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[{"key": "dc.contributor.advisor", "value": "Lehrb\u00e4ck, Juha", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Korpinen, Juho", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-08-01T05:13:08Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-08-01T05:13:08Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/96457", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa selvitet\u00e4\u00e4n er\u00e4iden geometristen kappaleiden pinta-alojen ja tilavuuksien laskemista samaan tapaan kuin antiikin kreikkalaiset tekiv\u00e4t yli 2000 vuotta sitten. Kyseisen aikakauden yksi tunnetuimmista matemaatikoista oli Arkhimedes, joka m\u00e4\u00e4ritti useita geometrisia ominaisuuksia, kuten piin likiarvon ja kappaleisiin liittyvi\u00e4 kaavoja, joista tutustumme ympyr\u00e4n, ellipsin ja pallon pinta-alan sek\u00e4 pallon tilavuuden kaavoihin.\n\nAluksi tutustumme egyptil\u00e4iseen ja babylonialaiseen matematiikkaan, jotka olivat m\u00e4\u00e4ritt\u00e4neet omat arvonsa piille, mink\u00e4 j\u00e4lkeen kerromme kreikkalaisen matematiikan syntym\u00e4st\u00e4 ja kehityksest\u00e4 aikav\u00e4lill\u00e4 600--300 eaa. Tuolloin Pythagoraan koulukunta tutki geometriaa ja Eudoksus kehitti kappaleiden pinta-alojen ja tilavuuden m\u00e4\u00e4ritt\u00e4misen kannalta hy\u00f6dyllisen suhteiden teorian ja ekshaustiomenetelm\u00e4n.\n\nT\u00e4m\u00e4n j\u00e4lkeen tutustumme paremmin Arkhimedeeseen ja t\u00e4m\u00e4n t\u00f6ihin sek\u00e4 tutkimme, miten h\u00e4n oli m\u00e4\u00e4ritt\u00e4nyt ympyr\u00e4n ja ellipsin pinta-alan kaavat sek\u00e4 m\u00e4\u00e4rit\u00e4mme piin likiarvon. Lopuksi todistamme pallon tilavuuden ja pinta-alan kaavat kahdella eri tavalla sek\u00e4 esit\u00e4mme Arkhimedeen tavan piin m\u00e4\u00e4ritt\u00e4miseen.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-08-01T05:13:08Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-08-01T05:13:08Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "49", "language": "", "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": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Tilavuuksien ja pinta-alojen historiallisia m\u00e4\u00e4ritystapoja", "language": "", "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-202408015279", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "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": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "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": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "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.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "historia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "antiikki", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "pinta-ala", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "geometria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "pii", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "tilavuus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "Kreikka", "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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