Zveza med obsegom in ploščino konveksnih štirikotnikov

Pečar, Lidija (author), Cencelj, Matija (mentor)

V magistrskem delu bomo predstavili zvezo med obsegom in ploščino za konveksne štirikotnike. S pomočjo enačbe p = 1/ 2or, kjer je o obseg in r radij včrtanega kroga, bomo predstavili zvezo med obsegom in ploščino konveksnih štirikotnikov. Pokazali bomo, da je zveza med ploščino in obsegom pri štirikotnikih, katerim lahko včrtamo krog, povezana z radijem včrtanega kroga. Podrobneje si bomo pogledali zvezo za tangentni enakokraki trapez. Pri štirikotnikih, katerim ne moremo včrtati kroga, pa si bomo pomagali z notranjima tangentnima krogoma. Tukaj je zveza p/o povezana z virtualnim radijem, ki pa je harmonična sredina radijev notranjih tangentnih krogov. V tem delu bomo raziskali razmerje p/o za poljubni konveksni štirikotnik, kateremu ne moremo včrtati kroga. Obdelali bomo tudi razmerje p/o za tetivne štirikotnike. Pobližje bomo pogledali pravokotnik, paralelogram in trapez, ki jim ne moremo včrtati kroga.

• Language: Slovenian
• Keywords: štirikotniki
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Year: 2020
• PID: 20.500.12556/RUL-116173
• COBISS.SI-ID: 16011779
• Publication date in RUL: 25.05.2020

Secondary language

• Language: English
• Title: Relationship between the perimeter and the area of convex quadrilaterals

Abstract

In the master's thesis, we will present the relation between the perimeter and the area for convex quadrilaterals. Using the equation p = 1/2or, where o is the perimeter and r is the radius of the incircle, we will represent the relation between the perimeter and the area of convex quadrilaterals. We will show that the relation between the area and the perimeter of quadrilaterals, that have an incircle, is connected to the radius of the incircle. We will take a closer look at the relation for tangent equilateral trapezoid. With quadrilaterals that do not have an incircle, we will use internal tangent circles. Here is a link p/o connected to the virtual radius, which is harmonic mean of radii of the inner tangent circles. In this thesis, we will explore the connection p/o for any convex quadrilateral that does not have an incircle. We will also include the relation p/o for cyclic quadrilaterals. We will take a closer look at the rectangle, the rhomboid and the trapezoid, which do not have an incircle.

• Keywords: quadrilaterals