Steinerjeva včrtana elipsa in lokacijski problemi : delo diplomskega seminarja

Višnjevec, Jaka (author), Kuzman, Uroš (mentor), Beorchia, Valentina (co-mentor)

V diplomski nalogi bomo predstavili Steinerjevo včrtano elipso. Na začetku si ogledamo povezavo med ničlami kubičnega polinoma in ničlami njegovega odvoda. Nato navedemo Steinerjev izrek in ga dokažemo z uporabo afinih transformacij. V nadaljevanju raziščemo povezavo med ploščino trikotnika in ploščino Steinerjeve včrtane elipse. V zadnjem poglavju se posvetimo aplikaciji rezultatov o Steinerjevi včrtani elipsi v lokacijski teoriji.

• Language: Slovenian
• Keywords: polinomi, trikotnik, Steinerjeva včrtana elipsa, afina transformacija, problem postavitve škodljivega objekta, kompleksni momentni problem
• Work type: Bachelor thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-147050
• UDC: 514.7
• COBISS.SI-ID: 156478979
• Publication date in RUL: 22.06.2023

Secondary language

• Language: English
• Title: Steiner inellipse and the three-city noxious location problem

Abstract

The main topic of this thesis is the Steiner inellipse and its properties. We establish the connection between the roots of a third-degree polynomial and the roots of its derivative. Then we state Steiner's theorem and prove it using affine transformations. Further we research the area of a triangle and its Steiner inellipse. In addition, we introduce the application of the Steiner inellipse in the noxious location problem.

• Keywords: polynomials, triangle, Steiner inellipse, affine transformation, noxious location problem, complex momentum problem