
emm. sii. esker

marits carnellis esture (; 17 juun 1898-27 marchi 1972) ganitasaastraparamgaa prerana pondina chekka kattirimpulu, lithographs mariyu mejotintsnu tayaaru chesina dutch graphic kalakarudu.
vistruta prajaadarana unnappatikee, esher thana jeevitamlo ekkuva bhaagam kalaa prapanchamlo, thana sthaanika netherlandslo kooda nirlakshyam cheyabaddaadu. oka punaraavrutta pradarsana jaragadaniki mundu ayana vayassu 70 samvatsaraalu. iravayyava sataabdam chivaralo, athanu marinta vistrutamgaa prasamsimchabaddaadu, iravai okatava sataabdamloo athanu prapanchavyaaptamgaa pradarsanalalo jarupukunnaru.
athani rachanalo asaadhyamaina vastuvulu, anantam yokka anveshanalu, pratibimbam, samaruupata, drukpatham, kattirinchina mariyu stellated polyheadra, hyperbolic jyaamiti mariyu tessellationlatho sahaa ganita vastuvulu mariyu karyakalapalu unnaayi. tanaku ganita saamarthyam ledani esture viswasinchinappatikii, athanu ganita saastravettalu georg polia, roser penros, harrold cauxeter mariyu sphatika shaastravetta friedrich haglatho sambhaashinchi, teslationpy thana sonta parisoedhananu nirvahinchaadu.
thana vrutti jeevitam praarambhamlo, athanu prakruti nundi prerana pondhi, keetakaalu, prakruti drushyaalu mariyu likenlu vanti mokkala gurinchi adhyayanam chesaadu, ivanni athanu thana kalaakrutulalo vivaraluga upayoginchaadu. athanu italii mariyu speyinlalo prayaaninchi, bhavanalu, pattana drushyaalu, vaastusilpam mariyu alhambra mariyu cardoba yokka mezqvita yokka vampulanu geesaadu mariyu vaati ganita nirmaanampai kramamga ekkuva aasakti kanabarichadu.
esher kala saastravettalu mariyu ganita saastravettalalo baga prachuryam pondindi, mariyu prajaadarana pondina samskrutilo, mukhyamgaa martin gardner thana april 1966 ganita aatala vyaasamlo "scientific american" loe pradarsinchina taruvaata. vividha rakaala saanketika patraalalo upayoginchabadatame kakunda, ayana rachanalu aneka pustakaalu mariyu albumla mukhachitraalapai kanipinchaayi. douglus hofstadder yokka pulitzer bahumati graheeta 1979 pustakam "godel, esture, baach" kuu pradhana preranalalo ayana okaru.
prarambha jeevitam.
marits carnellis esture 1898 juun 17naa netherlandsloni frieslandloni leewardenlo, eee roeju princessihoff seramics museumlo bhaagamaina intlo janminchaaru. athanu sivil injanir georg arnald esture mariyu athani rendava bhaarya saaraa gleachman la chinna kumarudu. 1903loe, aaa kutumbam arnhemku vellindi, akkada athanu 1918 varaku praathamika mariyu madhyamika paatasaalaku hajarayyadu. athani snehitulu mariyu kutumba sabhyulaku "mouk" anie piluvabade athanu anaarogyamtho unna pillavadu mariyu edu samvatsaraala vayassulo pratyeka paatasaalalo unchabaddaadu; athanu rendava taragatilo viphalamayyaadu. athanu droyinglo raaninchinappatikii, athani taragatulu saadhaaranamgaa paelavamgaa undevi. athanu padamudu samvatsaraala vayassu varaku vadrangi mariyu piano paataalu neerchukunnaadu.
1918loe ayana delft technical collegelo cheraaru. 1919 nundi 1922 varaku, esture harlem school off architecture und decorational arts, droying mariyu chekka kattirimpula kalanu neerchukunnaaru. athanu kontakaalam vaastusilpaanni abhyasinchaadu, conny athanu aneka vishayaalalo viphalamayyaadu (paakshikamgaa nirantara charma sankramana kaaranamgaa) mariyu graphic kalakarudu shamyul jesurun dii mesquita aadhvaryamlo chaduvutuu alankaara kalalaku maaradu.
adhyayana prayaanaalu.
1922loe, thana jeevitamlo oka mukhyamaina samvatsaram, esher italii gundaa prayaaninchi, florence, shaan gimignano, voltera, siana mariyu ravellolanu sandarsinchaadu. adhe samvatsaramlo, athanu speyin gundaa prayaaninchi, modrid, toledo mariyu grenadalanu sandarsinchaadu. athanu italian graameena praantaalu mariyu granadalo, padnaalugo sataabdapu alhambra yokka murish vaastusilpam dwara aakattukunnadu. varnapu palakalalo ledhaa godalu mariyu paikappulalo chekkabadina punaraavruta namuunaalanu kaligi unna rekhaganita samaruupatala aadhaaramgaa alhambra yokka klishtamaina alankaara namuunaalu, tessilation ganitamlo athani aasaktini prerepinchaayi mariyu athani panipai saktivantamaina prabhavanni chupayi.
esher italeeki tirigi vacchi 1923 nundi 1935 varaku romlo nivasinchaadu. italeelo unnappudu, esher jetta umikarnu kalusukunnadu-tanalaage italii vaipu aakarshinchabadina oka swiss mahila-atanni athanu 1924loe vivaham chesukunnadu. eee janta romlo sthirapaddaaru, akkada vaari modati kumarudu georgio (georg) arnaldo esher, athani taata paeru pettabadindi. esher mariyu jettaku taruvaata orther mariyu zaan anae maroe iddaru kumaarulu kaligaaru.
1926loe viterbo, 1927,1929loe abruzzi, 1928,1933loe coursica, 1930loe calabria, 1931,1934loe amalphy teeram, 1932,1935loe gargano, sisileelanu sandarsinchi ayana tarachugaa paryatinchaaru. eee pradaesaala pattana drushyaalu, prakruti drushyaalu ayana kalaakrutulalo pramukhamgaa kanipistaayi. 1936 mae mariyu juunlaloo, esher speyinku tirigi velli, alhambranu tirigi sandarsinchi, daani mosaic namuunaala vivaranaatmaka chitraalanu roopondinchadaaniki rojulanu gadipadu. ikkade athanu aakarshitudayyaadu, muttadi varaku, tesselationtho, vivaristuuh
ayana alahambraalo chesina rekhaachitraalu appati nundi ayana paniki pradhana vanarugaa marai. athanu cardoba yokka murish maseedu ayina mezqvita yokka nirmaanaanni kooda adhyayanam chesaadu. idhi ayana sudeergha adhyayana prayaanaalalo chivaridigaa maarindi; 1937 taruvaata, ayana kalaakrutulu kshetramlo kakunda ayana studiolo srushtinchabaddaayi. prakruti mariyu nirmaanamloo kanipinche vishayaala vaastavika vivaraalaku balamaina praadhaanyatanistuu, athani kala pradhanamgaa pariseelanaatmakamgaa undatam nundi athani rekhaganita vislaeshanha mariyu athani drushya kalpana yokka utpattigaa maarutundi. annintikante, athani prarambha rachana kooda ippatike antariksham yokka swabhaavam, asaadhaaranamaina, drukpatham mariyu bahula drukkoonaalapai athani aasaktini choopistundi.
taruvaati jeevitam.
1935loe, mussolini aadhvaryamlo italeelo raajakeeya vaataavaranam nundi tappinchukovadam aamodayogyam kaaledu. aayanaku rajakeeyaalapai aasakti ledhu, thana sonta nirdishta madhyamam dwara thana swantha bhavanala vyakteekaranalu tappa maray itara aadarsaalato tananu taanu nimagnam chesukovadam asadhyam anie bhaavinchaaru, conny athanu matabhrashtata mariyu kapatatvaaniki vyatiraekam. athani pedda kumarudu georg tommidella vayasulo paatasaalalo ballila unifam dharinchamani balavantam cheyabadinappudu, kutumbam italeeni vidichipetti switzerlandloni chaateyu-dii 'ex kuu vellindi, akkada vaaru rendu samvatsaraalu undipoyaaru.
netherlands tapala karyalayam 1935loe "air fund" (dutch "hett nationol luchtwartfands") kosam oka pakshika tapala stampnu roopondinchindi, mallee 1949loe athanu dutch stampulanu roopondinchaadu. ivi saarvatrika tapala sangham 75va vaarshikotsavam kosam; surinam mariyu netherlands antilles oke ghnaapakaartham vaerae designu upayoginchaayi.
italeelooni prakruti drushyaalanu chaalaa ishtapade mariyu prerana pondina esture, switzerlandlo nischayamgaa asantruptigaa unnadu. 1937loe aaa kutumbam belgiumloni brassels shivaaru praantamaina ukle (ukkel) kuu tirigi maarindi. rendava prapancha yuddham vaarini 1941 janavarilo netherlandsloni barnku taralinchavalasi vachindi, ikkada esher 1970 varaku nivasinchaaru. esher yokka atyanta prasiddha rachanalu chaalaavaraku eee kaalam nativi. netherlandslo konnisaarlu meghaavrutamaina, challani mariyu tadi vaataavaranam atanini thana panipai shraddhaga drushti pettadaniki anumatinchindi. 1953 taruvaata, esture vistrutamgaa upanyaasaalu icchaaru. 1962loe uttara americalo pranaalikaabaddhamaina upanyaasaala shreni anaaroogyam kaaranamgaa raddu cheyabadindi, mariyu athanu kontakaalam kalaakrutulanu srushtinchadam manesadu, conny upanyaasaala kosam drushtaamtaalu mariyu vachanam taruvaata "esture aann esture" pustakamlo bhaagamgaa prachurinchabaddaayi. 1955loe aayanaku nighthood off dhi arder off aurange-nassou labhinchindi; taruvaata 1967loe ayana adhikariga niyaminchabaddaaru.
1969 joolailo ayana thana chivari panini puurti chesaaru, "pamulu" anie piluvabade moodu retlu bhramana samaruupatatoe kuudina pedda chekkatho chesina chekka, dheenilo pamulu anusandhaaninchabadina valayala namuunaa dwara gaalini veestaayi. ivi vruttam yokka kendram mariyu anchu rendinti vaipu anantaniki kunchinchukupotayi. idhi anoohyamgaa vistrutamainadi, moodu blaakulanu upayoginchi mudrinchabadindi, prati okkati chitram madhyalo moodu saarlu tippabadindi mariyu prati puurtayina mudranaku mottam tommidi mudrana karyakalapala kosam antaraalu mariyu ativyaaptini nivaarinchadaaniki khachitamgaa samalekhanam cheyabadindi. eee chitram esher yokka samaruupata patla premanu, interlocking namuunaalanu, mariyu athani jeevitaantam, anantam patla athani vidhananni vivaristundi. eee chekkanu tayaaru chesi, mudrinchadamlo esher teesukunna jaagrattanu veediyo recordinglo chudavachu.
esher 1970loe laurenloni rosa spier hyuusku vellaaru, idhi kalaakaarula padavee viramana gruham, dheenilo aayanaku sonta studio undhi. athanu 1972 marchi 27naa 73 samvatsaraala vayasulo hilversamloni aasupatrilo maraninchaadu. athanu baarnlooni kotta smasaanavaatikalo khananam cheyabaddaadu.
ganitasastra preranatho chesina pani.
escher yokka paniloo ekkuva bhaagam anivaryamgaa ganita shaastram. idhi athani puurti prajaadarana pondina keerti mariyu kalaa prapanchamlo atanni chudabadina gowravam lekapovadam madhya sambandhaanni tenchukundi. athani vaastavikata mariyu graphic paddhatulapai naipunhyam gouravinchabadutunnaayi, conny athani rachanalu chaalaa medhoparamgaa mariyu taginantagaa saahityaparamgaa bhavinchabadaledu. sambhaavita kala vanti udyamaalu, kontavaraku, medhoparamgaa mariyu saahityam patla kalaa prapancham yokka vaikharini tippikottaayi, conny idhi esharnu punaravasam cheyaledu, endukante saampradaaya vimarsakulu ippatikee athani kathana itivruttaalanu mariyu athani drukpathaanni upayoginchadaanni ishtapadaledu. ayithe, idhe lakshanaalu ayana rachanalanu prajalaku chaalaa aakarshanheeyamgaa marchai.
ganita itivruttaalanu anveshinchina modati kalakarudu esher kaaduh parmigianino (1503-1540) thana 1524 loe "kumbhakara addamlo sweeya-chitram" loe golaakaara jyaamiti mariyu pratibimbamnu anveshinchaadu, vakra addamlo thana swantha chitraanni chithreekarinchaadu, ayithe vilium hogarth yokka 1754 "tappudu drukpathampai vyangya" drukpathamlo lopaala gurinchi esher yokka ullaasakaramaina anveshananu mundhe choopistundi. maroka prarambha kalaatmaka puurvagaami geovanni batista piranesi (1720-1778), athani "carcery" ("jaillu") kramamlo "drabridge" vanti cheekati "adbhuta" mudranalu aneka metlu mariyu ryaamplatoe sanklishta vaastusilpam yokka drukpathaalanu varnistaayi, ivi nadaka bommalatho nindi untaayi. esture piranesini entho mecchukunnadu mariyu piranesi yokka aneka mudranalanu thana studiolo velaadadeesaadu.
cubism, dii stizzle, daadaa matam mariyu adhivaastavikata vanti 20va sataabdapu udyamaalato matrame pradhana sravanti kala prapanchaanni ekakaalamlo aneka drukkoonaalatoe chuse eskar lanty maargaalanu anveshinchadam praarambhinchindi. ayithe, udaaharanaku, magrit yokka adhivaastavikata mariyu opp artho estureku chaalaa saaruupyata unnappatikee, athanu eee udyamaalalo dhenithonuu sambandham pettukoledu.
tesslation.
thana prarambha samvatsaraallo esher prakruti drushyaalu mariyu prakrutini geesaadu. athanu cheemalu, theneteegalu, midutalu mariyu montesses vanti keetakaalanu kooda geesaadu, ivi athani taruvaati rachanalo tarachugaa kanipinchaayi. roman mariyu italian prakruti drushyaalu mariyu prakruti patla aayanaku unna prarambha prema tessellationpy aasaktini srushtinchindi, dheenini ayana "plain yokka regular division" anie pilicharu; idhi athani 1958 pustakam yokka sheershikagaa maarindi, idhi plain yokka tesselationla aadhaaramgaa chekka kattirimpula shreni punarutpattito puurtayimdi, dheenilo athanu thana kalaakrutulalo ganita namuunaala kramabaddhamaina nirmaanaanni vivarinchaadu. ganita saastravettalu vistrutamaina domainku daariteese dwaranni terichaaru" anie ayana raasaaru.
1936loe alhambra mariyu cardobaloni laa mejkvitaaku thana prayaanam taruvaata, akkada athanu murish nirmaanam mariyu tessellated mosaic alankaranalanu geesaadu, esture thana rekhaachitraalaku aadhaaramgaa rekhaganita gridlanu upayoginchi tessilation yokka lakshanaalu mariyu avakaasaalanu anveshinchadam praarambhinchaadu. aaa taruvaata athanu veetini sanklishtamaina interlocking designlanu roopondinchadaaniki vistarinchaadu, udaaharanaku pakshulu, chepalu mariyu sareesrupaalu vanti jantuvulato. shatkona gridlo nirminchina athani pensil, india sira mariyu jalavarnam "sareesrupaalato vimanam yokka kramam tappakunda vibhajana adhyayanam" (1939) athani modati prayatnaalalo okati. erupu, aakupaccha mariyu telupu sareesrupaala talalu oka sheersham vadda kalustaayi; jantuvula thokalu, kaallu mariyu vaipula sarigga parasparam mudipadi untaayi. idhi athani 1943 lithograph "sareesrupaalu" kuu aadhaaramgaa upayoginchabadindi.
ganita saastrampai athani modati adhyayanam georg polia mariyu chrystallographer friedrich hogg yokka plain cemetry groupulapai vraasina patraalatoe praarambhamaindi, dheenini athani sodarudu, bhuuvignaana shaastravetta ayina sorend ataniki pampaaru. athanu 17 canonical walpaper samuuhaalanu jagrattagaa adhyayanam chesi, vividha rakaala samaruupatala yokka 43 draayinglatho aavartana vampulanu srushtinchaadu. eee dasha nundi, athanu thana swantha sangnaamaanaanni upayoginchi thana kalaakrutulalo samaruupata vyakteekaranalaku ganita vidhananni abhivruddhi chesaadu. 1937 nundi, athanu 17 samuuhaala aadhaaramgaa chekkanu srushtinchaadu. athani "roopaantaram I" (1937) chitraala vadakam dwara oka kathanu cheppe designla shrenini praarambhinchindi. roopaantaram I" loe, athanu maanava muulaamsaanni roopondinchadaaniki kumbhakara bahubhujaalanu samatalamlo saadhaarana namoonalugaa marchadu. daadaapu edu meterla podavu gala thana "roopaantaram III" loe ayana eee vidhananni vistarinchaaru.
1941 mariyu 1942loe esture thana kalaatmaka upayogam kosam thana parisoedhanalanu oka sketchbooklo sangrahinchaadu, daanini athanu (haagnu anusarinchi) "reselmatties vlackwerdelling inn asymmetrisk congruent wheelhoken" ("asymmetric congruent bahubhujaalato vimanam yokka kramam tappakunda vibhajana") anie label chesaadu. ganita shaastravetta doris scottionider eee notebooknu "ganita parisoedhana anie matrame pilavabade oka kramabaddhamaina parisoedhana" gaa nissandehamgaa abhivarninchaaru."athanu anusaristunna parisoedhanaa prasnalanu aame ilaa nirvachinchindih
jyaamitulu.
estureku ganita sikshana laenappatikee-ganita saastrampai athani avagahana ekkuvagaa drushya mariyu sahajamainadi-athani kalaku balamaina ganita bhaagam undhi, mariyu athanu geesina aneka prapanchaalu asaadhyamaina vastuvula chuttoo nirminchabaddaayi. 1924 taruvaata esture sahaja roopamlo asaadhyamaina kramarahita drukpathaalatho italii mariyu korsikaaloni prakruti drushyaalanu geeyadam vaipu moggu chuupaaru. ayana asaadhyamaina vaastavikata yokka modati mudrana "sthiramaina jeevitam mariyu veedhi" (1937); asaadhyamaina metlu mariyu bahula drushya mariyu gurutvakarshana drukpathaalu "saapekshata" (1953) vanti prasiddha rachanalalo kanipistaayi. "house off metlu" (1951) ganita shaastravetta roser penros mariyu athani tandri jeevasaastravetta lionel penros aasaktini aakarshinchindi. 1956loe, vaaru "asaadhyamaina vastuvulu oka pratyeka rakam drushya bhranti" anae kaagitaanni prachurinchaaru, taruvaata esharku oka kaapeeni pampaaru. esher badulichaadu, penros nirantaram perugutunna metla vimanalanu mecchukunnadu mariyu "aarohana mariyu avarohana" (1960) yokka mudrananu jatachesadu. aaa kaagitamlo tribar ledhaa penros tribhujam kooda undhi, idhi shaashwata chalana yantramgaa panichese "jalapaatam" (1961) gaa kanipinche oka bhavanam yokka thana lithographlo padepade upayoginchabadindi.
esher, hyronimus bosh yokka 1500 tryptich "dhi garden off erthley delites" paie aasakti kaligi, daani kudi chethi panello kontha bhaganni, "narakam" nuu 1935loe lithographga tirigi srushtinchaadu. athanu 1958loe thana lithograph "belveder" loe rendu koonaala sirastraanam mariyu podavaina gaunu dharinchina madhyayuga mahila bommanu tirigi upayoginchaadu; eee chitram, athani itara "asaadhaaranamaina kanugonna pradaesaala" maadirigaane, "gesterlu, kattulu mariyu aalochanaaparula" thoo nindi undhi. anduvalla, esture saadhyamayye ledhaa asaadhyamaina jyaamiti patla aasakti choopadame kakunda, thana maatallo cheppalante, "reality autsaahikudu"; athanu "adhikaarika ascharyaanni spashtamaina mariyu vilakshanhamaina drushtitoe" militam chesaadu.
esture pradhanamgaa lithographs mariyu kalapa kattirimpula madhyamalalo panicheesaaru, ayinappatikee athanu tayaaru chesina konni majotints eee saanketikata yokka kalakhandaluga pariganinchabadataayi. thana graphic kalalo, athanu akaaraalu, bommalu mariyu sthalam madhya ganita sambandhaalanu chithreekarinchaadu. ayana mudralalo sankuvulu, golaalu, ghanalu, valayalu mariyu vruttaakaaraala addam chitraalu vileenam cheyabaddaayi.
oke oka uparitalam unna mobius strip vanti ganita vastuvula patla kooda esture aakarshitulayyaaru. athani chekka chekkadam "mobius strip II" (1963) cheemala golusu, yea oka pradaesamloe ayina, vastuvu yokka rendu vyatiraeka mukhalu, vaatipai eppatikee kadulutuu undadaanni varnistundi-ivi tanikheelo strip yokka oke uparitalamlo bhagaluga kanipistaayi. esher sonta maatalalo
1936 taruvaata athani paniloo ganita prabhavam pramukhamgaa maarindi, adria shipping companyni vaari naukala chitraalanu geeyadaaniki badulugaa prayaana kalakarudiga vaaritho prayaaninchavachaa anie dhairyamgaa adiginappudu, vaaru aascharyakaramgaa angeekarinchaaru, mariyu athanu kramam mariyu samaruupatapai aasakti chuuputuu madhyadhara samudramlo prayaaninchaadu. esher eee prayaanaanni, thana punaraavruta alhambra sandarsanato sahaa, "neenu ippativaraku upayoginchina atyanta goppa prerana vanaru" gaa abhivarninchaaru.
vakrarekha drukpathampai esture aasaktini athani snehitudu mariyu "kindred spirit", kalaa charitrakaarudu mariyu kalakarudu albert flocon, nirmaanaatmaka paraspara prabhaavaaniki maroe udaaharanagaa prothsahinchaaru. piero della francesca, leonardo daa vincy, albrecht durer, vengel jamnitzer, abraham boses, girard desorgues mariyu pere nicon latho paatu esture nuu "aalochanaa kalakarudu" gaa flocon gurtinchaadu. flocon 1959loe chadivina esture yokka "graphic enn teckeningen" ("graphics inn droying") chuusi santoshinchaadu. idhi flocon mariyu andrey baarlanu eschartho anugunamgaa undataaniki mariyu "laa perspective karviligne" ("curvelinear perspective") anae pustakaanni vraayadaaniki prerepinchindi.
platonic mariyu itara ghanapadaarthaalu.
esture tarachugaa golaalu, tetrahedronlu mariyu ghanalu vanti platonic ghanapadaarthaalu vanti trimiteeya vastuvulanu thana rachanalalo, alaage cylinderlu mariyu stellated polyheadra vanti ganita vastuvulanu chaerchaaru. sareesrupaalu" anae mudranalo, athanu dvi-mariyu trimiteeya chitraalanu militam chesaadu. thana oka patramlo, esher dimensionality yokka praamukhyatanu nokki chepparu
esture yokka kalaakrutini doris scottionider vanti ganita saastravettalu mariyu roser penros vanti saastravettalu baga ishtapadataaru, veeru polyheadra mariyu rekhaganita vakreekaranala vadakanni aasvaadistaaru. udaaharanaku, "gurutvakarshana" loe, jantuvulu oka kommulagala dodecahedron chuttoo ekkutaayi.
jalapaatam" asadhyam bhavanam yokka rendu gopuraalu mishrama polyheadratho agrasthaanamlo unnaayi, okati moodu ghanaala sammelanam, marokati ippudu estures salid anie piluvabade stellated rambic dodecahedron. esture thana 1948 chekkatho chesina "nakshatraalu" loe eee ghanapadaarthaanni upayoginchaadu, indulo nakshatraalanu soochinche mottam aidu platonic ghanapadaarthaalu mariyu vividha stellated ghanapadaarthaalu kooda unnaayi; kendra ghanapadaartham antarikshamlo tirugutunnappudu frame gundaa ekki oosaravellula dwara animate cheyabadutundi. esture 6 centimeters vakreebhavana telescopenu kaligi unnadu mariyu dwaipaakshika nakshatraala pariseelanalanu namodu cheyagaliginanta autsaahika khagola shaastravetta.
vaastavikata sthaayilu.
esture yokka kalaatmaka vyakteekarana itara deshaalaku neerugaa pariseelanalu mariyu prayaanaala nundi kakunda athani manassulooni chitraala nundi srushtinchabadindi. kalalo vaastavikata yokka bahula sthaayilapai aayanaku unna aasakti "droying hands" (1948) vanti rachanalalo kanipistundi, ikkada rendu chetulu chuupimchabaddaayi, okkokkati okadaanikokati geestaayi. vimarsakudu steven pool ilaa vyakhyaaninchaadu
anantam mariyu hyperbolic jyaamiti.
1954loe ganita saastravettala antarjaateeya congress amsterdamlo samavesamaindi. zii. dii bruyne palgonevari kosam stedelizk museumlo esture yokka panini pradarsinchaaru. roser penros mariyu hetch. ess. emm. esher yokka ganita shaastram yokka sahajamaina avagaahanato cauxeter chaalaa prabhaavitamayyaadu. saapekshavaadam" nundi prerana pondina penros thana tribarnu roopondinchaadu, mariyu athani tandri, lionel penros, antuleni metlanu roopondinchaadu. roser penros rendu vastuvula sketchlanu esker cheyadaaniki pampaadu, mariyu eskar "jalapaatam" yokka shaashwata chalana yantraanni mariyu "aarohana mariyu avarohana" yokka sanyasi-bommala antuleni kavaatuni srushtinchinappudu aavishkarana chakram moosiveyabadindi.
1957loe cauxeter thana kaagitam "christal cemetry und itts generalisations" loe thana rendu draayinglanu upayoginchadaaniki esture anumati pondaadu. athanu kaagitam yokka kaapeeni esture kuu pampaadu; cauxeter yokka hyperbolic tessilation yokka bomma "naaku chaalaa shock ichindi" anie esture record chesadu hyperbolic plain looni tails yokka anantamaina kramam tappakunda punaraavrutam, vruttam anchu vaipu vaegamgaa chinnadigaa perugutuu, khachitamgaa athanu dvi-miteeya plain loe anantaanni suuchimchadaaniki anumatinchaalanukunnaadu.
esher cauxeter bommanu jagrattagaa adhyayanam chesi, daanini varusaga chinna vruttaalanu vislaeshimchadaaniki daanini gurtinchaadu (athanu oohinchaadu). aaa taruvaata athanu oka rekhaachitraanni nirminchaadu, daanini thana vislaeshanhanu chuupistuu coxetercu pampaadu; cauxeter adhi sarainadani dhruvikarinchaadu, conny thana atyanta saanketika samaadhaanamtho esharnu niraasaparichaadu. adevidhamgaa, esher hyperbolic tilingtho konasagaru, dheenini athanu "coxettering" anie pilichadu. phalitaalalo kalapa chekkadam yokka shreni "vrutta parimiti i-IV" unnaayi. 1959loe, cauxeter eee rachanalu asadhaaranamgaa khachitamainavani thana anveshananu prachurinchaaduh "esher daanini millimetreku puurtigaa sarigga pondaadu".
vaarasatvam.
esture yokka pratyeka aalochanaa vidhanam mariyu goppa graphics ganitam mariyu kalatho paatu prajaadarana pondina samskrutilo nirantara prabhavanni chupayi.
kalala sekaranalalo.
esker medho sampattini emm niyantristundi.sii. esher company, ayithe athani kalaakrutula pradarsanalanu emm vidigaa nirvahistaaru.sii. esker foundation.
m dwara asalu rachanala praathamika samsthaagata sekaranalu.sii. hage looni esture museum; national gallery off art (washington, disi); national gallery off kenada (ottava); izrael museum (jerusalem); mariyu hyuus tenn bosh (nagasaki, japan).
pradarsanalu.
vistruta prajaadarana unnappatikee, esher chaalaa kaalam paatu kalaa prapanchamlo kontavaraku nirlakshyam cheyabaddaadu; thana sthaanika netherlandslo kooda, punaraavrutta pradarsana jaragadaniki mundu ataniki 70 samvatsaraalu. iravai okatava sataabdamloo, prapanchavyaaptamgaa nagarallo pradhana pradarsanalu jarigaayi. reo dii janeerolo ayana rachanala pradarsana 2011loe 573,000 mandiki paiga sandarsakulanu aakarshinchindi; daani rojuvaaree sandarsakula sankhya 9,677, idhi prapanchamlo ekkadainaa, samvatsaramlo atyadhikamgaa sandarsinche museum pradarsanagaa nilichindi. 2015 varaku britainlo esture yokka pani yokka pedda pradarsana jaragaledu, appudu scottish national gallery off moderan art juun nundi september 2015 varaku edinberglo okati nadichindi, october 2015loe landanlooni dulwich picture gallerieki maarindi. pradarsana postaru "reflecting golam thoo chethi", 1935 aadhaaramgaa roopondinchabadindi, idhi athani intlo esher chethitho pattukune golam loe pratibimbistunnatlu choopistundi, tadwara kalakarudu, kalalo vaastavikata sthaayilapai athani aasaktini vivaristundi (udhaa.zii., mundu bhaagamlo unna chethi pratibimbimchina chethi kante ekkuva nijamainadaa?), drukpatham, mariyu golaakaara jyaamiti. eee pradarsana italeeki 2015-2016 loe taralinchabadindi, rome mariyu bolognalo 500,000 mandiki paiga sandarsakulanu aakarshinchindi, aapai milan.
ganitam mariyu vignaana saastramlo.
doris scottionider anchanaa vesina ledhaa neerugaa esher nundi prerana pondina ganita mariyu shaastreeya parisoedhana yokka padakondu tantuvulanu gurtistaadu. ivi palakala anchu sambandhaalanu upayoginchi kramabaddhamaina vampula vargeekaranah rendu-rangu mariyu rendu-prerana vampulu (prati-maarpu samaruupata ledhaa pratisamiti); rangu samaruupata (sphatika saastramlo); roopaantaram ledhaa sthalavignaana maarpu; samaroopa namuunaalatoe uparitalaalanu kappadam; esher yokka algorithm (alankarinchabadina chaturasraalanu upayoginchi namuunaalanu utpatti cheyadaaniki); tyle aakaralanu srushtinchadam; kramabaddhata yokka sthaanika verses prapancha nirvachanalu; tyle yokka samaruupata dwara prerepinchabadina tailing yokka samaruupata; samaruupata samuuhaala dwara prerepinchabadani kramabaddhata; esher yokka lithograph "print gallery" loe kendra shoonyatanu h dwara nimpadam. lenstra mariyu bii. dii smitt.
douglus hafstadder rachinchina pulitzer bahumati graheeta 1979 pustakam "godel, esture, baach" sweeya-suuchana mariyu esture kalalo vyakteekarinchabadina vintha loopla aalochanalanu charchistundi. grahasakalam 4444 esher kuu 1985loe esher gouravaartham paeru pettaru.
prajaadarana pondina samskrutilo.
martin gardner thana april 1966 "mathematical games" kaalamlo "scientific american" loe pradarsinchinappudu prajaadarana pondina samskrutilo esture keerti perigindi. esher yokka rachanalu aneka album kavarlalo kanipinchaayi, veetilo paranjaalo 1969 "ell dhi pii" "aarohana mariyu avarohana" thoo; hopal yokka 1969 rikaardunu "sareesrupaalu" thoo, beaver & crouse yokka 1970 "moodu prapanchaalato" oka adavi abhayaaranyamlo; mariyu mandrake memorial yokka 1970 "puzzle" "metla illu" mariyu (lopala) "curl up" thoo unnaayi. adevidhamgaa athani rachanalu aneka pustaka mukhachitraalalo upayoginchabaddaayi, veetilo edwin abot yokka "flatland" yokka konni sanchikalalo "moodu golaalu" upayoginchabaddaayi; udhaa. hetch. gurrapu swarry" thoo gombrich yokka "abhiruchi gurrampai dhyanalu"; pamela haall yokka "talalu meeru kolpotaru" "vimanam nimpadam 1" thoo; patrick a. droying hands" thoo horton yokka "katha yokka saktilo praaveenyam"; eric gaama mariyu itarulu.'roopakalpana namuunaalu" "hamsaalu" thoo punarviniyogaparachadagina vastuvu-aadhaarita software yokka amsaalu; mariyu "" sareesrupaalu "thoo orther markman yokka" ghnaana praatinidhyam ". esher yokka prapancham" esher yokka kalaakrutula posterlu, nectilu, tii-shartulu mariyu jigsa pajilsnu market chestundi. austria mariyu netherlands rendoo kalaakaarudini mariyu athani rachanalanu smarinchukoni tapala billalanu vidudala chesaayi.

