Radionica „Plohe od sapunice“

Professional paper - Professional paper

• Title (english): Workshop “Soap film surfaces”
• Author: Ivana Filipan
• Author: Ema Jurkin
• Author: Željka Milin Šipuš
• Author: Ljiljana Primorac Gajčić
• Author's institution: Josip Juraj Strossmayer University of Osijek; Department of Mathematics
• Author's institution: University of Zagreb; Faculty of Science; (Department of Mathematics)
• Author's institution: University of Zagreb; Faculty of Mining, Geology and Petroleum Engineering; (Department of Mathematics, Informatics and Descriptive Geometry)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract (croatian)

U radu je opisana radionica pod nazivom „Plohe od sapunice“ koja je održana na Rudarsko-geološko-naftnom fakultetu u Zagrebu u sklopu projekta Večer matematike 2021. Na radionici su promatrani, te matematički opisani mjehurići i plohe od sapunice. Dobiveni oblici se mogu shvatiti kao rješenja izoperimetrijskog problema, tj. problema određivanja plohe najmanje površine sa zadanim rubom, odnosno određivanja zatvorene plohe najmanje površine koja omeđuje zadani volumen. Na radionici je promatran i specijalan slučaj izoperimetrijskog problema —Steinerov problem, tj. problem pronalaska najkraćeg puta između različitih točaka u ravnini i prostoru. Sudionici radionice su pomoću pribora i sapunice pronalazili rješenja predstavljenih problema te dobivali poznate minimalne plohe kao što su katenoid, helikoid, te Scherkova ploha.

Abstract (english)

In this work we present the workshop "Soap film surfaces" that was organized at the Faculty of Mining, Geology and Petroleum Engineering in Zagreb as a part of the project Mathematical evening 2021. At this workshop, soap films and soap bubbles were analyzed and mathematically described. Obtained forms can be considered as solutions to an isoperimetric problem, i.e. problem of finding a surface of the largest possible area whose boundaries are prescribed, respectively finding a closed surface of the smallest possible area whose volume is prescribed. Another special type of isoperimetric problem is also considered — the Steiner problem, i.e. problem of finding the shortest path between points in the plane or space. Participants of the workshop were able to find solutions to the presented problems by using the given equipment and soap water, and they obtained famous minimal surfaces such as catenoid, helicoid, the Scherk surface and other.

• Keywords (croatian): plohe od sapunice; izoperimetrijski problem; Steinerov problem
• Keywords (english): soap film surfaces; isoperimetric problem; Steiner problem
• Language: croatian
• Language: english
• Publication type: Professional paper - Professional paper
• Publication status: Published
• Peer review: Peer review - domestic
• Publication version: Published version
• Journal title: Osječki matematički list
• Numbering: vol. 22, no. 2, pp. 131-141
• p-ISSN: 1845-4607
• e-ISSN: 1848-946X
• URN:NBN: urn:nbn:hr:169:050853
• Publication: 2022
• Document URL: https://hrcak.srce.hr/292254
• Type of resource: Text
• Access conditions: Open access
• Created on: 2023-07-11 08:49:00