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undergraduate thesis
Caseyev teorem
2024. urn:nbn:hr:126:011972
Lombarović, Lidija
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Lombarović, L. (2024). Caseyev teorem (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:011972

Lombarović, Lidija. "Caseyev teorem." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:011972

Lombarović, Lidija. "Caseyev teorem." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:011972

Lombarović, L. (2024). 'Caseyev teorem', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 25 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:011972

Lombarović L. Caseyev teorem [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:011972

L. Lombarović, "Caseyev teorem", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:011972

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Metadata
TitleCaseyev teorem
Title (english)Casey's Theorem
AuthorLidija Lombarović
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
Irski matematiˇcar John Casey, osnivač moderne geometrije trokuta i kružnice, najpoznatiji je po svojoj generalizaciji Ptolomejeva teorema, koja je prema njemu dobila naziv Caseyev teorem. Zato je u ovome radu prije svega iskazan i dokazan Ptolomejev teorem. Radi potpunog razumijevanja Caseyeva teorema, definirane su unutarnje i vanjske zajedničke tangente dviju kružnica te su izvedene formule duljina izmedu dirališta zajedničkih tangenti s kružnicama. Nakon toga, iskazan je i dokazan Caseyev teorem. Za kraj je definiran pojam kružnice devet točaka i primijenjen obrat Caseyeva teorema na dokaz Feuerbachova teorema.
Abstract (english)
Irish mathematician John Casey, founder of the Modern Geometry of the circle and the triangle, is best known for his generalization of Ptolemy’s theorem, which is named Casey’s theorem after him. Therefore, this paper first states and proves Ptolemy’s theorem. For a complete understanding of Casey’s theorem, internal and external common tangents of two circles are defined, and formulas for the lengths between the points of tangency of the common tangents with the circles are derived. Following this, Casey’s theorem is stated and proved. Finally, the concept of the nine-point circle is defined, and the converse of Casey’s theorem is applied to the proof of Feuerbach’s theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:011972
Study programmeTitle: University Bachelor of Mathematics (univ. bacc. math.)
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
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Created on2024-10-15 09:42:41