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Od kardioide do Morleyevega izreka : magistrsko delo
ID Rutar, Larisa (Author), ID Vavpetič, Aleš (Mentor) More about this mentor... This link opens in a new window, ID Kališnik, Jure (Comentor)

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Abstract
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.

Language:Slovenian
Keywords:Kardioida, Morleyev izrek, klinanta, trisektor
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2023
PID:20.500.12556/RUL-144276 This link opens in a new window
UDC:514
COBISS.SI-ID:141619459 This link opens in a new window
Publication date in RUL:09.02.2023
Views:1021
Downloads:98
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Secondary language

Language:English
Title:From the Cardioid to the Morley's Theorem
Abstract:
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.

Keywords:Cardioid, Morley's theorem, clinant, trisector

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