Od kardioide do Morleyevega izreka

magistrsko delo

Larisa Rutar (Author), Aleš Vavpetič (Mentor), Jure Kališnik (Co-mentor)

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.

Keywords

matematika;kardioida;Morleyev izrek;klinanta;trisektor;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[L. Rutar]
UDC:	514
COBISS:	141619459
Views:	687
Downloads:	67
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	From the Cardioid to the Morley's Theorem
Secondary 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.
Secondary keywords:	mathematics;cardioid;Morley theorem;clinant;trisector;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	VII, 72 str.
ID:	17962633