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master's thesis
Lemoineova točka
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:901125
Stepčić, Keti
University of Zagreb
Faculty of Science
Department of Mathematics

Cite this document

Stepčić, K. (2017). Lemoineova točka (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:901125

Stepčić, Keti. "Lemoineova točka." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:901125

Stepčić, Keti. "Lemoineova točka." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:901125

Stepčić, K. (2017). 'Lemoineova točka', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:217:901125

Stepčić K. Lemoineova točka [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:901125

K. Stepčić, "Lemoineova točka", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:901125

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Metadata
TitleLemoineova točka
AuthorKeti Stepčić
MentorMea Bombardelli (mentor)
Committee memberMea Bombardelli (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu definirali smo pojam simedijane trokuta na dva načina: kao pravac koji prolazi polovištima antiparalela stranica trokuta, te kao pravac koji je izogonalan pravcu kojem pripada težišnica. Zatim smo iskazali i dokazali neka od glavnih svojstava simedijana. U drugom dijelu rada orijentirali smo se više na Lemoineovu točku, koju smo definirali kao sjecište simedijana, te kao izogonalno konjugiranu točku težišta. Zatim smo istraživali neka od svojstava Lemoineove točke. Dokazali smo i povezanost Lemoineove točke s nekim drugim poznatim točkama u ravnini, pa je tako Lemoineova točka trokuta ujedno i težište nožišnog trokuta Lemoineove točke, te je Lemoineova točka Gergonneova točka njemu tangencijalnog trokuta.
Abstract (english)
In this paper we have defined the notion of the symmedian of a triangle in two ways: as the line that goes through the midpoints of the antiparallels to the sides of a triangle, and as the line that is isogonal to the triangle median. We have also presented and provided proof for some of the main properties of the symmedian. In the second part of the paper we have mostly focused on the Lemoine point, which can be defined as the symmedian intersection and as the isogonal conjugate of the triangle centroid. In addition, we have investigated some of the properties of the Lemoine point. We have also proved the connection of the Lemoine point with some other points within the plane, which leads to the conclusion that the Lemoine point of a triangle also serves as the centroid of its pedal triangle and the Lemoine point actually represents the Gergonne point of its tangential triangle.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:901125
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of the Faculty of Science
Created on2018-03-15 14:00:40

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