{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7E400FT4/3e3811b3-47ad-4599-8358-2f450c521223/PDF","dcterms:extent":"2382 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7E400FT4/0d9a2882-187a-423d-b2f0-1c3bbe3e6ff7/TEXT","dcterms:extent":"29 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-7E400FT4","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Ivrissimtzis, Ioannis","Singerman, David","Strudwick, James"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 37-50"}],"dc:identifier":["DOI:10.26493/1855-3974.2046.cb6","ISSN:1855-3966","COBISSID_HOST:91101187","URN:URN:NBN:SI:doc-7E400FT4"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"Farey tessellation"},{"@xml:lang":"sl","#text":"Fareyjevo tlakovanje"},{"@xml:lang":"sl","#text":"glavne kongruenčne podgrupe"},{"@xml:lang":"en","#text":"Klein quartic"},{"@xml:lang":"sl","#text":"Kleinov kvartik"},{"@xml:lang":"en","#text":"modular group"},{"@xml:lang":"sl","#text":"modularna grupa"},{"@xml:lang":"en","#text":"principal congruence subgroups"},{"@xml:lang":"en","#text":"regular maps"},{"@xml:lang":"sl","#text":"regularni zemljevidi"},{"@xml:lang":"en","#text":"Riemann surfaces"},{"@xml:lang":"sl","#text":"Riemannove ploskve"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"From Farey fractions to the Klein quartic and beyond|"},"dc:description":[{"@xml:lang":"sl","#text":"In a paper published in 1878/79 Klein produced his famous 14-sided polygon representing the Klein quartic, his Riemann surface of genus 3 which has ?$\\mathrm{PSL}(2, 7)$? as its automorphism group. The construction and method of side pairings are fairly complicated. By considering the Farey map modulo 7 we show how to obtain a fundamental polygon for Klein's surface using arithmetic. Now the side pairings are immediate and essentially the same as in Klein's paper. We also extend his work from 7 to 11 as Klein also did in a follow-up paper of 1879"},{"@xml:lang":"sl","#text":"V članku objavljenem leta 1878/79 je Klein prikazal svoj slavni 14-strani poligon, ki predstavlja t.i. Kleinov kvartik, Riemannovo ploskev z rodom enakim 3 in grupo avtomorfizmov ?$\\mathrm{PSL}(2, 7)$?. Njegova konstrukcija in metoda prirejanja stranic sta precej zapleteni. Upoštevaje Fareyjev zemljevid reduciran po modulu 7 pokažemo, kako dobimo fundamentalni poligon te Kleinove ploskve z uporabo aritmetike. Zdaj so prirejanja stranic lahka in v bistvu ista kot v Kleinovem članku. Prav tako razširimo njegovo raziskavo s primera 7 na primer 11, kot je to storil tudi Klein v svojem naslednjem članku iz leta 1879"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-7E400FT4","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7E400FT4"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7E400FT4/3e3811b3-47ad-4599-8358-2f450c521223/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-7E400FT4/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7E400FT4"}}}}