20.500.12556/RUL-144276 Od kardioide do Morleyevega izreka magistrsko delo From the Cardioid to the Morley's Theorem Kardioida je ena izmed najbolj znanih in široko obravnavanih ravninskih krivulj v matematiki. Po navedbi definicije se osredotočimo predvsem na njene geometrijske lastnosti in prezentacije v povezavi z njenimi tangentami. To nas privede do primera srečanja s kardioido v vsakdanjem življenju. V drugem delu te naloge pa postavimo kardioido v kompleksno ravnino, ki jo identificiramo z ${\mathbb R}^2$. Skozi lastnosti tangent v tem okolju izpeljemo Morleyev izrek za trikotnike in si s tem pogledamo pot, ki je Franka Morleya pripeljala do odkritja. Ob tem povemo še nekaj besed o zgodovinskem okviru in o življenju odkritelja. A curve called cardioid is one of the most famous and widely discussed plane curves in mathematics. After stating the definition we focus mainly on its geometric properties and presentations in connection with its tangents. This leads us to the example of an occurrence of the cardioid in everyday life. In the second part of this thesis we place the cardioid in the complex plane, identified with ${\mathbb R}^2$. We derive Morley's theorem for triangles through the properties of cardioid’s tangent lines as Frank Morley did in his studies. In passing we will say a few words about the historical context and the life of the discoverer. Kardioida Morleyev izrek klinanta trisektor Cardioid Morley's theorem clinant trisector true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2023-02-09 08:15:01 2023-02-09 08:15:06 2024-05-29 10:51:13 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514 130122 141619459 7669.pdf 7669.pdf 1 EDDDDD18873943E43C94F8204110B7AA cd308af5846a5a9c812c11eb02166415088a562da8162be27c9b384eb0bcfb4e 2bc319fa-a849-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=166494 Fakulteta za matematiko in fiziko 0 0 0