Points of a triangle with extremal properties
| Autor: | Bradarić, Danka |
|---|---|
| Přispěvatelé: | Varošanec, Sanja |
| Jazyk: | chorvatština |
| Rok vydání: | 2022 |
| Předmět: |
centroid
središte upisane kružnice trokuta incentre trokut triangle središte pripisane kružnice trokuta ekstremi Fermat-Torricelli point symmedians Lemoineova točka excentre circumcentre PRIRODNE ZNANOSTI. Matematika simedijane Fermat-Torricellijeva točka težište Lemoine point extrema ortocentar NATURAL SCIENCES. Mathematics orthocentre središte opisane kružnice trokuta |
| Popis: | U ovom su diplomskom radu navedeni neki primjeri točaka trokuta za koje odredene funkcije postižu svoju minimalnu ili maksimalnu vrijednost. Tako su se ekstremi raznih funkcija postizali u četiri karakteristične točke trokuta - težištu, ortocentru, središtu upisane i opisane kružnice, ali i u drugim točkama trokuta koje nisu sastavni dio kurikuluma nastavnog predmeta Matematike u osnovnim i srednjim školama poput Fermat-Torricellijeve točke, Lemoineove točke te središta trokutu pripisanih kružnica. Te su točke u radu definirane te su navedena i dokazana neka njihova posebna svojstva. In this thesis, some examples of triangle points for which certain functions reach their minimum or maximum value are given. Thus, it could be seen that the extremal values of various functions were reached in the four characteristic points of the triangle - the centroid, the orthocenter, the center of the inscribed and circumscribed circle, but also in other points of the triangle that are not an integral part of the curriculum of the subject of Mathematics in primary and secondary schools, such as the Fermat-Torricelli point, the Lemoine point and the excentres. These points were defined and some of their special properties were stated and proven. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|