-Misa kutsvaga! Takazviwana pakupedzisira,' akadaro Commissioner MacCarnigan.
- Ndiani changamire? akabvunza Second Lieutenant Pierron.
“Kune mumwe wevapambi vanotsvedza waungafungidzira. Ndave nemakore anoda kusvika makumi mashanu ndichiitsvaga.
- Ini ndakanga ndisingazive, Commissioner. Ndeyaani?
- Nhamba yake ndiEin Stein uye zvakanditora anenge hupenyu hwese kuti ndiiwane.
-Ndiani pamusoro? Iwe une chero mifananidzo yako kunze uko?
- Hongu, ndinayo pano, ndizvo zvazvinoita, asi usanyengerwa nekutaridzika kwayo isina mhosva, murume uyu ari pano akatichengeta mukusagadzikana kweanoda kusvika makumi emakore.
Saka MacCarnigan akaratidza Agent Pierron mufananidzo waEin Stein, mufananidzo uyu:
MuStein.
Iyi nhoroondo pfupi yemapurisa ingaite sejee, asi kana tikachinja matikitivha evanoongorora masvomhu, inova imwe yeakanakisa kuwanikwa kwemasvomhu kwakaitika mumakore achangopfuura. Asi kuti tinzwisise kukura kwenyaya iyi, tinofanira kutanga tataura nezveimwe yeminda umo masvomhu neunyanzvi zvinosangana: mosaics.
mosaic newspapers
Tese takaona mosaic pane imwe nguva muhupenyu hwedu. Aya mabasa madiki ehunyanzvi kana ekushongedza anogadzirwa uchishandisa zvidimbu zvidiki zvinokwana pamwechete.
Mimwe mienzaniso ye mosaics
Kana tichitaura nezve mosaic mumasvomhu, tinowanzo nongedzera kune inozivikanwa se tessellations, inova nzira yekuronga zvimedu kana mataira kuitira kuti zvidimbu izvi zvive nemicheto yakafanana uye zvisasiye maburi.
Kare kare nyanzvi dzemasvomhu nemasvomhu dzakamutsa mubvunzo unotevera
Ndedzipi zvidimbu zvandingagona kuita tile ndege nazvo?
Ndiko kuti, ndezvipi zvimedu zvandingashandisa kune izvozvo, ndichizviisa kuitira kuti matiles abatane pamativi akafanana, hapana mapeji mundege. Zviri pachena kuti madenderedzwa haasi muboka iri rakasarudzwa, sezvo kana ndichida kutaira ndege ndichishandisa denderedzwa chete vanondisiya nemakomba. Huya, ini ndichafanira kukanda fixed grout.
madenderedzwa anosiya mikaha
Nekudaro, kune mamwe akawanda maumbirwo atinogona nawo mataira ndege, senge matatu, masikweya kana hexagoni.
Tessellation ine imwechete yakajairika polygon
Kana kuti isu tinokwanisa tile ndege nemusanganiswa weaya kana mamwe manhamba.
Tessellation ine akati wandei akajairwa maporigoni
Kana iwe unogona kutoita mataira ndege nekuwedzera kusanganisa:
Mamwe matairi anogoneka
Asi wakafungisisa nezvemhando dzakasiyana-siyana dzematairi dzawaratidza, ese ane chimwe chinhu chakafanana, uye ndiko kuti, anongoitika nguva nenguva. Shoko rokuti periodic rinoreva kuti kune imwe shanduro, isiri zero, inosiya mufananidzo wose wakafanana. Kubva pane zvatinonzwisisa, zvakaenzana nenyaya yekuti kana isu takaisa pamusoro, ceramic maziso uye mumwe munhu anofambisa iyo mosaic yese munzira chaiyo obva avhara maziso zvakare, isu hatizokwanisa kukoshesa mutsauko uripo pakati peiyo yekutanga mosaic. uye akadzingwa.
mosaic pasina mapepanhau
Kusiyana neperiodic tiles tinowana non-periodic tiles, ayo ari iwo asina shanduro, kwete zero, anosiya mosaic ine chitarisiko chakafanana. Hazvina kuoma kuwana non-periodic mosaics, zvakakwana, semuenzaniso, kutora periodic tiling, ngatifungei, semuenzaniso, imwe inoumbwa chete nemakona, uye imwe mativi eiyo mosaic yese yakakamurwa kuita maviri matatu matatu. . Zviripachena kuti ichiri tessellation yendege, asi hakuzove neshanduro ichasiya yese tesserae yakafanana sezvo isu tichizokwanisa kusiyanisa pakati peiyo yekutanga mosaic neyayo yakadzingwa nekungoona yakagadziridzwa nzvimbo. makona matatu.
aperiodic tiling
Asi ikozvino ndipo pazvinoita zvinhu zvinonakidza, nekuti ndipo panoonekwa pfungwa yeaperiodic mosaic, inova iyo, kunyangwe isiri nguva nenguva, inogutsa iyo yekuwedzera mamiriro ekuti havana nzvimbo dzakakura dzakakura dziri nguva nenguva. Nenzira imwecheteyo pfungwa iyi inogona kunzwika semu aperiodic mosaic, kana tikatora chidimbu chakakura chakakwana, hachidzokeri mune yakasara yemosaic. Ita shuwa kuti muenzaniso wemosaic usina kumbotsanangurwa nekanguva hausi wenguva nenguva sezvo tichigona kuwana nzvimbo dzakakura zvisingaite nguva nenguva, ingotora zvidimbu zvihombe zvisingasanganisi kana katatu.
Saka, mubvunzo unomuka ndeuyu unotevera:
Pane aperiodic mosaics here?
Uyu mubvunzo, uyo wakatanga kudzidzwa muchikamu chechipiri chezana remakore rapfuura, munguva pfupi yakagamuchira mhinduro yechokwadi uye mumwe wekutanga kuwana aperiodic tessellation aiva Raphael M. Robinson. Iyo mosaic yakatsanangurwa naRobinson muna 1971 yaive ne6 inotevedzana tesserae.
Robinson tiles
Makore mashoma gare gare, zvakare muma70s, Roger Penrose akawana matiles maviri aperiodic anogona kuvakwa, rimwe nerimwe richishandisa mataira maviri akasiyana. Yekutanga yeiyi tessellations inoumbwa nemarhombuse maviri akasiyana:
Penrose tiles (rhombuses)
Iwe unogona kugadzira mosaic seizvi:
Penrose tiling
Yechipiri yeaperiodic tilings inopiwa nezvidimbu zviviri zvinonzi kite uye museve, nezvikonzero zviri pachena:
Penrose tiles (comet uye museve)
Zvakanaka, pane kupokana kuti plantar inogona kunge iri inotevera:
Pane aperiodic mosaics inoumbwa ne tile imwe chete?
Dambudziko iri rave richizivikanwa sedambudziko reEin Stein (kubva kuGerman rinoreva "dombo") uye kweanoda kusvika makore makumi mashanu rakaramba risina kugadziriswa. Kusvikira March apfuura!
Kuwanikwa kweEin Stein
Musi waKurume 20, masayendisiti David Smith, Joseph Samuel Myers, Craig S. Kaplan naChaim Goodman-Strauss vanobva kuYunivhesiti yeCambridge, Waterloo neArkansas vakaburitsa basa rekuti 'An aperiodic monotile' umo vakatsanangura nzira inobvira yeiyo yakanyanya kutsvakwa. mushure me tesserae iyo inopa aperiodic mosaic ine chidimbu chakasiyana.
Tile inotsanangurwa naSmith, Myers, Kaplan naGoodman-Strauss
Neiyi tile imwe chete, inoratidzika kwandiri kunge yakafanana neT-shirt, anoratidza kuti aperiodic mosaics senge anotevera anogona kuvakwa:
Aperiodic mosaic ye tile
Kana kuda kuziva kwako kwakadzama pamusoro penyaya, unogona kuzama zvakadzama mukuwanikwa uku muvhidhiyo inotevera,
umo vanoiwana vanotaura nevamwe vanhu vakakodzera munzvimbo iyi, kusanganisira iyo Nobel Prize muFizikisi Roger Penrose.
The ABCdario de las Matemáticas chikamu chinomuka kubva mukubatana neDissemination Commission yeRoyal Spanish Mathematics Society (RSME).
NEZVEMUNYORI
Victor M. Manero
