Dioklova cisoida : diplomsko delo

Pašagić, Edita (author), Razpet, Marko (mentor)

V diplomskem delu so predstavljeni trije klasični matematični problemi iz obdobja antike. Izpostavljen je problem podvojitve kocke, ki sprašuje po tem, kako konstruirati rob kocke, ki ima dvakrat večjo prostornino kot dana kocka. Ena izmed najbolj pomembnih ravninskih krivulj, ki pomaga rešiti ta problem, je Dioklova cisoida, ki je v diplomskem delu podrobneje opisana. Obravnavane so tudi katakavstike krivulj, ki so ovojnice odbitih žarkov danega snopa žarkov, ki padajo na Dioklovo cisoido. Vse to je tudi narisano v programu GeoGebra.

• Language: Slovenian
• Keywords: problem podvojitve kocke, cisoida, katakavstika, krivulja, Diokles
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [E. Pašagić]
• Year: 2016
• Number of pages: 53 str.
• PID: 20.500.12556/RUL-85792
• UDC: 51(043.2)
• COBISS.SI-ID: 11182409
• Publication date in RUL: 20.09.2017

PAŠAGIĆ, Edita, 2016, Dioklova cisoida : diplomsko delo [online]. Bachelor’s thesis. E. Pašagić. [Accessed 5 April 2025]. Retrieved from: http://pefprints.pef.uni-lj.si/3790/

Secondary language

• Language: English
• Title: Cissoid of Diocles

Abstract

In my thesis I present three classical mathematical problems of antiquity. I focus on the problem of doubling the cube, which is examining how can we, given an edge of a cube, construct an edge of a second cube, whose volume is double that of the first. One of the most important cubic plane curves that helps to solve this problem is the cissoid of Diocles, which I describe in greater detail in the present dissertation. Further discussion is given to catacaustics, the curves that are envelopes of reflected rays of a specific beam of rays falling on the cissoid of Diocles. All the stated problems are also modelled using GeoGebra software.

• Keywords: mathematics, matematika