Posplošitev Routhovega izreka : delo diplomskega seminarja

Možina, Mateja (author), Vavpetič, Aleš (mentor)

Cilj diplomske naloge je posplošiti oba Routhova izraza. Najprej to naredimo v ravnini za trikotnik, kjer oba izraza posplošimo na samo enega, potem pa še v prostoru, sedaj za tetraeder. Na koncu še izpeljemo formuli za Routhova izraza v večrazsežnem simpleksu.

• Language: Slovenian
• Keywords: Routhov izrek, trikotnik, Menelajev izrek, Cevov izrek, tetraeder, simpleks
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-150543
• UDC: 514
• COBISS.SI-ID: 165136131
• Publication date in RUL: 20.09.2023

Secondary language

• Language: English
• Title: Generalization of Routh's theorem

Abstract

The aim of this thesis is to generalize both of Routh’s expressions. Firstly, we do this on a plane for a triangle, where we generalize both expressions into one, then we do it in three-dimensional space. Lastly, we derive the formulas for Routh’s expressions in multi-dimensional simplex.

• Keywords: Routh’s theorem, triangle, Menelaus’s theorem, Ceva’s theorem, tetrahedron, simplex