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undergraduate thesis
Teorem o četiri boje i vektorski produkt
2019. urn:nbn:hr:126:956569
Kolembus, Darija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Computer Science and Machine Learning Research Group

Cite this document

Kolembus, D. (2019). Teorem o četiri boje i vektorski produkt (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:956569

Kolembus, Darija. "Teorem o četiri boje i vektorski produkt." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:956569

Kolembus, Darija. "Teorem o četiri boje i vektorski produkt." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:956569

Kolembus, D. (2019). 'Teorem o četiri boje i vektorski produkt', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:956569

Kolembus D. Teorem o četiri boje i vektorski produkt [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 November 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:956569

D. Kolembus, "Teorem o četiri boje i vektorski produkt", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:956569

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Metadata
TitleTeorem o četiri boje i vektorski produkt
Title (english)Four Colour Theorem and Cross Product
AuthorDarija Kolembus
MentorSnježana Majstorović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Computer Science and Machine Learning Research Group)
Osijek
Defense date and country2019-09-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Problem četiri boje postavio je matematičar F. Guthrie davne 1852. godine. Nakon toga su brojni vrsni matematičari, ali i amateri, pokušavali pronaći rješenje, a to je trajalo više od 150 godina. Tijekom tog razdoblja napravljeno je mnogo krivih dokaza, ali je takđer dobiveno mnogo djelomičnih rezultata, od kojih će neki biti sastavni dio ovog rada. Objasnit ćemo važne zaključke do kojih je došao A. Cayley (kubne karte, najmanji uljezi), zatim ćemo objasniti poznatu Eulerovu poliedarsku formulu, a onda predstaviti važne teoreme Teorem o ”Samo pet susjeda” i Teorem o šest boja. Bavit ćemo se i Kempeovim dokazom teorema o četiri boje koji koristi tzv. metodu Kempeovih lanaca. To je ujedno i najpoznatiji pogrešan dokaz, a njegovu netočnost ustanovio je Heawood te dokazao Teorem o pet boja. Konačno, objasnit ćemo dokaz teorema o četiri boje kojeg su predstavili K. Appel i W. Haken, a koji koristi računala te ga je zato teško proučavati. Postoje razni teoremi koji su ekvivalentni teoremu o četiri boje, a mi ćemo istaknuti kombinatorni problem vektorskog produkta u trodimenzionalnom prostoru.
Abstract (english)
The Four Color Theorem was first conjectured in the 1852. by matematician F. Guthrie. For more than 150 years great matematicians, as well as amateurs have tried to find the proof. There were many wrong proofs, but also a lot of partial results. Some of them are going to be mentioned in this thesis. We will present some conclusions obtained by A. Cayley (cubic maps, the smallest outsider), explain Euler’s famous Euler’s polyhedron formula and then show Five neighbors only theorem and Six colour theorem. We will also present Kempe’s proof of the theorem using so-called Kempe’s chain method. This is the most famous wrong proof of the four color theorem. Its incorrectness was discovered by Heawood who managed to prove Five colour theorem. Finally, we will mention the proof whch was given by K. Appel and W. Haken. Since it requires the use of a computer, it is not easy for studying. There are many theorems which are equivalent to the Four Color Theorem. We will mention a combinatorial problem related to the vector cross product algebra in three-dimensional space.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:956569
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-09-30 09:14:31