- Imitsani kusaka! Tazipeza potsiriza, "anadandaula Commissioner MacCarnigan.
– Bwana ndani? anafunsa Second Lieutenant Pierron.
"Kwa mmodzi wa zigawenga zoterera kwambiri zomwe mungaganizire. Ndakhala ndikuzifunafuna kwa zaka pafupifupi 50.
- Sindinadziwe, Commissioner. Ndi za ndani?
- Nambala yake ndi Ein Stein ndipo zanditengera pafupifupi moyo wonse kuti ndiyipeze.
- Ndi ndani? Kodi muli ndi zithunzi zanu kunja uko?
- Inde, ndili nazo pano, izi ndi momwe zimawonekera, koma musapusitsidwe ndi mawonekedwe ake osalakwa, njonda iyi yatipangitsa kuti tisakayikire kwa zaka pafupifupi khumi.
Chifukwa chake MacCarnigan adawonetsa Agent Pierron chithunzi cha Ein Stein, chithunzi ichi:
Mu Stein.
Mbiri yachidule iyi ya apolisi ingawoneke ngati nthabwala, koma ngati tisintha ofufuza a masamu, imakhala imodzi mwazinthu zodabwitsa kwambiri zomwe zapezeka m'zaka zaposachedwa. Koma kuti timvetse kukula kwa nkhaniyi, choyamba tiyenera kulankhula za imodzi mwa minda imene masamu ndi luso kuphatikiza: mosaics.
nyuzipepala mosaic
Tonse tawonapo mosaic nthawi ina m'miyoyo yathu. Izi ndi ntchito zazing'ono zojambulajambula kapena zokongoletsera zomwe zimagwiritsidwa ntchito pogwiritsa ntchito zidutswa zing'onozing'ono zomwe zimagwirizana.
Zitsanzo zina za zojambulajambula
Tikamalankhula za masamu a masamu, nthawi zambiri timatchula zomwe zimadziwika kuti tessellations, zomwe ndi njira yokonzera zidutswa kapena matailosi kuti zidutswazi zikhale ndi m'mphepete mwawo ndipo zisasiye mabowo.
Kalekale akatswiri a masamu ndi masamu anafunsa funso ili
Ndi zidutswa zamtundu wanji zomwe ndingatanire nazo ndege?
Ndiko kuti, ndi mitundu yanji ya zidutswa zomwe ndingagwiritsire ntchito pa izo, kuziyika kuti matailosi azikhudzana kumbali zonse, palibe mipata mu ndege. Mwachiwonekere mabwalo sali m'gulu losankhidwa ili, chifukwa ngati ndikufuna kuyika matailosi ndege pogwiritsa ntchito mabwalo okha adzandisiya ndi mabowo. Bwerani, ine ndiyenera kuponya grout yokhazikika.
mabwalo amasiya mipata
Komabe, pali mawonekedwe ena ambiri omwe tingathe kuyika nawo ndege, monga makona atatu, mabwalo kapena ma hexagon.
Tessellation yokhala ndi polygon imodzi yokhazikika
Kapena tikhoza matailosi ndege ndi osakaniza awa kapena ziwerengero zina.
Tessellation yokhala ndi ma polygon angapo wokhazikika
Kapena mutha kuyimitsa ndegeyo ndi kuphatikiza kopitilira muyeso:
Ma tiles ena okonzeka
Koma mwaganizira za mitundu yosiyanasiyana ya matailosi amene mwapereka, onse ali ndi zinthu zofanana, ndiko kuti, amakhala nthawi ndi nthawi. Mawu akuti periodic amatanthauza kuti pali kumasulira kwina, kusiyapo ziro, komwe kumasiya chithunzi chonse kukhala chofanana. Kuchokera ku zomwe timamvetsetsa, ndizofanana ndi mfundo yakuti ngati titayala pamwamba, maso a ceramic ndi wina amasuntha mosaic yonse kumalo enaake ndikuphimbanso maso, sitingathe kuyamikira kusiyana pakati pa zojambulazo zoyambirira ndi zomwe zasamutsidwa.
mosaic popanda nyuzipepala
Mosiyana ndi ma tiles a periodic timapeza ma tiles omwe si a periodic, omwe ndi omwe alibe kumasulira, osati ziro, omwe amasiya mosaic ndi mawonekedwe ofanana. Sikovuta kupeza mosadukiza mosadukiza nthawi, ndikokwanira, mwachitsanzo, kutenga ma tiles a periodic, tiyeni tiganizire, mwachitsanzo, imodzi yopangidwa ndi mabwalo, ndipo sikweya imodzi yamitundu yonseyo imagawidwa mu makona atatu. Mwachiwonekere ikadali tessellation ya ndegeyo, koma sipadzakhala kumasulira kulikonse komwe kungasiyire tesserae yonse mofanana popeza tidzatha kusiyanitsa pakati pa zojambula zoyamba ndi zomwe zimachotsedwa pongoyang'ana malo osinthidwa a katatu.
aperiodic tiling
Koma tsopano ndi pamene zinthu zimakhala zosangalatsa, chifukwa ndi pamene lingaliro la aperiodic mosaic likuwonekera, omwe ndi omwe, ngakhale kuti sakhala nthawi ndi nthawi, amakhutitsa chikhalidwe chowonjezera kuti alibe zigawo zazikulu zomwe zimakhala nthawi ndi nthawi. Momwemonso lingaliro ili limatha kumveka ngati muzithunzi za aperiodic, ngati titenga chidutswa chachikulu chokwanira, sichibwerezanso muzithunzi zina zonse. Onetsetsani kuti zitsanzo za zithunzi zomwe sizinafotokozedwe m'kanthawi kochepa sizichitika pafupipafupi chifukwa titha kupeza zigawo zazikulu zomwe zimangochitika pafupipafupi, ingotenga zidutswa zazikuluzikulu zomwe siziphatikiza makona atatu.
Chifukwa chake, funso lomwe limabuka mwachilengedwe ndi ili:
Kodi pali aperiodic mosaic?
Funsoli, lomwe linayamba kuphunziridwa mu theka lachiwiri la zaka zapitazi, posakhalitsa linalandira yankho lovomerezeka ndipo mmodzi mwa oyamba kupeza aperiodic tessellation anali Raphael M. Robinson. Zithunzi zojambulidwa ndi Robinson mu 1971 zinali ndi ma tesserae 6 otsatizana.
Robinson matailosi
Zaka zingapo pambuyo pake, komanso m'zaka za m'ma 70, Roger Penrose adapeza matailosi awiri aperiodic omwe amatha kumangidwa, aliyense akugwiritsa ntchito matailosi awiri okha osiyana. Yoyamba mwa ma tessellations awa imapangidwa ndi ma rhombuses awiri:
Penrose matailosi (rhombuses)
Mutha kupanga mosaics motere:
Penrose matayala
Yachiwiri mwa ma tiles awa amaperekedwa ndi zidutswa ziwiri zotchedwa kite ndi muvi, pazifukwa zodziwikiratu:
Ma tiles a penrose (comet ndi muvi)
Chabwino, pali kukayikira kuti plantar ikhoza kukhala motere:
Kodi pali ma aperiodic mosaics opangidwa ndi matailosi amodzi?
Vutoli lakhala likudziwika kuti vuto la Ein Stein (lochokera ku Chijeremani kutanthauza "mwala") ndipo kwa zaka pafupifupi 50 silinathetsedwe. Mpaka March watha!
Kupezeka kwa Ein Stein
Pa March 20, asayansi David Smith, Joseph Samuel Myers, Craig S. Kaplan ndi Chaim Goodman-Strauss ochokera ku Universities of Cambridge, Waterloo ndi Arkansas adafalitsa ntchito ya 'An aperiodic monotile' momwe iwo anafotokozera zotheka mawonekedwe a matailosi omwe amafunidwa kwambiri omwe amapereka chithunzi cha aperiodic ndi chidutswa chimodzi.
Tile wofotokozedwa ndi Smith, Myers, Kaplan ndi Goodman-Strauss
Ndi tile imodzi iyi, yomwe ikuwoneka ngati yofanana kwambiri ndi T-sheti, ikuwonetsa kuti zithunzi za aperiodic mosaic zitha kumangidwa:
Aperiodic mosaic wa tile
Ngati muli ndi chidwi chofuna kudziwa zambiri za nkhaniyi, mutha kufufuza mozama muvidiyoyi,
momwe otulukira ake amalankhula ndi anthu ena ofunikira m'derali, kuphatikiza Mphotho ya Nobel mu Fizikisi Roger Penrose.
ABCdario de las Matemáticas ndi gawo lomwe limachokera ku mgwirizano ndi Dissemination Commission of the Royal Spanish Mathematical Society (RSME).
ZA WOLEMBA
Victor M. Manero
