Konstrukcije pravilnih sedamnaesterokuta

master's thesis

• Author: Petra Mijoč
• Mentor: Dijana Ilišević (mentor)
• Committee member: Dijana Ilišević (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-02-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu izloženi su dokazi mogućnosti konstrukcije pravilnog sedamnaesterokuta samo pomoću ravnala i šestara. Tu mogućnost prvi je dokazao Gauss rješavajući jednadžbu \(x^{17}-1=0\). U ovom radu je opisano nekoliko konstrukcija pravilnog sedamnaesterokuta koje se temelje na Gaussovoj analizi, ali i nekoliko konstrukcija koje su po svojoj prirodi više geometrijske. Ukratko, konstrukcija pravilnog sedamnaesterokuta samo ravnalom i šestarom je izvediva, ali je vrlo složena.

Abstract (english)

In this work we present proofs of constructability of a regular heptadecagon (a seventeensided polygon) using only a ruler and a compass. This possibility was first proved by Gauss solving the equation \(x^{17}-1=0\). We describe several constructions of a regular heptadecagon which are based on the Gauss’s analysis, and also several constructions which are of a more geometric nature. Briefly, it is possible to construct a regular heptadecagon using only a ruler and a compass, but it is very complex.

• Keywords: sedamnaesterokut; konstrukcija pomoću ravnala i šestara; Gauss
• Keywords (english): heptadecagon; construction using a ruler and a compass; Gauss
• Language: croatian
• URN:NBN: urn:nbn:hr:217:753115
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-04-28 10:06:12