# Izoparametarske i izoperimetričke figure u ravnini

Protrka, Marija (2015) Izoparametarske i izoperimetričke figure u ravnini. Diploma thesis, Faculty of Science > Department of Mathematics.

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## Abstract

This paper presents a small part of isoperimetric geometry. In this work we study plane regions having equal areas and equal perimeters. Such regions are called isoparametric. The traditional isoperimetric problem consists of finding the region with the maximal area among all regions with equal perimeter. It is well known that among all regions with a given perimeter, the circle encloses the largest area. We investigate various examples of isoparametric plane regions. For that purpose the ratio is defined: $\kappa = \frac{O^2}{4P},$ where is $O$ perimeter and $P$ area of a plane region. It represents a necessary condition that the specified shapes are isoparametric. This problem provides more opportunities if we study for rings, respectively, figure bounded by two similar closed curves. Introducing ”holes” makes the problem more interesting and allows more possibilities. Although this particular branch of mathematics has been studied since the ancient Greece, it is not widely present in contemporary mathematics. Therefore, I hope that this work will give at least a small contribution to encouraging interest in the subject.

Item Type: Thesis (Diploma thesis) Šiftar, Juraj 2015 41 NATURAL SCIENCES > Mathematics Faculty of Science > Department of Mathematics Iva Prah 23 Oct 2015 11:43 23 Oct 2015 11:43 http://digre.pmf.unizg.hr/id/eprint/4184