prikaz prve stranice dokumenta Pravilni mnogokuti i njihove konstrukcije
  Download
PDF 656.62 KB
master's thesis
Pravilni mnogokuti i njihove konstrukcije
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:925886
Curavić, Lorena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Curavić, L. (2022). Pravilni mnogokuti i njihove konstrukcije (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:925886

Curavić, Lorena. "Pravilni mnogokuti i njihove konstrukcije." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:925886

Curavić, Lorena. "Pravilni mnogokuti i njihove konstrukcije." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:925886

Curavić, L. (2022). 'Pravilni mnogokuti i njihove konstrukcije', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:925886

Curavić L. Pravilni mnogokuti i njihove konstrukcije [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:925886

L. Curavić, "Pravilni mnogokuti i njihove konstrukcije", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:925886

Metadata
TitlePravilni mnogokuti i njihove konstrukcije
Title (english)Regular polygons and their constructions
AuthorLorena Curavić
MentorSanja Varošanec (mentor)
Committee memberSanja Varošanec (predsjednik povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-07-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Geometrijskim konstrukcijama pravilnih mnogokuta pomoću jednobridnog ravnala i šestara bavili su se još antički grčki matematičari. Glavno pitanje koje se javilo bilo je mogu li se svi pravilni mnogokuti konstruirati. Odgovor na to pitanje prvi je dao Carl Friedrich Gauss u svom djelu Disquisitiones Arithmeticae. On je dokazao konstruktibilnost pravilnog sedamnaesterokuta, a potom je i razvio teoriju koja mu je omogućila da formulira dovoljan uvjet za konstruktibilnost pravilnih mnogokuta. Njegov je dokaz s nužnošću upotpunio Pierre Wantzel. U radu je opisan dokaz Gauss - Wantzelovog teorema, a potom i nekoliko konstrukcija pravilnih mnogokuta koji se mogu konstruirati jednobridnim ravnalom i šestarom te nekoliko približnih konstrukcija.
Abstract (english)
The ancient Greek mathematicians were already engaged in the geometric constructions of the regular polygons with compass and straightedge. The main question that was being asked was that if it was possible to construct all of the regular polygons. The answer to that question was first given by Carl Frierdrich Gauss in his Disquisitiones Arithmeticae.He proved the constructability of the regular heptadecagon, and later developed theory which allowed him to formulate a sufficient condition for the constructability of the regular polygons. Pierre Wantzel completed his proof with necessity. This thesis describes the proof of the Gauss - Wantzel theorem, construction of several regular polygons that can be constructed with compass and straightedge and several approximate constructions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:925886
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-09-13 09:00:06