Search results for "tasogeometria"

showing 2 items of 2 documents

Projektiivinen geometria

2017

Tässä tutkielmassa käsittellään projektiivista geometriaa aksioomien ja mallien kautta. Tutkielma keskittyy pääasiassa äärellisiin projektiivisiin geometrioihin ja niistä erityisesti tasogeometriaan. Tutkielmassa luodaan kirjallisuuskatsaus projektiivisen geometrian alkuvaiheiden kautta aksioomajärjestelmän luomiseen ja päätyen tutustumaan yksinkertaisimpiin malleihin projektiiviselta tasolta. Samalla tulee todistettua myös projektiivisen geometrian peruslause ja tutustuttua projektiivisen geometrian hyödyllisyyteen käsiteltäessä euklidisen geometrian tilanteita. Euklidisessa geometriassa vallitsevia lauseita voidaan nimittäin tulkita projektiivisessa geometriassa ja tällöin projektiivisen …

aksioomajärjestelmäprojektiivinen geometriaideaalipistekuntatasoFanon-tasotasogeometriahomogeeniset koordinaatitprojektiivinen kuvausgeometriaaksioomat

researchProduct

Jäykät liikkeet ja Sivu-Kulma-Sivu -sääntö

2016

Venla Haapala, Jäykät liikkeet ja SKS -sääntö (engl. Rigid motions and SAS), matematiikan pro gradu -tutkielma, 57 s., Jyväskylän yliopisto, Matematiikan ja tilastotieteen laitos, kesä 2016. Tämän tutkielman tarkoituksena on selventää euklidisen tasogeometrian ja analyyttisen eli karteesisen geometrian välistä yhteyttä jäykkien liikkeiden tutkimisen kautta. Lisäksi tutkielman tarkoituksena on osoittaa, että jäykkien liikkeiden olemassaolo (ERM) on yhtäpitävä yhtenevyysaksiooman Sivu-Kulma-Sivu (SKS) kanssa, kun muut Hilbertin aksioomat ovat voimassa. Tutkielmassa lähdetään algebrallisista lähtökohdista rakentamaan geometrista mallia, jossa geometriset käsitteet määritetään kunnan ominaisuuk…

tasogeometriajäykät liikkeetanalyyttinen geometriaSivu-Kulma-Sivu -sääntö

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