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[{"key": "dc.contributor.advisor", "value": "Laukkarinen, Eija", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Per\u00e4m\u00e4ki, Katrianna", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2025-05-22T10:14:12Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2025-05-22T10:14:12Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2025", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/102690", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 pro gradu-tutkielmassa tutkitaan kaksiulotteisia ruusuk\u00e4yri\u00e4, niiden yleisi\u00e4 ominaisuuksia sek\u00e4 ter\u00e4lehtien ominaisuuksia. Esitietoina n\u00e4iden k\u00e4yrien ominaisuuksien todistamiseen tarvitaan tietoa napakoordinaateista sek\u00e4 tason k\u00e4yrist\u00e4.\nRuusuk\u00e4yr\u00e4 on tasok\u00e4yr\u00e4, joka koostuu ter\u00e4lehden muotoisista silmukois- ta. T\u00e4ss\u00e4 tutkielmassa pyrit\u00e4\u00e4n m\u00e4\u00e4rittelem\u00e4\u00e4n ja todistamaan t\u00e4sm\u00e4llisesti ruusuk\u00e4yr\u00e4n yleisen yht\u00e4l\u00f6n ominaisuuksia. Etenkin ruusuk\u00e4yr\u00e4n ter\u00e4lehtien muodostumiseen ja ominaisuuksiin liittyv\u00e4t k\u00e4sitteet ja v\u00e4itteet ovat keski\u00f6ss\u00e4. Ruusuk\u00e4yr\u00e4n yleisen yht\u00e4l\u00f6n muuttujat vaikuttavat esimerkiksi ter\u00e4lehtien kokoon ja lukum\u00e4\u00e4r\u00e4\u00e4n. Yleisen yht\u00e4l\u00f6n parametri, kulmataajuus, m\u00e4\u00e4rittelee ter\u00e4lehtien lukum\u00e4\u00e4r\u00e4n, muodon ja mahdollisen p\u00e4\u00e4llekk\u00e4isyyden. Tutkielmassa tarkastellaan, miten kulmataajuuden parillisuus, parittomuus, rationaalisuus tai irrationaalisuus vaikuttaa n\u00e4ihin ter\u00e4lehtien ominaisuuksiin.\nRuusuk\u00e4yr\u00e4n m\u00e4\u00e4ritteli ensimm\u00e4isen\u00e4 Luigi Guido Grandi (1671\u22121742), jonka el\u00e4m\u00e4\u00e4 tarkastellaan tutkielman lopuksi tarkemmin. Lis\u00e4ksi mainitaan joitakin k\u00e4yt\u00e4nn\u00f6nsovelluksia, miss\u00e4 ruusuk\u00e4yri\u00e4 k\u00e4ytet\u00e4\u00e4n.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2025-05-22T10:14:12Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2025-05-22T10:14:12Z (GMT). No. of bitstreams: 0\n Previous issue date: 2025", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "56", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "ruusuk\u00e4yr\u00e4t", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Ruusuk\u00e4yr\u00e4t", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202505224528", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": "fi", "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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