Tessellation me hoʻokahi polygon maʻamau
A i ʻole hiki iā mākou ke tile i ka mokulele me nā hui pū ʻana o kēia a i ʻole nā kiʻi ʻē aʻe.
Tessellation me kekahi mau polygon maʻamau
A i ʻole hiki iā ʻoe ke tessellate i ka mokulele me nā hui ʻoi aku ka maikaʻi:
ʻO nā hōʻailona ʻē aʻe hiki
Akā, ua noʻonoʻo ʻo ia i ka nui o nā tessellations āna i hōʻike ai, aia nā mea āpau i kahi mea like, a ʻo ia hoʻi, he mau manawa. ʻO ka huaʻōlelo periodic e pili ana i ka loaʻa ʻana o kekahi unuhi, ʻokoʻa ka zero, e waiho like ana ka mosaic holoʻokoʻa. Mai ka mea a mākou i hoʻomaopopo ai, ua like ia me ka mea inā mākou e hoʻoheheʻe i kahi ʻili, ka seramika i nā maka a hoʻoneʻe kekahi i ka mosaic holoʻokoʻa i kahi kuhikuhi kikoʻī a laila uhi hou i nā maka, ʻaʻole hiki iā mākou ke mahalo i ka ʻokoʻa ma waena o ka mosaic kumu a me ka haʻalele. ʻekahi.
Mosaics me ka nupepa ole
ʻOkoʻa me nā tessellations periodic loaʻa iā mākou nā tessellations non-periodic, ʻo ia nā mea ʻaʻohe unuhi, ʻaʻole null, e waiho ana i ka mosaic me ke ʻano like. ʻAʻole paʻakikī ka loaʻa ʻana o nā mosaics non-periodic, ua lawa, no ka laʻana, e lawe i kahi tessellation periodic, e noʻonoʻo kākou no ka laʻana i hana ʻia e nā ʻāpana wale nō, a ke puʻunaue mākou i kahi huinahā o ka mosaic holoʻokoʻa i ʻelua triangles. Akaka, he tessellation ia o ka mokulele, akā, ʻaʻohe unuhi e waiho like i ka tessera holoʻokoʻa no ka mea hiki iā mākou ke hoʻokaʻawale ma waena o ka mosaic kumu a me kāna mea i hoʻoneʻe ʻia ma ka nānā ʻana i ke kūlana hoʻololi o nā huinakolu ʻelua.
Nā mosaics aperiodic
Akā i kēia manawa ke loaʻa nā mea hoihoi, no ka mea, ʻo ia ka manawa e ʻike ʻia ai ka manaʻo o ka mosaic aperiodic, ʻo ia ka mea, i ka manawa, ʻaʻole e hoʻomāʻona i ke kūlana ʻokoʻa ʻaʻole i loaʻa iā lākou nā ʻāpana nui arbitrarily i periodic. Ma ke ala like e hiki ai ke lohe ʻia kēia manaʻo e like me ka mosaic aperiodic, inā lawe mākou i kahi ʻāpana nui, ʻaʻole ia e hana hou i ke koena o ka mosaic. E hōʻoia ʻaʻole aperiodic ka laʻana mosaic ʻaʻole i wehewehe ʻia ma mua no ka mea hiki iā mākou ke ʻike i nā ʻāpana nui i ka manawa, e lawe wale i nā ʻāpana nui ʻaʻole i hoʻokomo i kēlā me kēia triangle.
No laila, ʻo ka nīnau e kū mai nei:
Aia nā mosaics aperiodic?
ʻO kēia nīnau, i hoʻomaka e kūkākūkā ʻia ma ka hapa ʻelua o ke kenekulia i hala, ua loaʻa koke kahi pane ʻae a ʻo kekahi o ka mea mua i ʻike i kahi tessellation aperiodic ʻo Raphael M. Robinson. ʻO ka mosaic i hōʻike ʻia e Robinson i ka makahiki 1971, ua hana ʻia me 6 mau kile.
ʻO Robinson tile
I kekahi mau makahiki ma hope mai, i ka makahiki 70 hoʻi, ua loaʻa iā Roger Penrose ʻelua tile aperiodic i hiki ke kūkulu ʻia, ʻo kēlā me kēia me ka hoʻohana ʻana i ʻelua mau tile like ʻole. ʻO ka mua o kēia mau tessellations i hana ʻia i ʻelua rhombuses like ʻole:
Penrose tesserae (rhombuses)
Hiki iā ʻoe ke hana i nā mosaics e like me:
Mosaic Penrose
Hāʻawi ʻia ka lua o kēia mau tessellations aperiodic e nā ʻāpana ʻelua i kapa ʻia ʻo ka comet a me ka pua, no nā kumu maopopo.
Penrose tesserae (ka lupe a me ka pua)
ʻAe, aia ka nīnau e like paha ka plantar:
Loaʻa nā mosaics aperiodic i hana ʻia i hoʻokahi tile?
Ua kapa ʻia kēia pilikia ʻo ka pilikia ʻo Ein Stein (mai ka German no ka "pōhaku") a kokoke i 50 mau makahiki ʻaʻole i hoʻoholo ʻia. A hiki i Malaki i hala!
ʻO ka loaʻa ʻana o Ein Stein
Ma Malaki 20, ua hoʻopuka nā kānaka ʻepekema ʻo David Smith, Joseph Samuel Myers, Craig S. Kaplan a me Chaim Goodman-Strauss mai nā Kulanui o Cambridge, Waterloo a me Arkansas i ka hana 'An aperiodic monotile' a lākou i wehewehe ai i kahi ʻano o ka mea i ʻimi ʻia. -ma hope o ka tile e hoʻāla ai i kahi mosaic aperiodic me kahi ʻāpana kūʻokoʻa.
ʻO Tile i wehewehe ʻia e Smith, Myers, Kaplan a me Goodman-Strauss
Me kēia tile hoʻokahi, i koʻu manaʻo e like loa me ka T-shirt, hōʻike ia e hiki ke kūkulu ʻia nā mosaics aperiodic e like me kēia:
Mosaic aperiodic o kahi tile
Inā makemake ʻoe e pili ana i ke kumuhana, hiki iā ʻoe ke ʻimi hohonu i kēia ʻike ma kēia wikiō aʻe,
kahi e kamaʻilio ai kāna poʻe ʻike me nā poʻe kūpono ʻē aʻe ma ia wahi, me ka makana Nobel ma ka Physics Roger Penrose.
ʻO ka ABCdario de las Mathematics kahi ʻāpana i kū mai ka hui pū ʻana me ka Dissemination Commission o ka Royal Spanish Mathematical Society (RSME).
NO KA MEA KAKAU
Victor M. Manero
